# kb

id: integral-field-spectrograph-20260505-0
file: data/en.wikipedia.org/wiki/Integral_field_spectrograph-0.md
category: reference
title: Integral field spectrograph
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Integral_field_spectrograph
date_saved: 2026-05-05T09:47:41.610438+00:00
instance: kb-cron
parent: integral-field-spectrograph-20260505-0
summary:
Integral field spectrographs (IFS) combine spectrographic and imaging capabilities in the optical or infrared wavelength domains (0.32 μm – 24 μm) to get from a single exposure spatially resolved spectra in a bi-dimensional region. The name originates from the fact that the measurements result from integrating the light on multiple sub-regions of the field. Developed at first for the study of astronomical objects, this technique is now also used in many other fields, such as bio-medical science and Earth remote sensing. Integral field spectrography is part of the broader category of snapshot hyperspectral imaging techniques, itself a part of hyperspectral imaging. == Rationale == With the notable exception of individual stars, most astronomical objects are spatially resolved by large telescopes. For spectroscopic studies, the optimum would then be to get a spectrum for each spatial pixel in the instrument field of view, getting full information on each target. This is loosely called a datacube from its two spatial and one spectral dimensions. Since both visible charge-coupled devices (CCD) and infrared detector arrays (staring arrays) used for astronomical instruments are bi-dimensional only, it is a non-trivial feat to develop spectrographic systems able to deliver 3D data cubes from the output of


id: integral-field-spectrograph-20260505-1
file: data/en.wikipedia.org/wiki/Integral_field_spectrograph-1.md
category: reference
title: Integral field spectrograph
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Integral_field_spectrograph
date_saved: 2026-05-05T09:47:41.610438+00:00
instance: kb-cron
parent: integral-field-spectrograph-20260505-0
summary:
=== Fiber array === The sky image given by the telescope falls on a fiber-based image slicer. It is typically made of a few thousands fibers each about 0.1 mm diameter, with the square or circular input field reformatted into a narrow rectangular (long-slit-like) output. The image slicer output is then coupled to a classical long-slit spectrograph that delivers the datacubes. A sky demonstrator successfully undertook the first Fiber based IFS observation in 1990. It was followed by the full-fledged SILFID optical instrument some 5 years later. Coupling the circular fibers to a square or hexagonal lenslet array led to better light injection in the fiber and a nearly 100% filling factor of sky light. Pros are 100% on-sky spatial filling, an efficient use of detector pixels and commercially available fiber-based image slicers. Cons are the sizable light loss in the fibers (~ 25%), their relatively poor photometric accuracy and their inability to work in a cryogenic environment. The latter limits wavelength coverage to less than 1.6 μm. This technique is used by instruments in many telescopes (such as INTEGRAL at the William Herschel Telescope), and particularly in currently ongoing large surveys of galaxies, such as the Calar Alto Legacy


id: integral-field-spectrograph-20260505-2
file: data/en.wikipedia.org/wiki/Integral_field_spectrograph-2.md
category: reference
title: Integral field spectrograph
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Integral_field_spectrograph
date_saved: 2026-05-05T09:47:41.610438+00:00
instance: kb-cron
parent: integral-field-spectrograph-20260505-0
summary:
One such approach was used by the SDSS MaNGA program, Mapping Nearby Galaxies at Apache Point Observatory. MaNGA used IFUs composed of hexagonal fiber bundles to survey about ~10,000 nearby galaxies around redshift 0.03, studying their dynamical state, composition, and formation history. MaNGA was able to use 17 IFU fiber bundles per spectroscopic plate, efficiently targeting many objects simultaneously. A clever alternative approach to obtaining spatially resolved spectroscopy of many objects simultaneously is the MSA-3D program which uses the micro-shutter array of the JWST NIRSpec instrument to target many objects simultaneously. While not strictly an integral-field unit, the MSA-3D program takes many exposures while "stepping" the conventional slitmask provided by the MSA across the sky. These exposures can be combined after the fact to provide full, 3D spatial and spectral information on each object. While the MSA-3D approach provides much lower spatial resolution than the IFU provided with NIRSpec, and requires many more exposures, it has the advantage of being able to target dozens of nearby objects simultaneously. Even larger latitude in the choice of coverage of the patrol field has been proposed under the name of Diverse Field Spectroscopy (DFS) which would allow the observer to select arbitrary combinations


id: intensity-interferometer-20260505-0
file: data/en.wikipedia.org/wiki/Intensity_interferometer-0.md
category: reference
title: Intensity interferometer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Intensity_interferometer
date_saved: 2026-05-05T09:47:42.763419+00:00
instance: kb-cron
parent: intensity-interferometer-20260505-0
summary:
An intensity interferometer is the name given to devices that use the Hanbury Brown and Twiss effect. In astronomy, the most common use of such an astronomical interferometer is to determine the apparent diameter of a radio source or star. If the distance to the object can then be determined by parallax or some other method, the physical diameter of the star can then be inferred. An example of an optical intensity interferometer is the Narrabri Stellar Intensity Interferometer. In quantum optics, some devices which take advantage of correlation and anti-correlation effects in beams of photons might be said to be intensity interferometers, although the term is usually reserved for observatories. An intensity interferometer is built from two light detectors, typically either radio antenna or optical telescopes with photomultiplier tubes (PMTs), separated by some distance, called the baseline. Both detectors are pointed at the same astronomical source, and intensity measurements are then transmitted to a central correlator facility. A major advantage of intensity interferometers is that only the measured intensity observed by each detector must be sent to the central correlator facility, rather than the amplitude and phase of the signal. The intensity interferometer measures interferometric visibilities like all other


id: international-liquid-mirror-telescope-20260505-0
file: data/en.wikipedia.org/wiki/International_Liquid_Mirror_Telescope-0.md
category: reference
title: International Liquid Mirror Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/International_Liquid_Mirror_Telescope
date_saved: 2026-05-05T09:47:43.937211+00:00
instance: kb-cron
parent: international-liquid-mirror-telescope-20260505-0
summary:
The International Liquid Mirror Telescope is a 4-meter telescope located inside the premises of Aryabhatta Research Institute of Observational Sciences (ARIES) in the city of Nainital, Uttarakhand, India. It is the first liquid-mirror telescope for astronomy in Asia and currently the largest liquid-mirror telescope in the world after the decommissioning of the Large Zenith Telescope. == History == On 2 June 2022, the telescope saw its first light. On 12 June 2022, it came online. On 21 June 2022, it became ready to observe. On 21 March 2023, it was inaugurated by Jitendra Singh. == Mechanism == The telescope uses elemental mercury as its mirror surface. The mercury is rotated about the axis of the telescope, and due to centrifugal force, takes a parabolic shape to focus incoming light. == See also == Large Zenith Telescope NASA Orbital Debris Observatory == References ==


id: keyhole-problem-20260505-0
file: data/en.wikipedia.org/wiki/Keyhole_problem-0.md
category: reference
title: Keyhole problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Keyhole_problem
date_saved: 2026-05-05T09:47:45.084200+00:00
instance: kb-cron
parent: keyhole-problem-20260505-0
summary:
The keyhole problem, in the context of astronomy, refers to the difficulty that azimuth-elevation type telescopes or antenna gimbal systems encounter in crossing the zenith. == Area of visible sky == To track celestial objects as they move across the sky, these systems usually rotate on two axes. Often, a tilting mechanism (elevation) is mounted upon a panning base (azimuth). To cover the complete hemisphere of visible sky, a telescope gimbal can have a 360-degree azimuth range and a 0- to 90-degree elevation range. To visualize this shape, imagine drawing a quarter circle spanning from the horizon to directly above you and revolving it around the vertical axis. If, on the other hand, the gimbal has a range from 0 to slightly less than 90 degrees elevation, the telescope is unable to see a region of sky. == Gimbal behavior == A variation on the keyhole problem involves defining behavior for gimbals with full-circle azimuth range, and at least 90-degree but less than 180-degree elevation range. Imagine a satellite on an orbital path that crosses directly overhead. If the gimbal tilts to track the object from the horizon but must stop at 90 degrees, the entire telescope must pan 180


id: las-cumbres-observatory-20260505-0
file: data/en.wikipedia.org/wiki/Las_Cumbres_Observatory-0.md
category: reference
title: Las Cumbres Observatory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Las_Cumbres_Observatory
date_saved: 2026-05-05T09:47:46.290951+00:00
instance: kb-cron
parent: las-cumbres-observatory-20260505-0
summary:
Las Cumbres Observatory (LCO) is a network of astronomical observatories run by a non-profit private operating foundation directed by the technologist Wayne Rosing. Its offices are in Goleta, California. The telescopes are located at both northern and southern hemisphere sites distributed in longitude around the Earth. For some astronomical objects, the longitudinal spacing of telescopes allows continuous observations over 24 hours or longer. The operating network currently consists of two 2-meter telescopes, nine 1-meter telescopes, and seven 40-centimeter telescopes, placed at six astronomical observatories. The network operates as a single, integrated observing facility, using a software scheduler that continuously optimizes the planned observing schedule of each individual telescope. == History == Rosing incorporated Las Cumbres Observatory in 1993 with the goal of aiding universities, observatories, and individuals in the acquisition and improvement of telescopes, optics, and instrumentation. He also set the objective for the organization to build and implement a global telescope system. In 2005, Rosing established the global telescope version of Las Cumbres Observatory. LCO initially acquired the two Faulkes 2-meter telescopes. Faulkes Telescope North (FTN) located at Haleakala Observatory, on Maui, Hawaii, and Faulkes Telescope South (FTS) at Siding Spring Observatory (SSO), in eastern Australia. LCO also purchased


id: las-cumbres-observatory-20260505-1
file: data/en.wikipedia.org/wiki/Las_Cumbres_Observatory-1.md
category: reference
title: Las Cumbres Observatory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Las_Cumbres_Observatory
date_saved: 2026-05-05T09:47:46.290951+00:00
instance: kb-cron
parent: las-cumbres-observatory-20260505-0
summary:
== Research == The design and operation of the LCO global telescope network provide the unique capabilities required for time domain astronomy. The LCO network offers the ability to observe objects or events continuously and the ability to obtain data rapidly upon the discovery or announcement of an event. The LCO network has been used to study supernovae and other explosive transients; exoplanets, through observations of both transits and microlensing; asteroids; and AGN variability. In 2017 LCO played a critical part in two major discoveries: first visible counterpart of a gravitational wave event, and a new type of supernova with successive explosions. == Education == Since the beginning of LCO, education has been one of its core missions. In 2017, for the first time in LCO's history it issued an open call for education partners, Global Sky Partners—groups who could use their robotic telescopes to inspire diverse audiences with educational and outreach projects that they support. In 2019 there are 20 LCO Global Sky Partners based in the US, Europe, Sub-Saharan Africa, the Middle East, Australia, or running entirely online programs, for students, teachers, and the wider public. In 2019 the reported direct impact of the program was 13,000 individuals


id: liquid-mirror-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Liquid-mirror_telescope-0.md
category: reference
title: Liquid-mirror telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Liquid-mirror_telescope
date_saved: 2026-05-05T09:47:47.467249+00:00
instance: kb-cron
parent: liquid-mirror-telescope-20260505-0
summary:
Liquid-mirror telescopes are telescopes with mirrors made with a reflective liquid. The most common liquid used is mercury, but other liquids will work as well (for example, low-melting point alloys of gallium). The liquid and its container are rotated at a constant speed around a vertical axis, which causes the surface of the liquid to assume a paraboloidal shape. This parabolic reflector can serve as the primary mirror of a reflecting telescope. The rotating liquid assumes the same surface shape regardless of the container's shape; to reduce the amount of liquid metal needed, and thus weight, a rotating mercury mirror uses a container that is as close to the necessary parabolic shape as feasible. Liquid mirrors can be a low-cost alternative to conventional large telescopes. Compared to a solid glass mirror that must be cast, ground, and polished, a rotating liquid-metal mirror is much less expensive to manufacture. Isaac Newton noted that the free surface of a rotating liquid forms a circular paraboloid and can therefore be used as a telescope, but he could not build one because he had no way to stabilize the speed of rotation. The concept was further developed by Ernesto Capocci (1798–1864) of the Naples


id: liquid-mirror-telescope-20260505-1
file: data/en.wikipedia.org/wiki/Liquid-mirror_telescope-1.md
category: reference
title: Liquid-mirror telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Liquid-mirror_telescope
date_saved: 2026-05-05T09:47:47.467249+00:00
instance: kb-cron
parent: liquid-mirror-telescope-20260505-0
summary:
which relates the angular velocity of the rotation of the liquid to the focal length of the paraboloid that is produced by the rotation. Note that no other variables are involved. The density of the liquid, for example, has no effect on the focal length of the paraboloid. The units must be consistent, e.g. f {\displaystyle f} may be in metres, ω {\displaystyle \omega } in radians per second, and g {\displaystyle g} in metres per second-squared. If we write F {\displaystyle F} for the numerical value of the focal length in metres, and S {\displaystyle S} for the numerical value of the rotation speed in revolutions per minute (RPM), then on the Earth's surface, where g {\displaystyle g} is approximately 9.81 metres per second-squared, the last equation reduces to the approximation F S 2 ≈ 447. {\displaystyle FS^{2}\approx 447.} If the focal length is in feet instead of metres, this approximation becomes F S 2 ≈ 1467. {\displaystyle FS^{2}\approx 1467.} The rotation speed is still in RPM. == Liquid-mirror telescopes == === Conventional land-based liquid-mirror telescopes === These are made of liquid stored in a cylindrical container made of a composite material, such as Kevlar. The cylinder is spun


id: liquid-mirror-telescope-20260505-2
file: data/en.wikipedia.org/wiki/Liquid-mirror_telescope-2.md
category: reference
title: Liquid-mirror telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Liquid-mirror_telescope
date_saved: 2026-05-05T09:47:47.467249+00:00
instance: kb-cron
parent: liquid-mirror-telescope-20260505-0
summary:
Usually, the mirror of a liquid-mirror telescope is rotated around two axes simultaneously. For example, the mirror of a telescope on the surface of the Earth rotates at a speed of a few revolutions per minute about a vertical axis to maintain its parabolic shape, and also at a speed of one revolution per day about the Earth's axis because of the rotation of the Earth. Usually (except if the telescope is located at one of the Earth's poles), the two rotations interact so that, in a frame of reference that is stationary relative to the local surface of the Earth, the mirror experiences a torque about an axis that is perpendicular to both rotation axes, i.e. a horizontal axis aligned east–west. Since the mirror is liquid, it responds to this torque by changing its aim direction. The point in the sky at which the mirror is aimed is not exactly overhead, but is displaced slightly to the north or south. The amount of the displacement depends on the latitude, the rotation speeds, and the parameters of the telescope's design. On the Earth, the displacement is small, typically a few arcseconds, which can, nevertheless, be significant in astronomical observations. If


id: list-of-original-copies-of-the-porter-garden-telescope-20260505-0
file: data/en.wikipedia.org/wiki/List_of_original_copies_of_the_Porter_Garden_Telescope-0.md
category: reference
title: List of original copies of the Porter Garden Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_original_copies_of_the_Porter_Garden_Telescope
date_saved: 2026-05-05T09:47:48.653586+00:00
instance: kb-cron
parent: list-of-original-copies-of-the-porter-garden-telescope-20260505-0
summary:
This is a list of the known original copies of The Porter Garden Telescope. For information purposes, are also included those copies that their location are currently unknown, but there are records with some of their data. == See also == The Porter Garden Telescope == References ==


id: maunakea-spectroscopic-explorer-20260505-0
file: data/en.wikipedia.org/wiki/Maunakea_Spectroscopic_Explorer-0.md
category: reference
title: Maunakea Spectroscopic Explorer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Maunakea_Spectroscopic_Explorer
date_saved: 2026-05-05T09:47:49.872045+00:00
instance: kb-cron
parent: maunakea-spectroscopic-explorer-20260505-0
summary:
The Maunakea Spectroscopic Explorer (MSE) is a collaborative project to revitalize the Canada–France–Hawaii Telescope (CFHT). The group aims to replace the 1970s optical telescope with a modern segmented-mirror telescope and dedicated science instrumentation, while reusing the existing Maunakea summit building and facility. MSE will use an 11.25 meter aperture telescope and dedicated multiobject fibre spectroscopy instrumentation to perform survey science observations, collecting spectra from more than 4,000 astronomical targets simultaneously. The project completed a conceptual design in early 2018. However, the 2022 Maunakea moratorium on new leases for telescopes delays decision-making on MSE until after 2030; as of late 2024 the CFHT Board has curtailed funding of any MSE activities for the time being . == Background == === Partnership and funding === The MSE project initially took shape through a feasibility study led by the National Research Council of Canada, which showed the strength of the science case for a large aperture dedicated multiobject spectroscopic facility, as well as the technical feasibility of such a facility as an upgrade to CFHT. In 2014, the CFHT established a project office in Waimea HI, to lead and develop the project through to the start of construction. The MSE participants in 2018


id: maunakea-spectroscopic-explorer-20260505-1
file: data/en.wikipedia.org/wiki/Maunakea_Spectroscopic_Explorer-1.md
category: reference
title: Maunakea Spectroscopic Explorer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Maunakea_Spectroscopic_Explorer
date_saved: 2026-05-05T09:47:49.872045+00:00
instance: kb-cron
parent: maunakea-spectroscopic-explorer-20260505-0
summary:
==== 4. Examining the connection between galaxies and the large scale structure of the Universe ==== MSE will measure how galaxies evolve and grow relative to the dark matter structure in which they are embedded. This is done through mapping the distribution of stellar populations and supermassive black holes to the dark matter haloes and filamentary structures that dominate the mass density of the Universe, and doing so over all mass and spatial scales. MSE will provide a breakthrough in extragalactic astronomy by linking the formation and evolution of galaxies to the surrounding large-scale structure, across the full range of relevant spatial scales (from kiloparsecs to megaparsecs). ==== 5. Following time-variable events ==== MSE will perform spectroscopic follow-up of time-variable events discovered by LSST, SKA and other all-sky transient surveys. With its large multiplex advantage and good sky overlap with other surveys, MSE can provide large-aperture followup of faint transient events using a few fibres while simultaneously continuing uninterrupted observation of main survey programs with the remainder of the installed fibre set. ==== 6. The growth of supermassive black holes ==== MSE will undertake an extragalactic time domain program to measure directly the accretion rates and masses of a large


id: maunakea-spectroscopic-explorer-20260505-2
file: data/en.wikipedia.org/wiki/Maunakea_Spectroscopic_Explorer-2.md
category: reference
title: Maunakea Spectroscopic Explorer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Maunakea_Spectroscopic_Explorer
date_saved: 2026-05-05T09:47:49.872045+00:00
instance: kb-cron
parent: maunakea-spectroscopic-explorer-20260505-0
summary:
=== Science instrumentation === Science data can be acquired in two possible spectral resolution modes: a high resolution of about R = 20,000 | 40,000, and a low/moderate resolution mode spanning R = 2,000 to R = 6,000. MSE is designed to be able to take spectra in both modes simultaneously during any observation. A fibre optic transmission system relays light gathered into the fibre tips at the telescope optical focal plane, to two banks of spectrometers that will measure the spectrum of the light gathered by each fibre. The fibre tips are positioned precisely at the position of astronomical interest in the focal plane by the array of remotely commandable tilting spine fibre positioners, each responsible for one fibre delivering light to one of the two spectrometer banks. The fibre transmission system uses high numeric aperture fibres to optically directly match the telescope focal ratio, and to provide good mechanical stability and optical throughput while minimizing focal-ratio degradation. The fibre core diameter, which sets the size of the sky sampled by each fibre tip, is different in those fibres used in the high resolution mode from those used in the low/moderate resolution mode, due to the difference in angular


id: meridian-circle-20260505-0
file: data/en.wikipedia.org/wiki/Meridian_circle-0.md
category: reference
title: Meridian circle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Meridian_circle
date_saved: 2026-05-05T09:47:51.054683+00:00
instance: kb-cron
parent: meridian-circle-20260505-0
summary:
The meridian circle is an instrument for timing of the passage of stars across the local meridian, an event known as a culmination, while at the same time measuring their angular distance from the nadir. These are special purpose telescopes mounted so as to allow pointing only in the meridian, the great circle through the north point of the horizon, the north celestial pole, the zenith, the south point of the horizon, the south celestial pole, and the nadir. Meridian telescopes rely on the rotation of the sky to bring objects into their field of view and are mounted on a fixed, horizontal, east–west axis. The similar transit instrument, transit circle, or transit telescope is likewise mounted on a horizontal axis, but the axis need not be fixed in the east–west direction. For instance, a surveyor's theodolite can function as a transit instrument if its telescope is capable of a full revolution about the horizontal axis. Meridian circles are often called by these names, although they are less specific. For many years, transit timings were the most accurate method of measuring the positions of heavenly bodies, and meridian instruments were relied upon to perform this painstaking work. Before spectroscopy, photography,


id: meridian-circle-20260505-1
file: data/en.wikipedia.org/wiki/Meridian_circle-1.md
category: reference
title: Meridian circle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Meridian_circle
date_saved: 2026-05-05T09:47:51.054683+00:00
instance: kb-cron
parent: meridian-circle-20260505-0
summary:
Near each end of the axis, attached to the axis and turning with it, was a circle or wheel for measuring the angle of the telescope to the zenith or horizon. Generally of 1 to 3 feet or more in diameter, it was divided to 2 or 5 arcminutes, on a slip of silver set into the face of the circle near the circumference. These graduations were read by microscopes, generally four for each circle, mounted to the piers or a framework surrounding the axis, at 90° intervals around the circles. By averaging the four readings the eccentricity (from inaccurate centering of the circles) and the errors of graduation were greatly reduced. Each microscope was furnished with a micrometer screw, which moved crosshairs, with which the distance of the circle graduations from the centre of the field of view could be measured. The drum of the screw was divided to measure single seconds of arc (0.1" being estimated), while the number of revolutions were counted by a comb like scale in the field of view. The microscopes were given such magnification and placed at such a distance from the circle that one revolution of the micrometer screw corresponded to 1


id: meridian-circle-20260505-2
file: data/en.wikipedia.org/wiki/Meridian_circle-2.md
category: reference
title: Meridian circle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Meridian_circle
date_saved: 2026-05-05T09:47:51.054683+00:00
instance: kb-cron
parent: meridian-circle-20260505-0
summary:
=== Operation === At the focal plane, the eye end of the telescope had a number of vertical and one or two horizontal wires (crosshairs). In observing stars, the telescope was first directed downward at a basin of mercury forming a perfectly horizontal mirror and reflecting an image of the crosshairs back up the telescope tube. The crosshairs were adjusted until coincident with their reflection, and the line of sight was then perfectly vertical; in this position the circles were read for the nadir point. The telescope was next brought up to the approximate declination of the target star by watching the finder circle. The instrument was provided with a clamping apparatus, by which the observer, after having set the approximate declination, could clamp the axis so the telescope could not be moved in declination, except very slowly by a fine screw. By this slow motion, the telescope was adjusted until the star moved along the horizontal wire (or if there were two, in the middle between them), from the east side of the field of view to the west. Following this, the circles were read by the microscopes for a measurement of the apparent altitude of the star. The


id: meridian-circle-20260505-3
file: data/en.wikipedia.org/wiki/Meridian_circle-3.md
category: reference
title: Meridian circle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Meridian_circle
date_saved: 2026-05-05T09:47:51.054683+00:00
instance: kb-cron
parent: meridian-circle-20260505-0
summary:
Meridian circles required precise adjustment to do accurate work. The rotation axis of the main telescope needed to be exactly horizontal. A sensitive spirit level, designed to rest on the pivots of the axis, performed this function. By adjusting one of the V-shaped bearings, the bubble was centered. The line of sight of the telescope needed to be exactly perpendicular to the axis of rotation. This could be done by sighting a distant, stationary object, lifting and reversing the telescope on its bearings, and again sighting the object. If the crosshairs did not intersect the object, the line of sight was halfway between the new position of the crosshairs and the distant object; the crosshairs were adjusted accordingly and the process repeated as necessary. Also, if the rotation axis was known to be perfectly horizontal, the telescope could be directed downward at a basin of mercury, and the crosshairs illuminated. The mercury acted as a perfectly horizontal mirror, reflecting an image of the crosshairs back up the telescope tube. The crosshairs could then be adjusted until coincident with their reflection, and the line of sight was then perpendicular to the axis. The line of sight of the telescope needed to


id: meridian-circle-20260505-4
file: data/en.wikipedia.org/wiki/Meridian_circle-4.md
category: reference
title: Meridian circle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Meridian_circle
date_saved: 2026-05-05T09:47:51.054683+00:00
instance: kb-cron
parent: meridian-circle-20260505-0
summary:
The making of circles was shortly afterwards taken up by Edward Troughton, who constructed the first modern transit circle in 1806 for Groombridge's observatory at Blackheath, the Groombridge Transit Circle (a meridian transit circle). Troughton afterwards abandoned the idea and designed the mural circle to take the place of the mural quadrant. In the United Kingdom, the transit instrument and mural circle continued until the middle of the 19th century to be the principal instrument in observatories, the first transit circle constructed there being that at Greenwich (mounted in 1850). However, on the continent, the transit circle superseded them from the years 1818–1819, when two circles by Johann Georg Repsold and Georg Friedrich von Reichenbach were mounted at Göttingen, and one by Reichenbach at Königsberg. The firm of Repsold and Sons was for a number of years eclipsed by that of Pistor and Martins in Berlin, who furnished various observatories with first-class instruments. Following the death of Martins, the Repsolds again took the lead and made many transit circles. The observatories of Harvard College, Cambridge University and Edinburgh University had large circles by Troughton and Simms. The Airy Transit Circles at the Royal Greenwich Observatory (1851) and that at the


id: multi-conjugate-adaptive-optics-demonstrator-20260505-0
file: data/en.wikipedia.org/wiki/Multi-conjugate_Adaptive_optics_Demonstrator-0.md
category: reference
title: Multi-conjugate Adaptive optics Demonstrator
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multi-conjugate_Adaptive_optics_Demonstrator
date_saved: 2026-05-05T09:47:52.225578+00:00
instance: kb-cron
parent: multi-conjugate-adaptive-optics-demonstrator-20260505-0
summary:
Multi-conjugate Adaptive optics Demonstrator (MAD) is an instrument that allowed the European Southern Observatory's Very Large Telescope to observe celestial objects with most of the atmosphere's blurring removed. As with other adaptive optics systems, it works by performing real-time corrections to the atmospheric turbulence by means of computer-controlled deformable mirrors. Its particularity is the correction over a wider field of view than previous systems, which only used a single deformable mirror. == References ==


id: multicolor-active-galactic-nuclei-monitoring-20260505-0
file: data/en.wikipedia.org/wiki/Multicolor_Active_Galactic_Nuclei_Monitoring-0.md
category: reference
title: Multicolor Active Galactic Nuclei Monitoring
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multicolor_Active_Galactic_Nuclei_Monitoring
date_saved: 2026-05-05T09:47:53.404772+00:00
instance: kb-cron
parent: multicolor-active-galactic-nuclei-monitoring-20260505-0
summary:
Multicolor Active Galactic Nuclei Monitoring or MAGNUM was a project completed in 2008, that used a 2 meter (78.7 inch) telescope at Haleakala, Hawaii. The project started in 1995, and with telescope observations starting in 2000 for the scientific study of active galactic nuclei. It was run by the University of Tokyo, the National Astronomical Observatory of Japan, and Australian National University. MAGNUM was one of the telescopes that observed a cosmic explosion billions of years away in 2005. The telescope was used for a long-term study of the size of the universe; for example it studied the Seyfert 1 galaxies NGC 5548, NGC 4051, NGC 3227, and NGC 7469 The telescope was located at the Haleakala Observatory and was installed in north dome previously used by LURE. This was an astronomy project that used an automated telescope to look for AGN at visible and near infrared wavelengths. == References ==


id: narrabri-stellar-intensity-interferometer-20260505-0
file: data/en.wikipedia.org/wiki/Narrabri_Stellar_Intensity_Interferometer-0.md
category: reference
title: Narrabri Stellar Intensity Interferometer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Narrabri_Stellar_Intensity_Interferometer
date_saved: 2026-05-05T09:47:54.566878+00:00
instance: kb-cron
parent: narrabri-stellar-intensity-interferometer-20260505-0
summary:
The Narrabri Stellar Intensity Interferometer (NSII) was the first astronomical instrument to measure the diameters of a large number of stars at visible wavelengths. It was designed by (amongst others) Robert Hanbury Brown, who received the Hughes Medal in 1971 for this work. It was built by University of Sydney School of Physics and was located near the town of Narrabri in north-central New South Wales, Australia. Many of the components were constructed in the UK. The design was based on an earlier optical intensity interferometer built by Hanbury Brown and Richard Q. Twiss at Jodrell Bank in the UK. Whilst the original device had a maximum baseline of 10m, the NSII device consisted of a large circular track that allowed the detectors to be separated from 10 to 188m. The NSII operated from 1963 until 1974, and was used to measure the angular diameters of 32 stars. == See also == Lists of telescopes == References == == External links == The angular diameters of 32 stars, Mon. Not. R. Astron. Soc. Volume 167 pp 121–136 (1974) Hanbury Brown R, The intensity interferometer – its application to astronomy, Taylor & Francis, 1974


id: next-generation-transit-survey-20260505-0
file: data/en.wikipedia.org/wiki/Next-Generation_Transit_Survey-0.md
category: reference
title: Next-Generation Transit Survey
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Next-Generation_Transit_Survey
date_saved: 2026-05-05T09:47:55.779523+00:00
instance: kb-cron
parent: next-generation-transit-survey-20260505-0
summary:
The Next-Generation Transit Survey (NGTS) is a ground-based robotic search for exoplanets. The facility is located at Paranal Observatory in the Atacama Desert in northern Chile, about 2 km from ESO's Very Large Telescope and 0.5 km from the VISTA Survey Telescope. Science operations began in early 2015. The astronomical survey is managed by a consortium of seven European universities and other academic institutions from Chile, Germany, Switzerland, and the United Kingdom. Prototypes of the array were tested in 2009 and 2010 on La Palma, and from 2012 to 2014 at Geneva Observatory. The aim of NGTS is to discover super-Earths and exo-Neptunes transiting relatively bright and nearby stars with an apparent magnitude of up to 13. The survey uses transit photometry, which precisely measures the dimming of a star to detect the presence of a planet when it crosses in front of it. NGTS consists of an array of twelve commercial 0.2-metre telescopes (f/2.8), each equipped with a red-sensitive CCD camera operating in the visible and near-infrared at 600–900 nm. The array covers an instantaneous field of view of 96 square degrees (8 deg2 per telescope) or around 0.23% of the entire sky. NGTS builds heavily on experience with


id: next-generation-transit-survey-20260505-1
file: data/en.wikipedia.org/wiki/Next-Generation_Transit_Survey-1.md
category: reference
title: Next-Generation Transit Survey
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Next-Generation_Transit_Survey
date_saved: 2026-05-05T09:47:55.779523+00:00
instance: kb-cron
parent: next-generation-transit-survey-20260505-0
summary:
== Partnership == Although located at Paranal Observatory, NGTS is not in fact operated by ESO, but by a consortium of seven academic institutions from Chile, Germany, Switzerland, and the United Kingdom: DLR, Institute for Planetary Research Geneva Observatory Queen's University Belfast University of Cambridge University of Chile University of Leicester University of Warwick == Results == On 31 October 2017, the discovery of NGTS-1b, a confirmed hot Jupiter-sized extrasolar planet orbiting NGTS-1, an M-dwarf star, about half the mass and radius of the Sun, every 2.65 days, was reported by the survey team. Daniel Bayliss, of the University of Warwick, and lead author of the study describing the discovery of NGTS-1b, stated, "The discovery of NGTS-1b was a complete surprise to us—such massive planets were not thought to exist around such small stars – importantly, our challenge now is to find out how common these types of planets are in the Galaxy, and with the new Next-Generation Transit Survey facility we are well-placed to do just that." On 3 September 2018, the discovery of NGTS-4b, a sub-Neptune-sized planet transiting a 13th magnitude K-dwarf in a 1.34 day orbit. NGTS-4b has a mass 20.6 ± 3.0 M🜨 and radius 3.18


id: non-achromatic-objective-20260505-0
file: data/en.wikipedia.org/wiki/Non-achromatic_objective-0.md
category: reference
title: Non-achromatic objective
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Non-achromatic_objective
date_saved: 2026-05-05T09:47:56.934685+00:00
instance: kb-cron
parent: non-achromatic-objective-20260505-0
summary:
A non-achromatic objective is an objective lens which is not corrected for chromatic aberration. In telescopes they can a be pre-18th century simple single element objective lenses which were used before the invention of doublet achromatic lenses. They can also be specialty monochromatic lenses used in modern research telescopes and other instruments. == Non-achromatic telescope objectives == === Early non-achromatic objectives === Early telescope objective, such as those built by Johannes Hevelius and Christiaan Huygens and his brother Constantijn Huygens, Jr., utilized single small (2"-8") positive lenses with enormous focal lengths (up to 150 feet in length in tube telescopes and up to 600 feet in non-tube aerial telescopes). This allowed the observer to use higher magnification while limiting the interfering rainbow halos caused by chromatic aberration (the uncorrected chromatic aberration fell within the large diffraction pattern at focus). === Modern non-achromatic objectives === Modern instruments may use a non-achromatic objective lens which is well-corrected for spherical aberration and off-axis aberrations such as coma and astigmatism over the desired field of view at only one wavelength. Monochromatically corrected objectives can be found in solar telescopes working with narrow spectral lines such as the hydrogen alpha spectral line of 0.6562725 micrometres.


id: nuclear-compton-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Nuclear_Compton_Telescope-0.md
category: reference
title: Nuclear Compton Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_Compton_Telescope
date_saved: 2026-05-05T09:47:58.140551+00:00
instance: kb-cron
parent: nuclear-compton-telescope-20260505-0
summary:
The Nuclear Compton Telescope (NCT) is a balloon-borne Compton telescope to observe the gamma-ray sky in the energy range from a few hundred keV to several MeV. Its main goals are to improve the understanding of Galactic nucleosynthesis, gamma-ray bursts, supernovae, black holes, and more. == Instrumentation == The Compton telescope uses an array of twelve germanium detectors with high spectral resolution to detect gamma rays. On its bottom half the detector is surrounded by a bismuth germanate scintillator to shield it from atmospheric gamma rays. The telescope has an overall field of view (FOV) of 25% of the sky. == Flights == Since low-to-medium-energy gamma rays are only detectable from above the atmosphere, NCT is launched with a large 1-million m3 (35-million ft3) Helium balloon into the stratosphere. So far NCT had two successful and one unsuccessful balloon campaigns: A two-detector prototype was successfully test flown on 1 June 2005 from the Scientific Balloon Flight Facility, Fort Sumner, New Mexico. On 19 May 2009, the full instrument successfully launched from Fort Sumner in New Mexico and was able to observe the Crab Pulsar. Unfortunately, on 28 April 2010 a launch mishap occurred at Alice Springs, Australia, when the gondola


id: ohana-project-20260505-0
file: data/en.wikipedia.org/wiki/Ohana_project-0.md
category: reference
title: Ohana project
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ohana_project
date_saved: 2026-05-05T09:47:59.306726+00:00
instance: kb-cron
parent: ohana-project-20260505-0
summary:
The Ohana project aims to use seven big telescopes on top of Mauna Kea, Hawaiʻi Big Island, in an interferometer configuration. Mauna Kea is a former volcano whose height is 13,600 ft (4,145 m). It is a good site for telescopes which probe the universe in the optical and infrared wavelengths because of its altitude and low levels of light pollution. OHANA stands for Optical Hawaiian Array for Nanoradian Astronomy. In Hawaiʻian, ‘ohana means "family". == Telescopes involved in the project == Among the telescopes belonging to the Mauna Kea Observatory, seven are involved in the ‘OHANA project : Two Keck telescopes which each have a 10 m diameter primary mirror. Subaru with an 8.2 m primary mirror. Gemini North with an 8 m primary mirror. Canada France Hawaii Telescope (CFHT) with a prime focus/Cassegrain configuration with a usable aperture diameter of 3.58 meters. The Infrared Telescope Facility is a 3 m telescope. The United Kingdom Infrared Telescope is a 3.8 m telescope. == Stages of the project == The project's big improvement is the use of optic fiber instead of mirrors to guide the beams in the interferometer recombination system. Before doing some tests with the telescopes, scientists had


id: optical-gravitational-lensing-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Optical_Gravitational_Lensing_Experiment-0.md
category: reference
title: Optical Gravitational Lensing Experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_Gravitational_Lensing_Experiment
date_saved: 2026-05-05T09:48:00.497173+00:00
instance: kb-cron
parent: optical-gravitational-lensing-experiment-20260505-0
summary:
The Optical Gravitational Lensing Experiment (OGLE) is a Polish astronomical project based at the University of Warsaw that runs a long-term variability sky survey (1992–present). The main goals are the detection and classification of variable stars (pulsating and eclipsing), discovery of microlensing events, dwarf novae, and studies of the structure of the Galaxy and the Magellanic Clouds. Since the project began in 1992, it has discovered a multitude of extrasolar planets, together with the first planet discovered using the transit method (OGLE-TR-56b) and gravitational microlensing. The project has been led by professor Andrzej Udalski since its inception. == Description == The main targets of the experiment are the Magellanic Clouds and the Galactic Bulge, because of the large number of intervening stars that can be used for microlensing during a stellar transit. Most of the observations have been made at the Las Campanas Observatory in Chile. Cooperating institutions include Princeton University and the Carnegie Institution. The project is now in its fourth phase. The first phase, OGLE-I (1992–1995), used the 1.0-metre (3 ft 3 in) Swope telescope and a single-chip CCD sensor. For OGLE-II (1996–2000), a 1.3-metre (4 ft 3 in) telescope dedicated to the project (the Warsaw telescope) was


id: optical-system-for-imaging-and-low-resolution-integrated-spectroscopy-20260505-0
category: reference
title: Optical System for Imaging and low Resolution Integrated Spectroscopy
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_System_for_Imaging_and_low_Resolution_Integrated_Spectroscopy
date_saved: 2026-05-05T09:48:01.650993+00:00
instance: kb-cron
parent: optical-system-for-imaging-and-low-resolution-integrated-spectroscopy-20260505-0
file:
data/en.wikipedia.org/wiki/Optical_System_for_Imaging_and_low_Resolution_Integrated_Spectroscopy-0.md

summary:
The Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) is an optical spectrometer at the Gran Telescopio Canarias (GTC) in Spain. It was the first instrument in operation at the GTC. OSIRIS's key scientific project is OTELO. Sensitive in the wavelength range from 365 through 1000 nm, OSIRIS is a multiple purpose instrument for imaging and low-resolution long slit and multiple object spectroscopy (MOS). Imaging can be done using broad-band filters or narrow-band tunable filters with FWHM ranging from 0.2 to 0.9 nm at 365 nm, through 0.9 to 1.2 at 1000 nm. OSIRIS observing modes include also fast photometry and spectroscopy. OSIRIS's field of view is of 8.5×8.5 arcminutes and the maximum nominal spectral resolution is of 5000 for a slit width of 0.6 arcsec. MOS incorporates detector charge shuffling co-ordinated with telescope nodding for an excellent sky subtraction. The use of tunable filters is a completely new feature in 8 to 10 m class telescopes that will allow observing the very faint and distant emission line objects. == External links == Gran Telescopio CANARIAS OSIRIS instrument page OSIRIS Home Page (IAC)


id: optical-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Optical_telescope-0.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
An optical telescope gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electronic image sensors. There are three primary types of optical telescope : Refracting telescopes, which use lenses and less commonly also prisms (dioptrics) Reflecting telescopes, which use mirrors (catoptrics) Catadioptric telescopes, which combine lenses and mirrors An optical telescope's ability to resolve small details is directly related to the diameter (or aperture) of its objective (the primary lens or mirror that collects and focuses the light), and its light-gathering power is related to the area of the objective. The larger the objective, the more light the telescope collects and the finer detail it resolves. People use optical telescopes (including monoculars and binoculars) for outdoor activities such as observational astronomy, ornithology, pilotage, hunting and reconnaissance, as well as indoor/semi-outdoor activities such as watching performance arts and spectator sports. == History == The telescope is more a discovery of optical craftsmen than an invention of a scientist. The lens and the properties of refracting and reflecting light had been known since antiquity, and theory on how they worked


id: optical-telescope-20260505-1
file: data/en.wikipedia.org/wiki/Optical_telescope-1.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
Most telescope designs produce an inverted image at the focal plane; these are referred to as inverting telescopes. In fact, the image is both turned upside down and reversed left to right, so that altogether it is rotated by 180 degrees from the object orientation. In astronomical telescopes the rotated view is normally not corrected, since it does not affect how the telescope is used. However, a mirror diagonal is often used to place the eyepiece in a more convenient viewing location, and in that case the image is erect, but still reversed left to right. In terrestrial telescopes such as spotting scopes, monoculars and binoculars, prisms (e.g., Porro prisms) or a relay lens between objective and eyepiece are used to correct the image orientation. There are telescope designs that do not present an inverted image such as the Galilean refractor and the Gregorian reflector. These are referred to as erecting telescopes. === Design variants === Many types of telescope fold or divert the optical path with secondary or tertiary mirrors. These may be integral part of the optical design (Newtonian telescope, Cassegrain reflector or similar types), or may simply be used to place the eyepiece or detector at a


id: optical-telescope-20260505-2
file: data/en.wikipedia.org/wiki/Optical_telescope-2.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
=== Focal length and focal ratio === The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus. A system with a shorter focal length has greater optical power than one with a long focal length; that is, it bends the rays more strongly, bringing them to a focus in a shorter distance. In astronomy, the f-number is commonly referred to as the focal ratio notated as N {\displaystyle N} . The focal ratio of a telescope is defined as the focal length f {\displaystyle f} of an objective divided by its diameter D {\displaystyle D} or by the diameter of an aperture stop in the system. The focal length controls the field of view of the instrument and the scale of the image that is presented at the focal plane to an eyepiece, film plate, or CCD. An example of a telescope with a focal length of 1200 mm and aperture diameter of 254 mm is given by: N = f D = 1200 254 ≈ 4.7 {\displaystyle N={\frac {f}{D}}={\frac {1200}{254}}\approx


id: optical-telescope-20260505-3
file: data/en.wikipedia.org/wiki/Optical_telescope-3.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
==== Visual ==== The visual magnification M {\displaystyle M} of the field of view through a telescope can be determined by the telescope's focal length f {\displaystyle f} divided by the eyepiece focal length f e {\displaystyle f_{e}} (or diameter). The maximum is limited by the focal length of the eyepiece. An example of visual magnification using a telescope with a 1200 mm focal length and 3 mm eyepiece is given by: M = f f e = 1200 3 = 400 {\displaystyle M={\frac {f}{f_{e}}}={\frac {1200}{3}}=400} ==== Minimum ==== There are two issues constraining the lowest useful magnification on a telescope: The light beam exiting the eyepiece needs to be small enough to enter the pupil of the observer's eye. If the cylinder of light emerging from they eyepiece is too wide to enter the observer's eye, some of the light gathered by the telescope will be wasted, and the image seen will be dimmer and less clear than it would be at a higher magnification. For telescope designs with obstructions in the light path (e.g. most catadioptric telescopes, but not spyglass-style refracting telescopes) the magnification must be high enough to keep the central obstruction out of focus, to prevent


id: optical-telescope-20260505-4
file: data/en.wikipedia.org/wiki/Optical_telescope-4.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
Decreasing the magnification past this limit will not increase brightness nor improve clarity: Beyond this limit there is no benefit from lower magnification. Likewise calculating the exit pupil d e p {\displaystyle \ d_{\mathsf {ep}}\ } is a division of the aperture diameter D {\displaystyle \ D\ } and the visual magnification M {\displaystyle \ M\ } used. The minimum often may not be reachable with some telescopes, a telescope with a very long focal length may require a longer focal length eyepiece than is available. An example of the lowest usable magnification using a fairly common 10″ (254 mm) aperture and the standard adult 7 mm maximum exit pupil is given by: M m i n = D d e p = 254 7 ≈ 36 × . {\displaystyle \ M_{\mathsf {min}}={\frac {D}{\ d_{\mathsf {ep}}}}={\frac {\ 254\ }{7}}\approx 36\!\times ~.} If the telescope happened to have a 1200mm focal length ( L {\displaystyle \ L\ } ), the longest recommended eyepiece focal length ( ℓ {\displaystyle \ \ell \ } ) would be ℓ = L M ≈ 1 200 m m 36 ≈ 33 m m . {\displaystyle \ \ell ={\frac {\ L\ }{M}}\approx {\frac {\ 1\ 200{\mathsf


id: optical-telescope-20260505-5
file: data/en.wikipedia.org/wiki/Optical_telescope-5.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
==== Apparent ==== Apparent field of view (commonly referred to as AFOV) is the perceived angular size of the field stop of the eyepiece, typically measured in degrees. It is a fixed property of the eyepiece's optical design, with common commercially available eyepieces offering a range of apparent fields from 40° to 120°. The apparent field of view of an eyepiece is limited by a combination of the eyepiece's field stop diameter, and focal length, and is independent of magnification used. In an eyepiece with a very wide apparent field of view, the observer may perceive that the view through the telescope stretches out to their peripheral vision, giving a sensation that they are no longer looking through an eyepiece, or that they are closer to the subject of interest than they really are. In contrast, an eyepiece with a narrow apparent field of view may give the sensation of looking through a tunnel or small porthole window, with the black field stop of the eyepiece occupying most of the observer's vision. A wider apparent field of view permits the observer to see more of the subject of interest (that is, a wider true field of view) without reducing magnification


id: optical-telescope-20260505-6
file: data/en.wikipedia.org/wiki/Optical_telescope-6.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
=== Field of view and magnification relationship === Finding what can be seen through the optical system begins with the eyepiece providing the field of view and magnification; the magnification is given by the division of the telescope and eyepiece focal lengths. Using an example of an amateur telescope such as a Newtonian telescope with an aperture D {\displaystyle D} of 130 mm (5") and focal length f {\displaystyle f} of 650 mm (25.5 inches), one uses an eyepiece with a focal length d {\displaystyle d} of 8 mm and apparent FOV v a {\displaystyle v_{a}} of 52°. The magnification at which the observable world is viewed is given by: M = f d = 650 8 = 81.25 {\displaystyle M={\frac {f}{d}}={\frac {650}{8}}=81.25} . The field of view v t {\displaystyle v_{t}} requires the magnification, which is formulated by its division over the apparent field of view: v t = v a M = 52 81.25 = 0.64 {\displaystyle v_{t}={\frac {v_{a}}{M}}={\frac {52}{81.25}}=0.64} . The resulting true field of view is 0.64°, not allowing an object such as the Orion Nebula, which appears elliptical with an angular diameter of 65 × 60 arcminutes, to be viewable through the telescope in its


id: optical-telescope-20260505-7
file: data/en.wikipedia.org/wiki/Optical_telescope-7.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
The derivation of this equation is fairly straightforward and the result is the same for reflecting or refracting telescopes. However, conceptually it is easier to derive by considering a reflecting telescope. If an extended object with angular size α {\displaystyle \alpha } is observed through a telescope, then due to the Laws of reflection and Trigonometry the size of the image projected onto the focal plane will be s = tan ⁡ ( α ) f . {\displaystyle s=\tan(\alpha )f.} The image scale (angular size of object divided by size of projected image) will be i = α s = α tan ⁡ ( α ) f , {\displaystyle i={\frac {\alpha }{s}}={\frac {\alpha }{\tan(\alpha )f}},} and by using the small angle relation tan ⁡ ( a ) ≈ a {\displaystyle \tan(a)\approx a} , when a ≪ 1 {\displaystyle a\ll 1} (N.B. only valid if a {\displaystyle a} is in radians), we obtain i = α α f = 1 f . {\displaystyle i={\frac {\alpha }{\alpha f}}={\frac {1}{f}}.} == Imperfect images == No telescope can form a perfect image. Even if a reflecting telescope could have a perfect mirror, or a refracting telescope could have a perfect lens, the effects of


id: optical-telescope-20260505-8
file: data/en.wikipedia.org/wiki/Optical_telescope-8.md
category: reference
title: Optical telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optical_telescope
date_saved: 2026-05-05T09:48:03.007847+00:00
instance: kb-cron
parent: optical-telescope-20260505-0
summary:
Relatively cheap, mass-produced ~2 meter telescopes have recently been developed and have made a significant impact on astronomy research. These allow many astronomical targets to be monitored continuously, and for large areas of sky to be surveyed. Many are robotic telescopes, computer controlled over the internet (see e.g. the Liverpool Telescope and the Faulkes Telescope North and South), allowing automated follow-up of astronomical events. Initially the detector used in telescopes was the human eye. Later, the sensitized photographic plate took its place, and the spectrograph was introduced, allowing the gathering of spectral information. After the photographic plate, successive generations of electronic detectors, such as the charge-coupled device (CCDs), have been perfected, each with more sensitivity and resolution, and often with a wider wavelength coverage. Current research telescopes have several instruments to choose from such as: imagers, of different spectral responses spectrographs, useful in different regions of the spectrum polarimeters, that detect light polarization. The phenomenon of optical diffraction sets a limit to the resolution and image quality that a telescope can achieve, which is the effective area of the Airy disc, which limits how close two such discs can be placed. This absolute limit is called the diffraction limit (and


id: otto-struve-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Otto_Struve_Telescope-0.md
category: reference
title: Otto Struve Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Otto_Struve_Telescope
date_saved: 2026-05-05T09:48:04.179582+00:00
instance: kb-cron
parent: otto-struve-telescope-20260505-0
summary:
The Otto Struve Telescope was the first major telescope to be built at McDonald Observatory. Located in the Davis Mountains in West Texas, the Otto Struve Telescope was designed by Warner & Swasey Company and constructed between 1933 and 1939 by the Paterson-Leitch Company. Its 82-inch (2.1 m) mirror was the second largest in the world at the time. It was named after the Ukrainian-American astronomer of Baltic German origin Otto Struve in 1966, three years after his death; Struve had been the director of McDonald Observatory from 1932–1950. The Davis Mountains is an excellent location for astronomical research because of the clear dry air and moderately high elevation. The remote nature of the facility proved to be a significant challenge in transporting such a large mirror. It was a very precarious journey for the Otto Struve Telescope's mirror to this remote part of Texas and up to the top of Mount Locke. The mirror was transported from the local town of Fort Davis up the mountain by Carleton D. Wilson, owner of a local trucking company, while locals cheered as they looked on. The Otto Struve telescope is still in use today. It is updated with modern imaging detectors


id: palomar-testbed-interferometer-20260505-0
file: data/en.wikipedia.org/wiki/Palomar_Testbed_Interferometer-0.md
category: reference
title: Palomar Testbed Interferometer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Palomar_Testbed_Interferometer
date_saved: 2026-05-05T09:48:05.305594+00:00
instance: kb-cron
parent: palomar-testbed-interferometer-20260505-0
summary:
The Palomar Testbed Interferometer (PTI) was a near infrared, long-baseline stellar interferometer located at Palomar Observatory in north San Diego County, California, United States. It was built by Caltech and the Jet Propulsion Laboratory and was intended to serve as a testbed for developing interferometric techniques to be used at the Keck Interferometer. It began operations in 1995 and achieved routine operations in 1998, producing more than 50 refereed papers in a variety of scientific journals covering topics from high precision astrometry to stellar masses, stellar diameters and shapes. PTI concluded operations in 2008 and has since been dismantled. PTI was notable for being equipped with a "dual-star" system, making it possible to simultaneously observe pairs of stars; this cancels some of the atmospheric effects of astronomical seeing and makes very high precision measurements possible. A groundbreaking study with the Palomar Testbed Interferometer revealed that the star Altair is not spherical, but is rather flattened at the poles due to its high rate of rotation. == See also == List of astronomical interferometers at visible and infrared wavelengths List of observatories == References == == External links == Palomar Testbed Interferometer (PTI) at NASA Exoplanet Science Institute. Palomar Testbed Interferometer


id: list-of-telescope-parts-and-construction-20260505-0
file: data/en.wikipedia.org/wiki/List_of_telescope_parts_and_construction-0.md
category: reference
title: List of telescope parts and construction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_telescope_parts_and_construction
date_saved: 2026-05-05T09:48:06.544020+00:00
instance: kb-cron
parent: list-of-telescope-parts-and-construction-20260505-0
summary:
== Hardware == === Accessories === Finderscope Iron sight Reflector (reflex) sight Cheshire collimator: A simple tool to collimate a telescope === Control === Clock drive GoTo === Mechanical construction === Mirror support cell Serrurier truss Silvering === Mounts === Telescope mount - Types include: Altazimuth mount Equatorial mount Equatorial platform Poncet Platform Fork mount German equatorial mount Springfield mount === Optics === Mirrors and lenses are the critical light-bending components of a telescope. Objective: The first lens or curved mirror that collects and focuses the incoming light. Primary lens: The objective of a refracting telescope. Primary mirror: The objective of a reflecting telescope. Corrector plate: A full aperture negative lens placed before a primary mirror designed to correct the optical aberrations of the mirror. Schmidt corrector plate: An aspheric-shaped corrector plate used in the Schmidt telescope. Meniscus corrector: A meniscus-shaped corrector plate usually used in the Maksutov telescope. Focusing mask: A full aperture mask temporarily placed before the primary mirror to aid in focusing the telescope. Bahtinov mask Carey mask Hartmann mask Sub-aperture corrector: One or a series of corrective lens (sometimes combined with a corrective curved mirror) placed after (near the focus) a primary mirror designed to correct


id: periscope-lens-20260505-0
file: data/en.wikipedia.org/wiki/Periscope_lens-0.md
category: reference
title: Periscope lens
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Periscope_lens
date_saved: 2026-05-05T09:48:07.723099+00:00
instance: kb-cron
parent: periscope-lens-20260505-0
summary:
A periscope lens, sometimes called a folded lens, is a mechanical assembly of lens elements that uses a prism or mirror to redirect the light through the lenses with a 90° angle to the optical axis, as in a periscope. == Uses == The Kenworthy/Nettmann Snorkel Camera System, introduced in 1967 by N. Paul Kenworthy and Bob Nettmann, uses periscope lenses to allow filming very small scale models and objects from a very close distance. This system uses a full-size movie camera with downward-extending periscope attachment, which has a length of 24 inches (0.61 m) and a diameter of 2+1⁄2 to 1⁄2 inch (64 to 13 mm). Similar design is used to allow wide-angle lens protruding from aircraft for aerial cinematography. Minolta DiMAGE X introduced in 2002 was among the first digital cameras to use a folded lens; that design was later adopted on other compact digital cameras. Smartphones use periscope lenses to allow larger zoom ratios without increasing their thickness significantly. The increased optical zoom range is aimed to improve macro photography. With a periscope lens, the zoom lenses are turned by 90° and are aligned along the length or the width of the smartphone instead of its depth.


id: plate-optimizer-20260505-0
file: data/en.wikipedia.org/wiki/PLate_OPtimizer-0.md
category: reference
title: PLate OPtimizer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/PLate_OPtimizer
date_saved: 2026-05-05T09:48:09.010806+00:00
instance: kb-cron
parent: plate-optimizer-20260505-0
summary:
PLate OPtimizer, or PLOP is a CAD program used by amateur telescope makers to design primary mirror support cells for reflecting telescopes. It was developed by telescope maker David Lewis, first described in 1999, and used to simplify calculations needed in the design of mirror support cells. It was based on Toshimi Taki's 1993 program PLATE, with a simplified user interface, thus giving it wide acceptance among makers of large Dobsonian style amateur telescopes, with good support of mirrors as thin as two inches for a diameter of thirty inches. == Comparisons and limitations == A basic mirror cell may be built using minimal calculation and simple materials such as wood and outdoor carpet, with a good example being Dobson's original telescopes. However, as amateurs sought to build larger and thinner mirrors, they found such designs inadequate. Many amateur telescope makers use cells which are designed via equal area rule calculation, using programs such as David Chandler's public domain program, Cell. However, such calculation does not account for mechanical stresses introduced in one part of a telescope mirror by another part, whereas finite element analysis can be used to reduce such stress. Although general finite element analysis programs such as


id: polar-alignment-20260505-0
file: data/en.wikipedia.org/wiki/Polar_alignment-0.md
category: reference
title: Polar alignment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Polar_alignment
date_saved: 2026-05-05T09:48:10.199643+00:00
instance: kb-cron
parent: polar-alignment-20260505-0
summary:
Polar alignment is the act of aligning the rotational axis of a telescope's equatorial mount or a sundial's gnomon with a celestial pole to parallel Earth's axis. == Alignment methods == The method to use differs depending on whether the alignment is taking place in daylight or at night. Furthermore, the method differs if the alignment is done in the Northern Hemisphere or Southern Hemisphere. The purpose of the alignment also must be considered; for example, the value of accuracy is much more significant in astrophotography than in casual stargazing. === Aiming at the pole stars === In the Northern Hemisphere, sighting Polaris the North Star is the usual procedure for aligning a telescope mount's polar axis parallel to the Earth's axis. Polaris is approximately three-quarters of a degree from the North Celestial Pole, and is easily seen by the naked eye. σ Octantis, sometimes known as the South Star, can be sighted in the Southern hemisphere to perform a polar alignment. At magnitude +5.6, it is difficult for inexperienced observers to locate in the sky. Its declination of -88° 57′ 23″ places it 1° 2′ 37" from the South Celestial Pole. An even closer star BQ Octantis of magnitude


id: polar-alignment-20260505-1
file: data/en.wikipedia.org/wiki/Polar_alignment-1.md
category: reference
title: Polar alignment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Polar_alignment
date_saved: 2026-05-05T09:48:10.199643+00:00
instance: kb-cron
parent: polar-alignment-20260505-0
summary:
Δ α = Δ e ⋅ tan ⁡ δ ⋅ sin ⁡ h + Δ a ⋅ ( sin ⁡ Φ − cos ⁡ Φ ⋅ tan ⁡ δ ⋅ cos ⁡ h ) , Δ δ = Δ e ⋅ cos ⁡ h + Δ a ⋅ cos ⁡ Φ ⋅ sin ⁡ h , {\displaystyle {\begin{aligned}\Delta \alpha &=\Delta e\cdot \tan \delta \cdot \sin h+\Delta a\cdot (\sin \Phi -\cos \Phi \cdot \tan \delta \cdot \cos h),\\\Delta \delta &=\Delta e\cdot \cos h+\Delta a\cdot \cos \Phi \cdot \sin h,\end{aligned}}} where α {\displaystyle \alpha } is right ascension, δ {\displaystyle \delta } is declination, Φ {\displaystyle \Phi } is site latitude, h {\displaystyle h} is the hour angle of the reference point equals ( α {\displaystyle \alpha } − local sidereal time), Δ α {\displaystyle \Delta \alpha } is error in right ascension, Δ δ {\displaystyle \Delta \delta } is error in declination, Δ e {\displaystyle \Delta e} is polar error in elevation (altitude), Δ a {\displaystyle \Delta a} is polar error in azimuth. The inverse can be calculated if the above formula is written in matrix notation. So the polar error expressed in Δe and Δa can be calculated from the


id: purple-crow-lidar-20260505-0
file: data/en.wikipedia.org/wiki/Purple_Crow_Lidar-0.md
category: reference
title: Purple Crow Lidar
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Purple_Crow_Lidar
date_saved: 2026-05-05T09:48:11.428444+00:00
instance: kb-cron
parent: purple-crow-lidar-20260505-0
summary:
The Purple Crow Lidar is a powerful lidar (laser radar) that emits pulses of intensely bright light. The bright light scatters off air molecules, and the reflections are collected by a large telescope. == Telescope == The telescope is formed by rotating liquid mercury at 10 r.p.m. in a 2.65-m diameter container. This liquid mirror technology has been made and developed at Université Laval in Québec City. Such rotating measurement allow air density, pressure, temperature, and composition to be measured. Which can be useful to collect data for global warming and weather prediction. == Weather prediction == This chart is used to determine and predict the weather at Purple Crow Lidar Facility in London Ontario for astronomical observing. == Location == The Purple Crow operates from the Echo Base Observatory located at Western's Environmental Science Field Station located near London, Ontario, Canada. == People in charge == The Purple Crow Lidar research project is headed by Professor Robert J. Sica in the Physics Department at UWO London Ontario. Its main support comes from the Natural Science and Engineering Research Council of Canada (NSERC). == See also == Large Zenith Telescope Liquid-mirror telescope == References ==


id: ronchi-test-20260505-0
file: data/en.wikipedia.org/wiki/Ronchi_test-0.md
category: reference
title: Ronchi test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ronchi_test
date_saved: 2026-05-05T09:48:12.773082+00:00
instance: kb-cron
parent: ronchi-test-20260505-0
summary:
In optical testing a Ronchi test is a method of determining the surface shape (figure) of a mirror used in telescopes and other optical devices. == Description == In 1923 Italian physicist Vasco Ronchi published a description of the eponymous Ronchi test, which is a variation of the Foucault knife-edge test and which uses simple equipment to test the quality of optics, especially concave mirrors. [1]. A "Ronchi tester" consists of: A light source A diffuser A Ronchi grating A Ronchi grating consists of alternate dark and clear stripes. One design is a small frame with several evenly spaced fine wires attached. Light is emitted through the Ronchi grating (or a single slit), reflected by the mirror being tested, then passes through the Ronchi grating again and is observed by the person doing the test. The observer's eye is placed close to the centre of curvature of the mirror under test looking at the mirror through the grating. The Ronchi grating is a short distance (less than 2 cm) closer to the mirror. The observer sees the mirror covered in a pattern of stripes that reveal the shape of the mirror. The pattern is compared to a mathematically generated diagram


id: rotating-furnace-20260505-0
file: data/en.wikipedia.org/wiki/Rotating_furnace-0.md
category: reference
title: Rotating furnace
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Rotating_furnace
date_saved: 2026-05-05T09:48:14.170841+00:00
instance: kb-cron
parent: rotating-furnace-20260505-0
summary:
A rotating furnace is a device for making solid objects which have concave surfaces that are segments of axially symmetrical paraboloids. Usually, the objects are made of glass. The furnace makes use of the fact, already known to Newton, that the centrifugal-force-induced shape of the top surface of a spinning liquid is a concave paraboloid, identical to the shape of a reflecting telescope's primary focusing mirror. Paraboloids can be used in various ways, including (after being silvered) as primary mirrors in reflecting telescopes and solar cookers. == Design == The furnace includes a mechanism that rotates an open-topped container at constant speed around a vertical axis. A quantity of glass sufficient to make the mirror is placed in the container, heated until it is completely molten, and then allowed to cool while continuing to rotate until it has completely solidified. When the glass is solid, the rotation is stopped and the paraboloidal shape of its top surface is preserved. This process is called spin casting. The same process can be used to make a lens with a concave paraboloidal surface. The other surface is shaped by the container that holds the molten glass acting as a mold. Lenses made this


id: rtt-150-20260505-0
file: data/en.wikipedia.org/wiki/RTT-150-0.md
category: reference
title: RTT-150
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/RTT-150
date_saved: 2026-05-05T09:48:15.458747+00:00
instance: kb-cron
parent: rtt-150-20260505-0
summary:
RTT-150 (Russian: РТТ-150) is a Russian-Turkish 1.5-m optical telescope. It is an international project, jointly led by the Ministry of Education and Science of the Russian Federation and the Council for Technical and Scientific Research of Turkey (TÜBİTAK, TUBITAK). The main performers are Kazan Federal University and the Space Research Institute of the Russian Academy of Sciences from the Russian side and the TUBITAK State Observatory (TUG; observatory code “A84”) from Turkey. Observational time of telescope is shared in the following proportion: 45% - KSU, 15% - IKI RAS (accordance with agreement between parties), and another 40% - are shared between Turkish universities through the TUG. One of the main tasks of the telescope is the optical support of orbital X-ray observatories: INTEGRAL observatory and Spektr-RG. == References == == External links == Official site. TÜBİTAK ULUSAL GÖZLEMEV (Turkey)


id: schiefspiegler-20260505-0
file: data/en.wikipedia.org/wiki/Schiefspiegler-0.md
category: reference
title: Schiefspiegler
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Schiefspiegler
date_saved: 2026-05-05T09:48:16.819579+00:00
instance: kb-cron
parent: schiefspiegler-20260505-0
summary:
The Schiefspiegler (lit. oblique reflector in German), also called tilted-component telescopes (TCT) and off-axis reflecting telescopes, are a type of reflecting telescope featuring an off-axis secondary mirror, and therefore an obstruction-free light path. This is accomplished by tilting the primary mirror so that the secondary mirror does not block incoming light. William Herschel was one of the first to have tilted the mirror of his telescope in order to avoid light loss due to the low reflectivity of his speculum metal mirror. The obstructions in telescope tubes, such as secondary mirrors and their mechanical supports, cut off the intensity of captured light and cause diffraction. The diffraction causes artifacts such as the radial spikes that project from images of bright stars, and it also reduces the contrast of fine details. Schiefspieglers offer a significant increase in contrast, which is useful, for instance, for lunar and planetary study. Tilting the mirrors causes severe coma and astigmatism, however as Anton Kutter showed in the 1950s, by a suitable choice of radii these aberrations can be corrected to an acceptable level. == Implementations == The 1.6 meter New Solar Telescope at the Big Bear Solar Observatory, and the 4 meter Daniel K. Inouye


id: schmidt-v-is-l-camera-20260505-0
file: data/en.wikipedia.org/wiki/Schmidt–Väisälä_camera-0.md
category: reference
title: Schmidt–Väisälä camera
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Schmidt–Väisälä_camera
date_saved: 2026-05-05T09:48:20.279612+00:00
instance: kb-cron
parent: schmidt-v-is-l-camera-20260505-0
summary:
The Schmidt–Väisälä camera is a type of astronomical telescope intended for wide-field (5 to 10 degrees of arc) photographic work. It was designed by Finnish physicist Yrjö Väisälä. == Invention and design == Professor Väisälä originally designed an "astronomical camera" similar to Bernhard Schmidt's Schmidt camera, but the design was unpublished. Väisälä did mention it in a lecture notes in 1924 with a footnote: "problematic spherical focal plane". Once Väisälä saw Schmidt's publication, he promptly went ahead and solved the field-flattening problem in Schmidt's design by placing a doubly convex lens slightly in front of the film holder. This resulting system is known as a Schmidt–Väisälä camera or sometimes as Väisälä camera. This flat-field correction is not perfect, as images suffer from chromatic aberration with different colors ending up at slightly different places. However the approach has attracted interest for modern electronic image sensors with a flat focal plane which cannot be forced into spherical surface shape, nor even manufactured as such. Learning that he lost the inventor status motivated Väisälä to publish his "less than perfect" designs. Professor Väisälä not only designed the new optics, but also built several implementations of the design after Schmidt's publication. His two first


id: secondary-mirror-20260505-0
file: data/en.wikipedia.org/wiki/Secondary_mirror-0.md
category: reference
title: Secondary mirror
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Secondary_mirror
date_saved: 2026-05-05T09:48:21.470642+00:00
instance: kb-cron
parent: secondary-mirror-20260505-0
summary:
A secondary mirror (or secondary) is the second deflecting or focusing mirror element in a reflecting telescope. Light gathered by the primary mirror is directed towards a focal point typically past the location of the secondary. Secondary mirrors in the form of an optically flat diagonal mirror are used to re-direct the light path in designs such as Newtonian reflectors. They are also used to re-direct and extend the light path and modify the final image in designs such as Cassegrain reflectors. The secondary is typically suspended by X-shaped struts (sometimes called a "spider") in the path of light between the source and the primary, but can be mounted on other types of mounts or optical elements such as optical windows, or schmidt and meniscus corrector plates. Employing secondary mirrors in optical systems causes some image distortion due to the obstruction of the secondary itself, and distortion from the spider mounts, commonly seen as cross-shaped diffraction spikes radiating from bright stars seen in astronomical images. For large telescopes, the secondary mirror can reach a significant size. At the Vera C. Rubin Observatory, the secondary for the Simonyi Survey Telescope is nearly four meters in diameter. == See also == List


id: setting-circles-20260505-0
file: data/en.wikipedia.org/wiki/Setting_circles-0.md
category: reference
title: Setting circles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Setting_circles
date_saved: 2026-05-05T09:48:22.678565+00:00
instance: kb-cron
parent: setting-circles-20260505-0
summary:
Setting circles are used on telescopes equipped with an equatorial mount to find celestial objects by their equatorial coordinates, often used in star charts and ephemerides. == Description == Setting circles consist of two graduated disks attached to the axes – right ascension (RA) and declination (DEC) – of an equatorial mount. The RA disk is graduated into hours, minutes, and seconds. The DEC disk is graduated into degrees, arcminutes, and arcseconds. Since the RA coordinates are fixed onto the celestial sphere, the RA disk is usually driven by a clock mechanism in sync with sidereal time. Locating an object on the celestial sphere using setting circles is similar to finding a location on a terrestrial map using latitude and longitude. Sometimes the RA setting circle has two scales on it: one for the Northern Hemisphere and one for the Southern. == Application == === Research telescopes === Historically setting circles have rivaled the telescopes optics as far as difficulty in construction. Making a set of setting circles required a lot of precision crafting on a dividing engine. Setting circles usually had a large diameter and when combined with a vernier scale could point a telescope to nearly an arc


id: hyeronymus-sirturus-20260505-0
file: data/en.wikipedia.org/wiki/Hyeronymus_Sirturus-0.md
category: reference
title: Hyeronymus Sirturus
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hyeronymus_Sirturus
date_saved: 2026-05-05T09:48:23.925773+00:00
instance: kb-cron
parent: hyeronymus-sirturus-20260505-0
summary:
Hieronymus Sirturus (Geronimo Sirtori (Italian: [ˈsirtori])) was a Milanese scholar who wrote at least two books on politics and telescopes between 1614 and 1618. The Compendium politicum: ex universa civili doctrina Justi Lipsii pro principatu, tum ex Notis integra fide concinnatum was published by Persius in Frankfurt in 1614.., and the Telescopium: sive ars perficiendi novum illud Galilaei virorium instrumentum ad sydera, by Paul Jacob in 1618 His Telescopium book was written around 1612, only 4 years after the telescope was invented. The book contained a complete set of instructions and diagrams for building a refracting telescope. Sirtori pointed out that "a workman had to be most careful in polishing otherwise the lens became lopsided or aspherical with peripheral distortion". The book states that the goal is to create a lens with perfectly spherical surfaces. He may have also invented the method of the spherical grinding of moulds, which improved lens grinding and polishing techniques dramatically. With the rapid dissemination of the telescope the priority question about the inventor soon arose. Sirtori downplayed the achievement of the first discovery of the telescope by presenting the story of Johannes Lippersein, who would have grasped the idea from ‘a genius or some


id: skymapper-20260505-0
file: data/en.wikipedia.org/wiki/SkyMapper-0.md
category: reference
title: SkyMapper
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/SkyMapper
date_saved: 2026-05-05T09:48:25.145232+00:00
instance: kb-cron
parent: skymapper-20260505-0
summary:
SkyMapper is a fully automated 1.35 m (4.4 ft) wide-angle optical telescope at Siding Spring Observatory in northern New South Wales, Australia. It is one of the telescopes of the Research School of Astronomy and Astrophysics of the Australian National University (ANU). The telescope has a compact modified Cassegrain design with a large 0.69 m secondary mirror, which gives it a very wide field of view: its single, dedicated instrument, a 268-million pixel imaging camera, can photograph 5.7 square degrees of sky. The camera has six light filters which span from ultraviolet to near infrared wavelengths. The SkyMapper telescope was built to carry out the Southern Sky Survey, which will image the entire southern sky several times over in SkyMapper's six spectral filters over the course of five years. This survey will be analogous to the Sloan Digital Sky Survey of the Northern hemisphere sky. It has several enhancements, including temporal coverage, more precise measurements of stellar properties and coverage of large parts of the plane of the Galaxy. The telescope and its camera were built by the ANU as a successor to the Great Melbourne Telescope at Mount Stromlo after that telescope was burnt in the 2003 Canberra bushfires.


id: slooh-20260505-0
file: data/en.wikipedia.org/wiki/Slooh-0.md
category: reference
title: Slooh
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Slooh
date_saved: 2026-05-05T09:48:26.404482+00:00
instance: kb-cron
parent: slooh-20260505-0
summary:
Slooh is a robotic telescope service that can be viewed live through a web browser. It was not the first robotic telescope, but it was the first that offered "live" viewing through a telescope via the web. Other online telescopes traditionally email a picture to the recipient. The site has a patent on their live image processing method. Slooh is an online astronomy platform with live-views and telescope rental for a fee. Observations come from a global network of telescopes located in places including Spain and Chile and Siding Spring Australia. The name Slooh comes from the word "slew" to indicate the movement of a telescope, modified with "ooh" to express pleasure and surprise. Slooh, LLC is based in Washington, Connecticut. == History == The service was founded in 2002 by Michael Paolucci. Its Canary Islands telescope went online December 25, 2003, but was not available to the public until 2004. == Participating observatories == The original astronomical observatory is located on the island Tenerife in the Canary Islands on the volcano called Teide. The site is at the 2,300-metre (7,500 ft) elevation and situated away from city light pollution. This (Canary Islands) site includes 2 domes, each with 2


id: space-solar-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Space_Solar_Telescope-0.md
category: reference
title: Space Solar Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Space_Solar_Telescope
date_saved: 2026-05-05T09:48:27.628752+00:00
instance: kb-cron
parent: space-solar-telescope-20260505-0
summary:
The Space Solar Telescope (SST) is a planned Chinese optical space solar telescope. It was first proposed in the 1990s, and is intended to be a 1 metre (3.3 ft) telescope. == See also == List of solar telescopes == References ==


id: spin-casting-mirrors-20260505-0
file: data/en.wikipedia.org/wiki/Spin_casting_(mirrors)-0.md
category: reference
title: Spin casting (mirrors)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spin_casting_(mirrors)
date_saved: 2026-05-05T09:48:28.829459+00:00
instance: kb-cron
parent: spin-casting-mirrors-20260505-0
summary:
Spin casting is a technique for constructing large parabolic mirrors by using the curved surface formed by a rotating liquid (e.g. in a rotating furnace). It is distinct from the spin casting or centrifugal rubber mold casting (CRMC) technique used for casting metal or plastics. Pioneered by Roger Angel at the Steward Observatory's mirror lab, this makes large (8.4 metres or 28 feet) thin parabolic mirrors by spinning the oven as the glass is melted and cooled. The term is applied to the fabrication of large telescope mirrors, where the natural paraboloid curve followed by the molten glass greatly reduces the amount of grinding required. Rather than being cast by pouring glass into a mold (with top and bottom), an entire turntable containing the peripheral mold, and the back pattern (a honeycomb pattern to lighten the finished product) is contained within a furnace and charged with the glass material used. The assembly (or rotating furnace) is then heated while spun at slow speed until the glass is liquid, then gradually cooled over a period of months. == See also == Rotating furnace – Device for making axially symmetric paraboloids technique Liquid-mirror telescope – Telescope whose mirror is a reflective liquid


id: subaru-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Subaru_Telescope-0.md
category: reference
title: Subaru Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Subaru_Telescope
date_saved: 2026-05-05T09:48:30.022822+00:00
instance: kb-cron
parent: subaru-telescope-20260505-0
summary:
Subaru Telescope (すばる望遠鏡, Subaru Bōenkyō) is the 8.2-metre (320 in) telescope of the National Astronomical Observatory of Japan, located at the Mauna Kea Observatory on Hawaii. It is named after the open star cluster known in English as the Pleiades. It had the largest monolithic primary mirror in the world from its commissioning until the Large Binocular Telescope opened in 2005. == Overview == The Subaru Telescope is a Ritchey-Chretien reflecting telescope. Instruments can be mounted at a Cassegrain focus below the primary mirror; at either of two Nasmyth focal points in enclosures on the sides of the telescope mount, to which light can be directed with a tertiary mirror; or at the prime focus in lieu of a secondary mirror, an arrangement rare on large telescopes, to provide a wide field of view suited to deep wide-field surveys. In 1984, the University of Tokyo formed an engineering working group to develop and study the concept of a 7.5-metre (300 in) telescope. In 1985, the astronomy committee of Japan's science council gave top priority to the development of a "Japan National Large Telescope" (JNLT), and in 1986, the University of Tokyo signed an agreement with the University of Hawaiʻi to


id: subaru-telescope-20260505-1
file: data/en.wikipedia.org/wiki/Subaru_Telescope-1.md
category: reference
title: Subaru Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Subaru_Telescope
date_saved: 2026-05-05T09:48:30.022822+00:00
instance: kb-cron
parent: subaru-telescope-20260505-0
summary:
Hyper Suprime-Cam (HSC) This 900-megapixel ultra-wide-field (1.5° field of view) camera saw first light in 2012, and was offered for open use in 2014. The extremely large wide-field correction optics (a seven-element lens with some elements up to a meter in diameter) was manufactured by Canon and delivered March 29, 2011. It will be used for surveys of weak lensing to determine dark matter distribution. Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) The Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) instrument is a high-contrast imaging system for directly imaging exoplanets. The coronagraph uses a Phase Induced Amplitude Apodization (PIAA) design which means it will be able to image planets closer to their stars than conventional Lyot type coronagraph designs. For example, at a distance of 100 pc, the PIAA coronagraph on SCExAO would be able to image from 4 AU outwards while Gemini Planet Imager and VLT-SPHERE from 12 AU outwards. The system also has several other types of coronagraph: Vortex, Four-Quadrant Phase Mask and 8-Octant Phase Mask versions, and a shaped-pupil coronagraph. Phase 1 of construction is complete, and phase 2 construction is expected to be complete by end of 2014 for science operations in 2015. SCExAO will initially use the


id: telescope-mount-20260505-0
file: data/en.wikipedia.org/wiki/Telescope_mount-0.md
category: reference
title: Telescope mount
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Telescope_mount
date_saved: 2026-05-05T09:48:31.212999+00:00
instance: kb-cron
parent: telescope-mount-20260505-0
summary:
A telescope mount is a mechanical structure which supports a telescope. Telescope mounts are designed to support the mass of the telescope and allow for accurate pointing of the instrument. Many sorts of mounts have been developed over the years, with the majority of effort being put into systems that can track the motion of the fixed stars as the Earth rotates. == Fixed mounts == Fixed telescope mounts are entirely fixed in one position, such as Zenith telescopes that point only straight up and the National Radio Astronomy Observatory's Green Bank fixed radio 'horn' built to observe Cassiopeia A. == Fixed altitude mounts == Fixed-altitude mounts usually have the primary optics fixed at an altitude angle while rotating horizontally (in azimuth). They can cover the whole sky but only observe objects for the short time when that object passes a specific altitude and azimuth. == Transit mounts == Transit mounts are single axis mounts fixed in azimuth while rotating in altitude, usually oriented on a north-south axis. This allows the telescope to view the whole sky, but only when the Earth's rotation allows the objects to cross (transit) through that narrow north-south line (the meridian). This type of mount


id: the-porter-garden-telescope-20260505-0
file: data/en.wikipedia.org/wiki/The_Porter_Garden_Telescope-0.md
category: reference
title: The Porter Garden Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/The_Porter_Garden_Telescope
date_saved: 2026-05-05T09:48:32.433614+00:00
instance: kb-cron
parent: the-porter-garden-telescope-20260505-0
summary:
The Porter Garden Telescope was an innovative ornamental telescope for the garden designed by Russell W. Porter and commercialized by Jones & Lamson Machine Company at the beginning of the 1920s in the United States. Oriented to users with high purchasing power, and constructed in statuary bronze, it could be left permanently outdoors like sculptures and sundials, keeping the delicate optics in a case. It was embellished with floral ornament, with a style close to the art nouveau. In its base were the names of celebrated astronomers: Galileo, Kepler, and Newton. The part called the bowl bore the commercial logo "The Porter Garden Telescope", the name and address of the manufacturer, the serial number of manufacture, and the number and date of the patent. == Technical characteristics == Material of construction: Bronze. Reflecting telescope, Newtonian type. Without tube that wrap the optics. Mount: Combination of altazimuth (terrestrial use) and equatorial type horseshoe (astronomical use). Able to follow the movement of the apparent place of the stars, when it is used between the latitudes 25º-55º of both hemispheres north and south. Primary mirror of 6 inches (6": roughly 152mm). Focal relation f/4. Prism of 1.5 inches as secondary reflecting element. The


id: thirty-meter-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Thirty_Meter_Telescope-0.md
category: reference
title: Thirty Meter Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Thirty_Meter_Telescope
date_saved: 2026-05-05T09:48:33.714678+00:00
instance: kb-cron
parent: thirty-meter-telescope-20260505-0
summary:
The Thirty Meter Telescope (TMT) is a proposal for an extremely large telescope (ELT), intended to be built on Mauna Kea, on the island of Hawai'i. Scientists have been considering ELTs since the mid 1980s. In 2000, astronomers considered the possibility of a telescope with a light-gathering mirror larger than 20 meters (66 ft) in diameter, using either small segments that create one large mirror, or a grouping of larger 8-meter (26 ft) mirrors working as one unit. The US National Academy of Sciences recommended a 30-meter (98 ft) telescope be the focus of US interests, seeking to see it built within the decade. Scientists at the University of California, Santa Cruz and Caltech began development of a design that would eventually become the TMT, consisting of a 492-segment primary mirror with nine times the power of the Keck Observatory. Due to its light-gathering power and the optimal observing conditions which exist atop Mauna Kea, the TMT would enable astronomers to conduct research which is infeasible with current instruments. The TMT is designed for near-ultraviolet to mid-infrared (0.31 to 28 μm wavelengths) observations, featuring adaptive optics to assist in correcting image blur. The TMT would be at the highest altitude


id: thirty-meter-telescope-20260505-1
file: data/en.wikipedia.org/wiki/Thirty_Meter_Telescope-1.md
category: reference
title: Thirty Meter Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Thirty_Meter_Telescope
date_saved: 2026-05-05T09:48:33.714678+00:00
instance: kb-cron
parent: thirty-meter-telescope-20260505-0
summary:
Roque de los Muchachos Observatory, La Palma, Canary Islands, Spain Cerro Armazones, Antofagasta Region, Republic of Chile Cerro Tolanchar, Antofagasta Region, Republic of Chile Cerro Tolar, Antofagasta Region, Republic of Chile Mauna Kea, Hawaii, United States (This site was chosen and approval was granted in April 2013) San Pedro Mártir, Baja California, Mexico Hanle, Ladakh, India The TMT Observatory Corporation board of directors narrowed the list to two sites, one in each hemisphere, for further consideration: Cerro Armazones in Chile's Atacama Desert and Mauna Kea on Hawaii Island. On July 21, 2009, the TMT board announced Mauna Kea as the preferred site. The final TMT site selection decision was based on a combination of scientific, financial, and political criteria. Chile is also where the European Southern Observatory is building the ELT. If both next-generation telescopes were in the same hemisphere, there would be many astronomical objects that neither could observe. The telescope was given approval by the state Board of Land and Natural Resources in April 2013. There has been opposition to the building of the telescope, based on potential disruption to the fragile alpine environment of Mauna Kea due to construction, traffic, and noise, which is a concern for


id: thirty-meter-telescope-20260505-2
file: data/en.wikipedia.org/wiki/Thirty_Meter_Telescope-2.md
category: reference
title: Thirty Meter Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Thirty_Meter_Telescope
date_saved: 2026-05-05T09:48:33.714678+00:00
instance: kb-cron
parent: thirty-meter-telescope-20260505-0
summary:
Integral to the observatory is a Multi-Conjugate Adaptive Optics (MCAO) system. This MCAO system will measure atmospheric turbulence by observing a combination of natural (real) stars and artificial laser guide stars. Based on these measurements, a pair of deformable mirrors will be adjusted many times per second to correct optical wave-front distortions caused by the intervening turbulence. This system will produce diffraction-limited images over a 30-arc-second diameter field-of-view, which means that the core of the point spread function will have a size of 0.015 arc-second at a wavelength of 2.2 micrometers, almost ten times better than the Hubble Space Telescope. === Scientific instrumentation === ==== Early-light capabilities ==== Three instruments are planned to be available for scientific observations: Wide Field Optical Spectrometer (WFOS) provides a seeing limit that goes down to the ultraviolet with optical (0.3–1.0 μm wavelength) imaging and spectroscopy capable of 40-square arc-minute field-of-view. The TMT will use precision cut focal plane masks and enable long-slit observations of individual objects as well as short-slit observations of hundreds of different objects at the same time. The spectrometer will use natural (uncorrected) seeing images. Infrared Imaging Spectrometer (IRIS) mounted on the observatory MCAO system, capable of diffraction-limited imaging and integral-field


id: thirty-meter-telescope-20260505-3
file: data/en.wikipedia.org/wiki/Thirty_Meter_Telescope-3.md
category: reference
title: Thirty Meter Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Thirty_Meter_Telescope
date_saved: 2026-05-05T09:48:33.714678+00:00
instance: kb-cron
parent: thirty-meter-telescope-20260505-0
summary:
=== 2017-2019: BLNR hearings, Court validates revised permit === In March 2017, the BLNR hearing officer, retired judge Riki May Amano, finished six months of hearings in Hilo, Hawaii, taking 44 days of testimony from 71 witnesses. On July 26, 2017, Amano filed her recommendation that the Land Board grant the construction permit. On September 28, 2017, the BLNR, acting on Amano's report, approved, by a vote of 5-2, a Conservation District Use Permit (CDUP) for the TMT. Numerous conditions, including the removal of three existing telescopes and an assertion that the TMT is to be the last telescope on the mountain, were attached to the permit. On October 30, 2018, the Supreme Court of Hawaii ruled 4-1, that the revised permit was acceptable, allowing construction to proceed. On July 10, 2019, Hawaii Gov. David Ige and the Thirty Meter Telescope International Observatory jointly announced that construction would begin the week of July 15, 2019. === 2019 blockade and aftermath === On July 15, 2019, renewed protests blocked the access road, again preventing construction from commencing. On July 17, 38 protestors were arrested, all of whom were kupuna (elders) as the blockage of the access road continued. The blockade lasted


id: thirty-meter-telescope-20260505-4
file: data/en.wikipedia.org/wiki/Thirty_Meter_Telescope-4.md
category: reference
title: Thirty Meter Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Thirty_Meter_Telescope
date_saved: 2026-05-05T09:48:33.714678+00:00
instance: kb-cron
parent: thirty-meter-telescope-20260505-0
summary:
== Alternative site in the Canary Islands == In response to the ongoing protests that occurred in July 2019, the TMT project officials requested a building permit for a second site choice, the Spanish Observatorio del Roque de los Muchachos on the island of La Palma in the Canary Islands. Rafael Rebolo, the director of the Instituto de Astrofísica de Canarias, confirmed that he had received a letter requesting a building permit for the site as a backup in case the Hawaii site cannot be constructed. Some astronomers argue however that La Palma is not an adequate site to build the telescope due to the island’s comparatively low elevation, which would enable water vapor to frequently interfere with observations due to water vapor’s tendency to absorb light at midinfrared wavelengths. Such atmospheric interference could impact observing times for research into exoplanets, galactic formation, and cosmology. Other astronomers argue that construction of the telescope in La Palma would disrupt projected international collaboration between the United States and other involved countries such as Japan, Canada, and India. Environmentalists such as Ben Magec and the environmental advocacy organization Ecologistas en Acción in the Canary Islands geared up to oppose its construction there as


id: timeline-of-telescope-technology-20260505-0
file: data/en.wikipedia.org/wiki/Timeline_of_telescope_technology-0.md
category: reference
title: Timeline of telescope technology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Timeline_of_telescope_technology
date_saved: 2026-05-05T09:48:34.990249+00:00
instance: kb-cron
parent: timeline-of-telescope-technology-20260505-0
summary:
The following timeline lists the significant events in the invention and development of the telescope. == BC == === 2560 BC to 1 BC === c.2560 BC–c.860 BC — Egyptian artisans polish rock crystal, semi-precious stones, and latterly glass to produce facsimile eyes for statuary and mummy cases. The intent appears to be to produce an optical illusion. 424 BC Aristophanes "lens" is a glass globe filled with water.(Seneca says that it can be used to read letters no matter how small or dim) 3rd century BC Euclid is the first to study reflection and refraction using mathematical theorems based on the fact that light travels in straight lines == AD == === 1 AD to 999 AD === 2nd century AD — Ptolemy (in his work Optics) wrote about the properties of light including: reflection, refraction, and colour. 984 — Ibn Sahl completes a treatise On Burning Mirrors and Lenses, describing plano-convex and biconvex lenses, and parabolic and ellipsoidal mirrors. === 1000 AD to 1999 AD === 1011–1021 — Ibn al-Haytham (also known as Alhacen or Alhazen) writes the Kitab al-Manazir (Book of Optics) 1230–1235 — Robert Grosseteste describes the use of 'optics' to "...make small things placed at


id: timeline-of-telescope-technology-20260505-1
file: data/en.wikipedia.org/wiki/Timeline_of_telescope_technology-1.md
category: reference
title: Timeline of telescope technology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Timeline_of_telescope_technology
date_saved: 2026-05-05T09:48:34.990249+00:00
instance: kb-cron
parent: timeline-of-telescope-technology-20260505-0
summary:
1668 — Isaac Newton produces the first functioning reflecting telescope using a spherical primary mirror and a flat diagonal secondary mirror. This design is termed the 'Newtonian'. 1672 — Laurent Cassegrain, produces a design for a reflecting telescope using a paraboloid primary mirror and a hyperboloid secondary mirror. The design, named 'Cassegrain', is still used in astronomical telescopes used in observatories in 2006. 1674 — Robert Hooke produces a reflecting telescope based on the Gregorian design. 1684 — Christiaan Huygens publishes "Astroscopia Compendiaria" in which he described the design of very long aerial telescopes. 1720 — John Hadley develops ways of aspherizing spherical mirrors to make very accurate parabolic mirrors and produces a much improved Gregorian telescope 1721 — John Hadley experiments with the neglected Newtonian telescope design and demonstrates one with a 6-inch parabolic mirror to the Royal Society. 1730s — James Short succeeds in producing a Gregorian telescopes to true paraboloidal primary and ellipsoidal secondary design specifications. 1733 — Chester Moore Hall invents the achromatic lens. 1758 — John Dollond re-invents and patents the achromatic lens. 1783 — Jesse Ramsden invents his eponymous eyepiece. 1803 — The "Observatorio Astronómico Nacional de Colombia (OAN)" is inaugurated as the first


id: timeline-of-telescopes-observatories-and-observing-technology-20260505-0
file: data/en.wikipedia.org/wiki/Timeline_of_telescopes,_observatories,_and_observing_technology-0.md
category: reference
title: Timeline of telescopes, observatories, and observing technology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Timeline_of_telescopes,_observatories,_and_observing_technology
date_saved: 2026-05-05T09:48:36.155717+00:00
instance: kb-cron
parent: timeline-of-telescopes-observatories-and-observing-technology-20260505-0
summary:
Timeline of telescopes, observatories, and observing technology. == Before the Common Era (BCE) == === 1900s BCE === Taosi Astronomical Observatory, Xiangfen County, Linfen City, Shanxi Province, China === 1500s BCE === Shadow clocks invented in ancient Egypt and Mesopotamia === 600s BCE === 11th–7th century BCE, Zhou dynasty astronomical observatory (灵台) in Fenghao (today's Xi'an), China === 200s BCE === Thirteen Towers solar observatory, Chankillo, Peru Antikythera Mechanism, a geared astronomical computer that calculates lunar and solar eclipses, the position of the Sun and the Moon the lunar phase (age of the Moon as seen from Earth), has several lunisolar calendars, including the Olympic Games calendar. It is at the National Archaeological Museum, Athens, Greece. === 100s BCE === 220-206 BCE, Han dynasty astronomical observatory (灵台) in Chang'an and Luoyang. During East Han dynasty, astronomical observatory (灵台) built in Yanshi, Henan Province, China 220-150 BCE, Astrolabe invented by Apollonius of Perga == Common Era (CE) == === 400s === 5th century – Observatory at Ujjain, India === 600s === 632–647 – Cheomseongdae observatory is built in the reign of Queen Seondeok at Gyeongju, then the capital of Silla (present day South Korea) 618–1279 – Tang dynasty-Song dynasty, observatories built


id: timeline-of-telescopes-observatories-and-observing-technology-20260505-1
file: data/en.wikipedia.org/wiki/Timeline_of_telescopes,_observatories,_and_observing_technology-1.md
category: reference
title: Timeline of telescopes, observatories, and observing technology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Timeline_of_telescopes,_observatories,_and_observing_technology
date_saved: 2026-05-05T09:48:36.155717+00:00
instance: kb-cron
parent: timeline-of-telescopes-observatories-and-observing-technology-20260505-0
summary:
=== 1800s === 1803 National Astronomical Observatory (Colombia), the first observatory in the Americas 1836 Swathithirunal opened Trivandrum observatory 1839 Louis Jacques Mandé Daguerre (inventor of the daguerreotype photographic process) attempts to photograph the moon. Tracking errors in guiding the telescope during the long exposure made the photograph came out as an indistinct fuzzy spot 1840 – John William Draper takes make a successful photographic image of the Moon, the first astronomical photograph 1845 – Lord Rosse finishes the Birr Castle 72-inch (1.8 m) optical reflecting telescope, located in Parsonstown, Ireland 1849 – Santiago observatory set up by USA, later becomes Chilean National Observatory (now part of the University of Chile) 1859 – Kirchhoff and Bunsen develop spectroscopy 1864 – Herschel's so-called GC (General Catalogue) of nebulae and star clusters published 1868 – Janssen and Lockyer discover Helium observing spectra of the Sun 1871 – German Astronomical Association organized network of 13 (later 16) observatories for stellar proper motion studies 1863 – William Allen Miller and Sir William Huggins use the photographic wet collodion plate process to obtain the first ever photographic spectrogram of a star, Sirius and Capella. 1872 – Henry Draper photographs a spectrum of Vega that shows


id: timeline-of-telescopes-observatories-and-observing-technology-20260505-2
file: data/en.wikipedia.org/wiki/Timeline_of_telescopes,_observatories,_and_observing_technology-2.md
category: reference
title: Timeline of telescopes, observatories, and observing technology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Timeline_of_telescopes,_observatories,_and_observing_technology
date_saved: 2026-05-05T09:48:36.155717+00:00
instance: kb-cron
parent: timeline-of-telescopes-observatories-and-observing-technology-20260505-0
summary:
==== 1970s ==== 1970 – Cerro Tololo 158-inch (4.0 m) optical reflecting telescope begins operation, located in Cerro Tololo, Chile 1970 – Kitt Peak National Observatory 158-inch (4.0 m) optical reflecting telescope begins operation, located near Tucson, Arizona 1970 – Uhuru x-ray telescope satellite 1970 – Antoine Labeyrie performs the first high-resolution optical speckle interferometry observations 1970 – Westerbork Synthesis Radio Telescope completed, near Westerbork, Netherlands 1972 – 100 m Effelsberg radio telescope inaugurated (Germany) 1973 – UK Schmidt Telescope 1.2 metre optical reflecting telescope begins operation, located in Anglo-Australian Observatory near Coonabarabran, Australia 1974 – Anglo-Australian Telescope 153-inch (3.9 m) optical reflecting telescope begins operation, located in Anglo-Australian Observatory near Coonabarabran, Australia 1975 – Gerald Smith, Frederick Landauer, and James Janesick use a CCD to observe Uranus, the first astronomical CCD observation 1975 – Antoine Labeyrie builds the first two-telescope optical interferometer 1976 – The 6-m BTA-6 (Bolshoi Teleskop Azimutalnyi or “Large Altazimuth Telescope”) goes into operation on Mt. Pashtukhov in the Russian Caucasus 1978 – Multiple Mirror 176-inch (4.5 m) equivalent optical/infrared reflecting telescope begins operation, located in Amado, Arizona 1978 – International Ultraviolet Explorer (IUE) telescope satellite 1978 – Einstein High Energy Astronomy Observatory x-ray telescope satellite


id: tpoint-20260505-0
file: data/en.wikipedia.org/wiki/Tpoint-0.md
category: reference
title: Tpoint
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tpoint
date_saved: 2026-05-05T09:48:37.334647+00:00
instance: kb-cron
parent: tpoint-20260505-0
summary:
TPoint is computer software that implements a mathematical model of conditions leading to errors in telescope pointing and tracking. The model can then be used in a telescope control system to correct the pointing and tracking. Such errors are typically caused by mechanical or structural defects. For example, TPoint can analyze and compensate for systematic errors such as polar misalignment, mechanical and optical non-orthogonality, lack of roundness in telescope mounting drive gears, as well as for flexure of the mounting caused by gravity. TPoint is in use on the majority of professional telescopes worldwide, including among many others the Anglo-Australian Telescope, Keck Observatory, Gemini Observatory and the Large Binocular Telescope. It has significantly improved the performance and efficiency of telescope operation and has had an especially strong impact on the development of automated and robotic telescopes. TPoint is also widely used by amateur astronomers. Software Bisque distributes TPoint as an add-on to TheSkyX Serious Astronomer Edition and TheSkyX Professional; this version is used to improve the pointing on amateur telescopes. == History == TPoint was invented and developed by Patrick Wallace. It grew out of work he and John Straede performed at the Anglo-Australian Telescope (AAT) between 1974 and 1980


id: transient-array-radio-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Transient_Array_Radio_Telescope-0.md
category: reference
title: Transient Array Radio Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Transient_Array_Radio_Telescope
date_saved: 2026-05-05T09:48:38.538730+00:00
instance: kb-cron
parent: transient-array-radio-telescope-20260505-0
summary:
The Transient Array Radio Telescope (TART) is a low-cost open-source array radio telescope consisting of 24 all-sky GNSS receivers operating at the L1-band (1.575 GHz). TART was designed as an all-sky survey instrument for detecting radio bursts, as well as providing a test-bed for the development of new synthesis imaging and calibration algorithms. All of the telescope hardware including radio receivers, correlators and operating software are open source. A TART-2 radio-telescope can be built for approximately 1000 Euros, and the telescope antenna array requires 4m x 4m area for deployment. The TART project is managed by the Electronics Research Foundation, a non-profit based in New Zealand. == Design == All of the components of TART, from the hardware, FPGA firmware and the operation and imaging software are open source. released under the GPLv3 license. A TART radio telescope consists of four main sub-assemblies, the antenna array, RF Front End, radio Hub and basestation. === Antenna array === The antenna array consists of 24 antennas arranged on four identical 'tiles' with 6 antennas each. Each tile is a 1x1 meter square. The antennas used are low-cost, widely available commercial GPS active antennas. More recent installations use multi-arm antenna arrays in either


id: unistellar-20260505-0
file: data/en.wikipedia.org/wiki/Unistellar-0.md
category: reference
title: Unistellar
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Unistellar
date_saved: 2026-05-05T09:48:39.767085+00:00
instance: kb-cron
parent: unistellar-20260505-0
summary:
Unistellar is a French manufacturer of computer-connected telescopes that allow non-professional skywatchers to observe astronomical objects at relatively low cost. The first product launched was named the eVscope, and used digital astrophotographic techniques. SETI Institute has partnered with Unistellar and will be able to send requests for information and notifications to users, and receive information about transient astronomical events. == History == The company was founded in Marseille, France, in 2015, with incubator investment from Incubateur Impulse and Pépinières d'Entreprises Innovantes with subsequent VC round capital from private investors and a VC firm named Brighteye Ventures. Unistellar unveiled their electronic telescope technology prototype in 2017 at CES2017 in Las Vegas and at IFA Next in Berlin. The company experienced difficulties bringing the product to market. The consumer-grade electronic telescope was originally planned to be available in the "fall 2018" which subsequently shifted to "early 2019," then later in 2019. By January 2020, the telescope was expected to be shipped worldwide between May and August 2020. As of December 2021, over 5000 telescopes had been delivered to customers The kit included a custom tripod and mount, a Bahtinov mask and a protective cap. Later, Unistellar introduced two new telescopes, eVscope 2


id: vacuum-tower-telescope-20260505-0
file: data/en.wikipedia.org/wiki/Vacuum_Tower_Telescope-0.md
category: reference
title: Vacuum Tower Telescope
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Vacuum_Tower_Telescope
date_saved: 2026-05-05T09:48:40.940941+00:00
instance: kb-cron
parent: vacuum-tower-telescope-20260505-0
summary:
The Vacuum Tower Telescope (VTT) is an evacuated-optics solar telescope located at the Teide Observatory on Tenerife in the Canary Islands. It is operated by the Kiepenheuer-Institut für Sonnenphysik (KIS). It was built between 1983 and 1986, with first light in 1988. It has a 70-centimetre-diameter (28 in) primary mirror and a focal length of 46 metres (151 ft). Thanks to an adaptive optics system KAOS (Kiepenheuer-institute Adaptive Optic System), in operation since spring 2000, it is able to resolve details down to 0.2 arc seconds (150 km) on the Sun's surface. == Description == The VTT and the GREGOR are operated by four German institutes: the Astrophysikalisches Institut Potsdam, the Kiepenheuer-Institut für Sonnenphysik (Freiburg, chair), the Max-Planck-Institut für Sonnensystemforschung (Lindau), and the Universitäts-Sternwarte Göttingen. The telescope is used for scientific observations from mid-April through mid-December. Typically 30 to 40 observing campaigns are carried out every year. == History == In the early seventies, the 40-centimetre Newton telescope, built at the Kiepenheuer-Institut, was installed at the Observatorio del Teide. In 1982, the Federal Republic of Germany joined the international Agreement on the Cooperation in Astrophysical Research between Spain, Great Britain, Sweden and Denmark. Construction work for the German solar telescopes


id: zoom-lens-20260505-0
file: data/en.wikipedia.org/wiki/Zoom_lens-0.md
category: reference
title: Zoom lens
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Zoom_lens
date_saved: 2026-05-05T09:48:43.309513+00:00
instance: kb-cron
parent: zoom-lens-20260505-0
summary:
A zoom lens is a system of camera lens elements for which the focal length (and thus angle of view) can be varied, as opposed to a fixed-focal-length (FFL) lens (prime lens). A true zoom lens or optical zoom lens is a type of parfocal lens, one that maintains focus when its focal length changes. Most consumer zoom lenses do not maintain perfect focus, but are still nearly parfocal. Most camera phones that are advertised as having optical zoom actually use a few cameras of different but fixed focal length, combined with digital zoom to make a hybrid system. The convenience of variable focal length comes at the cost of complexity – and some compromises on image quality, weight, dimensions, aperture, autofocus performance, and cost. For example, all zoom lenses suffer from at least slight, if not considerable, loss of image resolution at their maximum aperture, especially at the extremes of their focal length range. This effect is evident in the corners of the image, when displayed in a large format or high resolution. The greater the range of focal length a zoom lens offers, the more exaggerated these compromises must become. == Characteristics == Zoom lenses are often described


id: zoom-lens-20260505-1
file: data/en.wikipedia.org/wiki/Zoom_lens-1.md
category: reference
title: Zoom lens
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Zoom_lens
date_saved: 2026-05-05T09:48:43.309513+00:00
instance: kb-cron
parent: zoom-lens-20260505-0
summary:
The Kilfitt 36–82 mm/2.8 Zoomar lens introduced in 1959 was the first varifocal lens in regular production for still 35mm photography. The first modern film zoom lens, the Pan-Cinor, was designed around 1950 by Roger Cuvillier, a French engineer working for SOM-Berthiot. It had an optical compensation zoom system. In 1956, Pierre Angénieux introduced the mechanical compensation system, enabling precise focus while zooming, in his 17-68mm lens for 16mm released in 1958. The same year a prototype of the 35mm version of the Angénieux 4x zoom, the 35-140mm was first used by cinematographer Roger Fellous for the production of Julie La Rousse. Angénieux received a 1964 technical award from the academy of motion pictures for the design of the 10 to 1 zoom lenses, including the 12-120mm for 16mm film cameras and the 25-250mm for 35mm film cameras. Because of their relative bulk, it wasn't until as recently as 1986 that a zoom lens was designed with sufficiently compact dimensions and finally found its way into a consumer compact (point and shoot) camera, this being the Pentax Zoom 70. Since then advances in optical lens design, particularly the use of computers for optical ray tracing, has made the design and


id: design-of-experiments-20260505-0
file: data/en.wikipedia.org/wiki/Design_of_experiments-0.md
category: reference
title: Design of experiments
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_of_experiments
date_saved: 2026-05-05T09:48:44.910356+00:00
instance: kb-cron
parent: design-of-experiments-20260505-0
summary:
The design of experiments (DOE), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify control variables that must be held constant to prevent external factors from affecting the results. Experimental design involves not only the selection of suitable independent, dependent, and control variables, but planning the delivery of the experiment under statistically optimal conditions given the constraints of available resources. There are multiple approaches


id: design-of-experiments-20260505-1
file: data/en.wikipedia.org/wiki/Design_of_experiments-1.md
category: reference
title: Design of experiments
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_of_experiments
date_saved: 2026-05-05T09:48:44.910356+00:00
instance: kb-cron
parent: design-of-experiments-20260505-0
summary:
Comparison In some fields of study it is not possible to have independent measurements to a traceable metrology standard. Comparisons between treatments are much more valuable and are usually preferable, and often compared against a scientific control or traditional treatment that acts as baseline. Randomization Random assignment is the process of assigning individuals at random to groups or to different groups in an experiment, so that each individual of the population has the same chance of becoming a participant in the study. The random assignment of individuals to groups (or conditions within a group) distinguishes a rigorous, "true" experiment from an observational study or "quasi-experiment". There is an extensive body of mathematical theory that explores the consequences of making the allocation of units to treatments by means of some random mechanism (such as tables of random numbers, or the use of randomization devices such as playing cards or dice). Assigning units to treatments at random tends to mitigate confounding, which makes effects due to factors other than the treatment to appear to result from the treatment. The risks associated with random allocation (such as having a serious imbalance in a key characteristic between a treatment group and a control group)


id: design-of-experiments-20260505-2
file: data/en.wikipedia.org/wiki/Design_of_experiments-2.md
category: reference
title: Design of experiments
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_of_experiments
date_saved: 2026-05-05T09:48:44.910356+00:00
instance: kb-cron
parent: design-of-experiments-20260505-0
summary:
Let yi be the measured difference for i = 1, ..., 8. The relationship between the true weights and experimental measurements may be represented with a general linear model, with the design matrix W {\displaystyle W} having entries from { − 1 , 0 , 1 } {\displaystyle \{-1,0,1\}} : y = W θ + ϵ {\displaystyle y=W\theta +\epsilon } The first design is represented by an identity matrix while the second design is represented by an 8x8 Hadamard matrix, H {\displaystyle H} , both examples of weighing matrices. The weights are typically estimated using the method of least squares. Using a weighing matrix, this is equivalent to inverting on the measurements: θ ^ A = I − 1 y = y {\displaystyle {\hat {\theta }}_{A}=I^{-1}y=y} θ ^ B = H − 1 y {\displaystyle {\hat {\theta }}_{B}=H^{-1}y} The question of design of experiments is: which experiment is better? Investigating estimate A vs B for the first weight: Var ⁡ ( θ ^ A , 1 ) = Var ⁡ ( y 1 ) = σ 2 {\displaystyle \operatorname {Var} ({\hat {\theta }}_{A,1})=\operatorname {Var} (y_{1})=\sigma ^{2}} Var ⁡ ( θ ^ B , 1 ) = Var ⁡ ( y


id: design-of-experiments-20260505-3
file: data/en.wikipedia.org/wiki/Design_of_experiments-3.md
category: reference
title: Design of experiments
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_of_experiments
date_saved: 2026-05-05T09:48:44.910356+00:00
instance: kb-cron
parent: design-of-experiments-20260505-0
summary:
== Causal attributions == In the pure experimental design, the independent (predictor) variable is manipulated by the researcher – that is – every participant of the research is chosen randomly from the population, and each participant chosen is assigned randomly to conditions of the independent variable. Only when this is done is it possible to certify with high probability that the reason for the differences in the outcome variables are caused by the different conditions. Therefore, researchers should choose the experimental design over other design types whenever possible. However, the nature of the independent variable does not always allow for manipulation. In those cases, researchers must be aware of not certifying about causal attribution when their design doesn't allow for it. For example, in observational designs, participants are not assigned randomly to conditions, and so if there are differences found in outcome variables between conditions, it is likely that there is something other than the differences between the conditions that causes the differences in outcomes, that is – a third variable. The same goes for studies with correlational design. == Statistical control == It is best that a process be in reasonable statistical control prior to conducting designed experiments. When


id: design-of-experiments-20260505-4
file: data/en.wikipedia.org/wiki/Design_of_experiments-4.md
category: reference
title: Design of experiments
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_of_experiments
date_saved: 2026-05-05T09:48:44.910356+00:00
instance: kb-cron
parent: design-of-experiments-20260505-0
summary:
== See also == Adversarial collaboration – Method of research Bayesian experimental design – Experimental design framework Block design – Structure in combinatorial mathematics Box–Behnken design – Experimental designs for response surface methodology Central composite design – Experimental design in statistical mathematics Clinical study design – Plan for research in clinical medicine Computer experiment – Experiment used to study computer simulation Controlling for a variable – Binning data according to measured values of the variable Experimetrics (econometrics-related experiments) Factor analysis – Statistical method Fractional factorial design – Statistical experimental design approach Glossary of experimental design Grey box model – Mathematical data production model with limited structure Industrial engineering – Branch of engineering which deals with the optimization of complex processes or systems Instrument effect Law of large numbers – Averages of repeated trials converge to the expected value Manipulation checks Multifactor design of experiments software One-factor-at-a-time method – Method of designing experiments Optimal design – Experimental design that is optimal with respect to some statistical criterionPages displaying short descriptions of redirect targets Plackett–Burman design – Type of experimental design Probabilistic design – Discipline within engineering design Protocol (natural sciences) – Procedural method for the design and implementation of an experimentPages


id: adaptive-design-medicine-20260505-0
file: data/en.wikipedia.org/wiki/Adaptive_design_(medicine)-0.md
category: reference
title: Adaptive design (medicine)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Adaptive_design_(medicine)
date_saved: 2026-05-05T09:48:46.125163+00:00
instance: kb-cron
parent: adaptive-design-medicine-20260505-0
summary:
In an adaptive design of a clinical trial, the parameters and conduct of the trial for a candidate drug or vaccine may be changed based on an interim analysis. Adaptive design typically involves advanced statistics to interpret a clinical trial endpoint. This is in contrast to traditional single-arm (i.e. non-randomized) clinical trials or randomized clinical trials (RCTs) that are static in their protocol and do not modify any parameters until the trial is completed. The adaptation process takes place at certain points in the trial, prescribed in the trial protocol. Importantly, this trial protocol is set before the trial begins with the adaptation schedule and processes specified. Adaptions may include modifications to: dosage, sample size, drug undergoing trial, patient selection criteria and/or "cocktail" mix. The PANDA (A Practical Adaptive & Novel Designs and Analysis toolkit) provides not only a summary of different adaptive designs, but also comprehensive information on adaptive design planning, conduct, analysis and reporting. == Purpose == The aim of an adaptive trial is to more quickly identify drugs or devices that have a therapeutic effect, and to zero in on patient populations for whom the drug is appropriate. When conducted efficiently, adaptive trials have the potential to


id: adaptive-design-medicine-20260505-1
file: data/en.wikipedia.org/wiki/Adaptive_design_(medicine)-1.md
category: reference
title: Adaptive design (medicine)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Adaptive_design_(medicine)
date_saved: 2026-05-05T09:48:46.125163+00:00
instance: kb-cron
parent: adaptive-design-medicine-20260505-0
summary:
=== Group sequential design === Group sequential design is the application of sequential analysis to clinical trials. At each interim analysis, investigators will use the current data to decide whether the trial should either stop or should continue to recruit more participants. The trial might stop either because the evidence that the treatment is working is strong ("stopping for benefit") or weak ("stopping for futility"). Whether a trial may stop for futility only, benefit only, or either, is stated in advance. A design has "binding stopping rules" when the trial must stop when a particular threshold of (either strong or weak) evidence is crossed at a particular interim analysis. Otherwise it has "non-binding stopping rules", in which case other information can be taken into account, for example safety data. The number of interim analyses is specified in advance, and can be anything from a single interim analysis (a "two-stage" design") to an interim analysis after every participant ("continuous monitoring"). For trials with a binary (response/no response) outcome and a single treatment arm, a popular and simple group sequential design with two stages is the Simon design. In this design, there is a single interim analysis partway through the trial, at


id: adaptive-design-medicine-20260505-2
file: data/en.wikipedia.org/wiki/Adaptive_design_(medicine)-2.md
category: reference
title: Adaptive design (medicine)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Adaptive_design_(medicine)
date_saved: 2026-05-05T09:48:46.125163+00:00
instance: kb-cron
parent: adaptive-design-medicine-20260505-0
summary:
==== I-SPY 1 ==== For its predecessor I-SPY 1, 10 cancer centers and the National Cancer Institute (NCI SPORE program and the NCI Cooperative groups) collaborated to identify response indicators that would best predict survival for women with high-risk breast cancer. During 2002–2006, the study monitored 237 patients undergoing neoadjuvant therapy before surgery. Iterative MRI and tissue samples monitored the biology of patients to chemotherapy given in a neoadjuvant setting, or presurgical setting. Evaluating chemotherapy's direct impact on tumor tissue took much less time than monitoring outcomes in thousands of patients over long time periods. The approach helped to standardize the imaging and tumor sampling processes, and led to miniaturized assays. Key findings included that tumor response was a good predictor of patient survival, and that tumor shrinkage during treatment was a good predictor of long-term outcome. Importantly, the vast majority of tumors identified as high risk by molecular signature. However, heterogeneity within this group of women and measuring response within tumor subtypes was more informative than viewing the group as a whole. Within genetic signatures, level of response to treatment appears to be a reasonable predictor of outcome. Additionally, its shared database has furthered the understanding of drug response


id: adaptive-design-medicine-20260505-3
file: data/en.wikipedia.org/wiki/Adaptive_design_(medicine)-3.md
category: reference
title: Adaptive design (medicine)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Adaptive_design_(medicine)
date_saved: 2026-05-05T09:48:46.125163+00:00
instance: kb-cron
parent: adaptive-design-medicine-20260505-0
summary:
For regulatory submission of Bayesian clinical trial design, there exist two Bayesian decision rules that are frequently used by trial sponsors. First, posterior probability approach is mainly used in decision-making to quantify the evidence to address the question, "Does the current data provide convincing evidence in favor of the alternative hypothesis?" The key quantity of the posterior probability approach is the posterior probability of the alternative hypothesis being true based on the data observed up to the point of analysis. Second, predictive probability approach is mainly used in decision-making is to answer the question at an interim analysis: "Is the trial likely to present compelling evidence in favor of the alternative hypothesis if we gather additional data, potentially up to the maximum sample size (or current sample size)?" The key quantity of the predictive probability approach is the posterior predictive probability of the trial success given the interim data. In most regulatory submissions, Bayesian trial designs are calibrated to possess good frequentist properties. In this spirit, and in adherence to regulatory practice, regulatory agencies typically recommend that sponsors provide the frequentist type I and II error rates for the sponsor's proposed Bayesian analysis plan. In other words, the Bayesian designs


id: adversarial-collaboration-20260505-0
file: data/en.wikipedia.org/wiki/Adversarial_collaboration-0.md
category: reference
title: Adversarial collaboration
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Adversarial_collaboration
date_saved: 2026-05-05T09:48:47.307037+00:00
instance: kb-cron
parent: adversarial-collaboration-20260505-0
summary:
In science, adversarial collaboration is a modality of collaboration wherein opposing views work together in order to jointly advance knowledge of the area under dispute. This can take the form of a scientific experiment conducted by two groups of experimenters with competing hypotheses, with the aim of constructing and implementing an experimental design in a way that satisfies both groups that there are no obvious biases or weaknesses in the experimental design. Adversarial collaboration can involve a neutral moderator and lead to a co-designed experiment and joint publishing of findings in order to resolve differences. With its emphasis on transparency throughout the research process, adversarial collaboration has been described as sitting within the open science framework. == History == One of the earliest modern examples of adversarial collaboration was a 1988 collaboration between Erez and Latham with Edwin Locke working as a neutral third party. This collaboration came about as the result of a disagreement from the field of Goal-Setting research between Erez and Latham on an aspect of goal-setting research around the effect of participation on goal commitment and performance. Latham and Erez designed four experiments which explained the differences between their individual findings, but did not coin the


id: age-adjustment-20260505-0
file: data/en.wikipedia.org/wiki/Age_adjustment-0.md
category: reference
title: Age adjustment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Age_adjustment
date_saved: 2026-05-05T09:48:48.499475+00:00
instance: kb-cron
parent: age-adjustment-20260505-0
summary:
In epidemiology and demography, age adjustment, also called age standardization, is a technique used to allow statistical populations to be compared when the age profiles of the populations are quite different. == Example == For example, in 2004/5, two Australian health surveys investigated rates of long-term circulatory system health problems (e.g. heart disease) in the general Australian population, and specifically in the Indigenous Australian population. In each age category over age 24, Indigenous Australians had markedly higher rates of circulatory disease than the general population: 5% vs 2% in age group 25–34, 12% vs 4% in age group 35–44, 22% vs 14% in age group 45–54, and 42% vs 33% in age group 55+. However, overall, these surveys estimated that 12% of all Indigenous Australians had long-term circulatory problems compared to 18% of the overall Australian population. == Standard populations == In order to adjust for age, a standard population must be selected. Some agencies which produce health statistics also publish standard populations for age adjustment. Standard populations have been developed for specific countries and regions. World standard populations have also been developed to compare data from different countries, including the Segi World Standard and the World Health Organization (WHO)


id: aliasing-factorial-experiments-20260505-0
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-0.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
In the statistical theory of factorial experiments, aliasing is the property of fractional factorial designs that makes some effects "aliased" with each other – that is, indistinguishable from each other. A primary goal of the theory of such designs is the control of aliasing so that important effects are not aliased with each other. In a "full" factorial experiment, the number of treatment combinations or cells (see below) can be very large. This necessitates limiting observations to a fraction (subset) of the treatment combinations. Aliasing is an automatic and unavoidable result of observing such a fraction. The aliasing properties of a design are often summarized by giving its resolution. This measures the degree to which the design avoids aliasing between main effects and important interactions. Fractional factorial experiments have long been a basic tool in agriculture, food technology, industry, medicine and public health, and the social and behavioral sciences. They are widely used in exploratory research, particularly in screening experiments, which have applications in industry, drug design and genetics. In all such cases, a crucial step in designing such an experiment is deciding on the desired aliasing pattern, or at least the desired resolution. As noted below, the concept of


id: aliasing-factorial-experiments-20260505-1
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-1.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
== Definitions == The factors in the design are allowed to have different numbers of levels, as in a 2 × 3 × 3 {\displaystyle 2\times 3\times 3} factorial experiment (an asymmetric or mixed-level experiment). Fix a fraction of a full factorial design. Let U {\displaystyle U} be a set of contrast vectors representing an effect (in particular, a main effect or interaction) in the full factorial design, and let U ~ {\displaystyle {\widetilde {U}}} consist of the restrictions of those vectors to the fraction. One says that the effect is preserved in the fraction if U ~ {\displaystyle {\widetilde {U}}} consists of contrast vectors; completely lost in the fraction if U ~ {\displaystyle {\widetilde {U}}} consists of constant vectors, that is, vectors whose components are equal; and partly lost otherwise. Similarly, let U 1 {\displaystyle U_{1}} and U 2 {\displaystyle U_{2}} represent two effects and let U ~ 1 {\displaystyle {\widetilde {U}}_{1}} and U ~ 2 {\displaystyle {\widetilde {U}}_{2}} be their restrictions to the fraction. The two effects are said to be unaliased in the fraction if each vector in U ~ 1 {\displaystyle {\widetilde {U}}_{1}} is orthogonal (perpendicular) to all the vectors in U ~ 2 {\displaystyle {\widetilde


id: aliasing-factorial-experiments-20260505-2
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-2.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
=== The 2 × 2 × 2 (or 2³) experiment === This is a "two-level" experiment with factors A , B {\displaystyle A,B} and C {\displaystyle C} . In such experiments the factor levels are often denoted by 0 and 1, for reasons explained below. A treatment combination is then denoted by an ordered triple such as 101 (more formally, (1, 0, 1), denoting the cell in which A {\displaystyle A} and C {\displaystyle C} are at level "1" and B {\displaystyle B} is at level "0"). The following table lists the eight cells of the full 2 × 2 × 2 factorial experiment, along with a contrast vector representing each effect, including a three-factor interaction: Suppose that only the fraction consisting of the cells 000, 011, 101, and 110 is observed. The original contrast vectors, when restricted to these cells, are now 4 × 1, and can be seen by looking at just those four rows of the table. (Sorting the table on A B C {\displaystyle ABC} will bring these rows together and make the restricted contrast vectors easier to see. Sorting twice puts them at the top.) The following can be observed concerning these restricted vectors: The


id: aliasing-factorial-experiments-20260505-3
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-3.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
where the equation is modulo s {\displaystyle s} if s {\displaystyle s} is prime, and is in the finite field G F ( s ) {\displaystyle GF(s)} if s {\displaystyle s} is a power of a prime. Such equations are called defining equations of the fraction. When the defining equation or equations are homogeneous, the fraction is said to be principal. One defining equation yields a fraction of size s k − 1 {\displaystyle s^{k-1}} , two independent equations a fraction of size s k − 2 , {\displaystyle s^{k-2},} and so on. Such fractions are generally denoted as s k − r {\displaystyle s^{k-r}} designs. The half-fractions described above are 2 3 − 1 {\displaystyle 2^{3-1}} designs. The notation often includes the resolution as a subscript, in Roman numerals; the above fractions are thus 2 I I I 3 − 1 {\displaystyle 2_{III}^{3-1}} designs. Associated to each expression a 1 t 1 + ⋯ + a k t k {\displaystyle a_{1}t_{1}+\cdots +a_{k}t_{k}} is another, namely A 1 a 1 ⋯ A k a k {\displaystyle A_{1}^{a_{1}}\cdots A_{k}^{a_{k}}} , which rewrites the coefficients as exponents. Such expressions are called "words", a term borrowed from group theory. (In a particular example


id: aliasing-factorial-experiments-20260505-4
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-4.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
The use of arithmetic modulo 2 explains why the factor levels in such designs are labeled 0 and 1. === Example 2 === In a 3-level design, factor levels are denoted 0, 1 and 2, and arithmetic is modulo 3. If there are four factors, say A , B , C {\displaystyle A,B,C} and D {\displaystyle D} , the effects group G {\displaystyle \mathbb {G} } will have the relations A 3 = B 3 = C 3 = D 3 = I . {\displaystyle A^{3}=B^{3}=C^{3}=D^{3}=I.} From these it follows, for example, that D 4 = D {\displaystyle D^{4}=D} and D 6 = I {\displaystyle D^{6}=I} . A defining equation such as t 1 + t 2 + t 3 + 2 t 4 = 0 ( mod 3 ) {\displaystyle t_{1}+t_{2}+t_{3}+2t^{4}=0{\pmod {3}}} would produce a regular 1/3-fraction of the 81 (= 3 4 {\displaystyle 3^{4}} ) treatment combinations, and the corresponding defining word would be A B C D 2 {\displaystyle ABCD^{2}} . Since its powers are ( A B C D 2 ) 2 = A 2 B 2 C 2 D {\displaystyle (ABCD^{2})^{2}=A^{2}B^{2}C^{2}D} and ( A B C D 2 ) 3 = I {\displaystyle (ABCD^{2})^{3}=I} ,


id: aliasing-factorial-experiments-20260505-5
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-5.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
In the 2 3 − 1 {\displaystyle 2^{3-1}} fraction with defining word A B C {\displaystyle ABC} , the maximum resolution is 3 (the length of that word), while the fraction with defining word A B {\displaystyle AB} has maximum resolution 2. The defining words of the 3 4 − 1 {\displaystyle 3^{4-1}} fraction were A B C D 2 {\displaystyle ABCD^{2}} and A 2 B 2 C 2 D {\displaystyle A^{2}B^{2}C^{2}D} , both of length 4, so that the fraction has maximum resolution 4, as indicated. In the 2 5 − 2 {\displaystyle 2^{5-2}} fraction with defining words A B D , A C E {\displaystyle ABD,ACE} and B C D E {\displaystyle BCDE} , the maximum resolution is 3, which is the shortest "wordlength". One could also construct a 2 5 − 2 {\displaystyle 2^{5-2}} fraction from the defining words A B C D {\displaystyle ABCD} and B C D E {\displaystyle BCDE} , but the defining subgroup H {\displaystyle \mathbb {H} } will also include A E {\displaystyle AE} , their product, and so the fraction will only have resolution 2 (the length of A E {\displaystyle AE} ). This is true starting with any two words


id: aliasing-factorial-experiments-20260505-6
file: data/en.wikipedia.org/wiki/Aliasing_(factorial_experiments)-6.md
category: reference
title: Aliasing (factorial experiments)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aliasing_(factorial_experiments)
date_saved: 2026-05-05T09:48:49.670316+00:00
instance: kb-cron
parent: aliasing-factorial-experiments-20260505-0
summary:
== Partial aliasing == In regular 2 k {\displaystyle 2^{k}} fractions there is no partial aliasing: Each effect is either preserved or completely lost, and effects are either unaliased or completely aliased. The same holds in regular s k {\displaystyle s^{k}} experiments with s > 2 {\displaystyle s>2} if one considers only main effects and components of interaction. However, a limited form of partial aliasing occurs in the latter. For example, in the 3 4 − 1 {\displaystyle 3^{4-1}} design described above the overall A × B × C × D {\displaystyle A\times B\times C\times D} interaction is partly lost since its A B C D 2 {\displaystyle ABCD^{2}} component is completely lost in the fraction while its other components (such as A B 2 C 2 D {\displaystyle AB^{2}C^{2}D} ) are preserved. Similarly, the main effect of A {\displaystyle A} is partly aliased with the B × C × D {\displaystyle B\times C\times D} interaction since A {\displaystyle A} is completely aliased with its B C D 2 {\displaystyle BCD^{2}} component and unaliased with the others. In contrast, partial aliasing is uncontrolled and pervasive in nonregular fractions. In the 12-run Plackett-Burman design described in the previous section, for example,


id: all-pairs-testing-20260505-0
file: data/en.wikipedia.org/wiki/All-pairs_testing-0.md
category: reference
title: All-pairs testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/All-pairs_testing
date_saved: 2026-05-05T09:48:50.876127+00:00
instance: kb-cron
parent: all-pairs-testing-20260505-0
summary:
In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a system (typically, a software algorithm), tests all possible discrete combinations of those parameters. Using carefully chosen test vectors, this can be done much faster than an exhaustive search of all combinations of all parameters by "parallelizing" the tests of parameter pairs. == Rationale == In most cases, a single input parameter or an interaction between two parameters is what causes a program's bugs. Bugs involving interactions between three or more parameters are both progressively less common and also progressively more expensive to find, such testing has as its limit the testing of all possible inputs. Thus, a combinatorial technique for picking test cases like all-pairs testing is a useful cost-benefit compromise that enables a significant reduction in the number of test cases without drastically compromising functional coverage. More rigorously, if we assume that a test case has N {\displaystyle N} parameters given in a set { P i } = { P 1 , P 2 , . . . , P N } {\displaystyle \{P_{i}\}=\{P_{1},P_{2},...,P_{N}\}} . The range of the parameters are given by R


id: allocation-concealment-20260505-0
file: data/en.wikipedia.org/wiki/Allocation_concealment-0.md
category: reference
title: Allocation concealment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Allocation_concealment
date_saved: 2026-05-05T09:48:52.131762+00:00
instance: kb-cron
parent: allocation-concealment-20260505-0
summary:
In a randomized experiment, allocation concealment hides the sorting of trial participants into treatment groups so that this knowledge cannot be exploited. Adequate allocation concealment serves to prevent study participants from influencing treatment allocations for subjects. Studies with poor allocation concealment (or none at all) are prone to selection bias. Some standard methods of ensuring allocation concealment include sequentially numbered, opaque, sealed envelopes (SNOSE); sequentially numbered containers; pharmacy controlled randomization; and central randomization. CONSORT guidelines recommend that allocation concealment methods be included in a study's protocol, and that the allocation concealment methods be reported in detail in their publication; however, a 2005 study determined that most clinical trials have unclear allocation concealment in their protocols, in their publications, or both. A 2008 study of 146 meta-analyses concluded that the results of randomized controlled trials with inadequate or unclear allocation concealment tended to be biased toward beneficial effects only if the trials' outcomes were subjective as opposed to objective. Allocation concealment is different from blinding. An allocation concealment method prevents influence on the randomization process, while blinding conceals the outcome of the randomization. However, allocation concealment may also be called "randomization blinding". == Impact == Without the use of allocation concealment,


id: analysis-of-variance-20260505-0
file: data/en.wikipedia.org/wiki/Analysis_of_variance-0.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation between the group means to the amount of variation within each group. If the between-group variation is substantially larger than the within-group variation, it suggests that the group means are likely different. This comparison is done using an F-test. The underlying principle of ANOVA is based on the law of total variance, which states that the total variance in a dataset can be broken down into components attributable to different sources. In the case of ANOVA, these sources are the variation between groups and the variation within groups. ANOVA was developed by the statistician Ronald Fisher. In its simplest form, it provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. == History == While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in the 1770s. Around


id: analysis-of-variance-20260505-1
file: data/en.wikipedia.org/wiki/Analysis_of_variance-1.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
== Classes of models == There are three classes of models used in the analysis of variance, and these are outlined here. === Fixed-effects models === The fixed-effects model (class I) of analysis of variance applies to situations in which the experimenter applies one or more treatments to the subjects of the experiment to see whether the response variable values change. This allows the experimenter to estimate the ranges of response variable values that the treatment would generate in the population as a whole. === Random-effects models === Random-effects model (class II) is used when the treatments are not fixed. This occurs when the various factor levels are sampled from a larger population. Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments (a multi-variable generalization of simple differences) differ from the fixed-effects model. === Mixed-effects models === A mixed-effects model (class III) contains experimental factors of both fixed and random-effects types, with appropriately different interpretations and analysis for the two types. === Example === Teaching experiments could be performed by a college or university department to find a good introductory textbook, with each text considered a treatment. The fixed-effects model would compare a


id: analysis-of-variance-20260505-2
file: data/en.wikipedia.org/wiki/Analysis_of_variance-2.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
The normal-model based ANOVA analysis assumes the independence, normality, and homogeneity of variances of the residuals. The randomization-based analysis assumes only the homogeneity of the variances of the residuals (as a consequence of unit-treatment additivity) and uses the randomization procedure of the experiment. Both these analyses require homoscedasticity, as an assumption for the normal-model analysis and as a consequence of randomization and additivity for the randomization-based analysis. However, studies of processes that change variances rather than means (called dispersion effects) have been successfully conducted using ANOVA. There are no necessary assumptions for ANOVA in its full generality, but the F-test used for ANOVA hypothesis testing has assumptions and practical limitations which are of continuing interest. Problems which do not satisfy the assumptions of ANOVA can often be transformed to satisfy the assumptions. The property of unit-treatment additivity is not invariant under a "change of scale", so statisticians often use transformations to achieve unit-treatment additivity. If the response variable is expected to follow a parametric family of probability distributions, then the statistician may specify (in the protocol for the experiment or observational study) that the responses be transformed to stabilize the variance. Also, a statistician may specify that logarithmic transforms be


id: analysis-of-variance-20260505-3
file: data/en.wikipedia.org/wiki/Analysis_of_variance-3.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
The textbook method is to compare the observed value of F with the critical value of F determined from tables. The critical value of F is a function of the degrees of freedom of the numerator and the denominator and the significance level (α). If F ≥ FCritical, the null hypothesis is rejected. The computer method calculates the probability (p-value) of a value of F greater than or equal to the observed value. The null hypothesis is rejected if this probability is less than or equal to the significance level (α). The ANOVA F-test is known to be nearly optimal in the sense of minimizing false negative errors for a fixed rate of false positive errors (i.e. maximizing power for a fixed significance level). For example, to test the hypothesis that various medical treatments have exactly the same effect, the F-test's p-values closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced. Such permutation tests characterize tests with maximum power against all alternative hypotheses, as observed by Rosenbaum. The ANOVA F-test (of the null-hypothesis that all treatments have exactly the same effect) is recommended as a practical test, because of its robustness against many


id: analysis-of-variance-20260505-4
file: data/en.wikipedia.org/wiki/Analysis_of_variance-4.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
==== The number of experimental units ==== In the design of an experiment, the number of experimental units is planned to satisfy the goals of the experiment. Experimentation is often sequential. Early experiments are often designed to provide mean-unbiased estimates of treatment effects and of experimental error. Later experiments are often designed to test a hypothesis that a treatment effect has an important magnitude; in this case, the number of experimental units is chosen so that the experiment is within budget and has adequate power, among other goals. Reporting sample size analysis is generally required in psychology. "Provide information on sample size and the process that led to sample size decisions." The analysis, which is written in the experimental protocol before the experiment is conducted, is examined in grant applications and administrative review boards. Besides the power analysis, there are less formal methods for selecting the number of experimental units. These include graphical methods based on limiting the probability of false negative errors, graphical methods based on an expected variation increase (above the residuals) and methods based on achieving a desired confidence interval. ==== Power analysis ==== Power analysis is often applied in the context of ANOVA in order to


id: analysis-of-variance-20260505-5
file: data/en.wikipedia.org/wiki/Analysis_of_variance-5.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
== Cautions == Balanced experiments (those with an equal sample size for each treatment) are relatively easy to interpret; unbalanced experiments offer more complexity. For single-factor (one-way) ANOVA, the adjustment for unbalanced data is easy, but the unbalanced analysis lacks both robustness and power. For more complex designs the lack of balance leads to further complications. "The orthogonality property of main effects and interactions present in balanced data does not carry over to the unbalanced case. This means that the usual analysis of variance techniques do not apply. Consequently, the analysis of unbalanced factorials is much more difficult than that for balanced designs." In the general case, "The analysis of variance can also be applied to unbalanced data, but then the sums of squares, mean squares, and F-ratios will depend on the order in which the sources of variation are considered." ANOVA is (in part) a test of statistical significance. The American Psychological Association (and many other organisations) holds the view that simply reporting statistical significance is insufficient and that reporting confidence bounds is preferred. == Generalizations == ANOVA is considered to be a special case of linear regression which in turn is a special case of the general linear


id: analysis-of-variance-20260505-6
file: data/en.wikipedia.org/wiki/Analysis_of_variance-6.md
category: reference
title: Analysis of variance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Analysis_of_variance
date_saved: 2026-05-05T09:48:53.349210+00:00
instance: kb-cron
parent: analysis-of-variance-20260505-0
summary:
== References == Anscombe, F. J. (1948). "The Validity of Comparative Experiments". Journal of the Royal Statistical Society. Series A (General). 111 (3): 181–211. doi:10.2307/2984159. JSTOR 2984159. MR 0030181. Bailey, R. A. (2008). Design of Comparative Experiments. Cambridge University Press. ISBN 978-0-521-68357-9. Pre-publication chapters are available on-line. Belle, Gerald van (2008). Statistical rules of thumb (2nd ed.). Hoboken, N.J: Wiley. ISBN 978-0-470-14448-0. Cochran, William G.; Cox, Gertrude M. (1992). Experimental designs (2nd ed.). New York: Wiley. ISBN 978-0-471-54567-5. Cohen, Jacob (1988). Statistical power analysis for the behavior sciences (2nd ed.). Routledge ISBN 978-0-8058-0283-2 Cohen, Jacob (1992). "Statistics a power primer". Psychological Bulletin. 112 (1): 155–159. doi:10.1037/0033-2909.112.1.155. PMID 19565683. S2CID 14411587. Cox, David R. (1958). Planning of experiments. Reprinted as ISBN 978-0-471-57429-3 Cox, David R. (2006). Principles of statistical inference. Cambridge New York: Cambridge University Press. ISBN 978-0-521-68567-2. Freedman, David A.(2005). Statistical Models: Theory and Practice, Cambridge University Press. ISBN 978-0-521-67105-7 Gelman, Andrew (2005). "Analysis of variance? Why it is more important than ever". The Annals of Statistics. 33: 1–53. arXiv:math/0504499. doi:10.1214/009053604000001048. S2CID 13529149. Gelman, Andrew (2008). "Variance, analysis of". The new Palgrave dictionary of economics (2nd ed.). Basingstoke, Hampshire New York: Palgrave Macmillan. ISBN 978-0-333-78676-5. Hinkelmann, Klaus & Kempthorne, Oscar


id: animal-perception-of-magic-20260505-0
file: data/en.wikipedia.org/wiki/Animal_perception_of_magic-0.md
category: reference
title: Animal perception of magic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Animal_perception_of_magic
date_saved: 2026-05-05T09:48:54.537395+00:00
instance: kb-cron
parent: animal-perception-of-magic-20260505-0
summary:
Researchers study the reactions of animals observing humans performing magic tricks in order to better understand animal cognition. Using these studies, evolutionary psychologists aim to gain insights into the evolution of perception and attention by comparing responses of different species, including humans. == Background == Magic is about violating expectations. It capitalises on specific blind spots in attention and perception. While scientific interest in humans' perception of magic dates back to the late 19th century, when in 1896 Alfred Binet presented his work, this faded quickly, and has only recently, in the early 21st century, been revived. Some researchers have coined terms such as neuromagic or magicology for the study of magic. Other scientists are critical of the new field, saying it is not worthy to stand as a field of its own. Scientists aim to get insight into how the human mind operates. Some animal species are capable of misdirection, an important skill magicians possess to trick humans. For example, chimpanzees have been observed to deliberately look away from an object they desire as to avoid it being noticed by a competitor. Jays and other corvids pretend to store food in various places, trying to obscure the cache's true


id: antecedent-variable-20260505-0
file: data/en.wikipedia.org/wiki/Antecedent_variable-0.md
category: reference
title: Antecedent variable
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Antecedent_variable
date_saved: 2026-05-05T09:48:55.799600+00:00
instance: kb-cron
parent: antecedent-variable-20260505-0
summary:
In statistics and social sciences, an antecedent variable is a variable that cannot help to explain the apparent relationship (or part of the relationship) between other variables that are nominally in a cause and effect relationship. In a regression analysis, an antecedent variable would be one that influences both the independent variable and the dependent variable. == See also == Path analysis (statistics) Latent variable Intervening variable Confounding variable == References == Olobatuyi, M. E. (2006). "Definition of Basic Terms and Concepts". A User's Guide to Path Analysis. University Press of America. pp. 21–52. ISBN 0-7618-3230-0.


id: arrive-guidelines-20260505-0
file: data/en.wikipedia.org/wiki/ARRIVE_guidelines-0.md
category: reference
title: ARRIVE guidelines
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/ARRIVE_guidelines
date_saved: 2026-05-05T09:48:57.054025+00:00
instance: kb-cron
parent: arrive-guidelines-20260505-0
summary:
The ARRIVE guidelines (short for Animals in Research: Reporting In Vivo Experiments) are a set of guidelines for improving experimental design and reporting standards for animal research, drawn up by the National Centre for the Replacement, Refinement and Reduction of Animals in Research. First published in 2010 as a checklist of 20 items, a revision, titled ARRIVE 2.0, was published in 2020 as two checklists of 10 "essential" items and 11 "recommended" items. While the guidelines have been endorsed by over a thousand scientific journals, their adoption and enforcement has remained limited. == Origin == A 2009 review of the quality of experimental design, analysis, and reporting methods of animal research conducted by the National Centre for the Replacement, Refinement and Reduction of Animals in Research (NC3Rs) found that most biomedical journals were providing little or no guidance on how animal research should be analyzed and reported, outside of ethical guidelines for experimental design, such as the Three Rs. Additionally, it found issues with the way animal research is reported, with large proportions of articles not stating a hypothesis or objective of the study, lacking specifics about the characteristics of the animals used, not having used techniques such as randomization


id: association-scheme-20260505-0
file: data/en.wikipedia.org/wiki/Association_scheme-0.md
category: reference
title: Association scheme
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Association_scheme
date_saved: 2026-05-05T09:48:58.210111+00:00
instance: kb-cron
parent: association-scheme-20260505-0
summary:
The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. In algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and the theory of error-correcting codes. In algebra, the theory of association schemes generalizes the character theory of linear representations of groups. == Definition == An n-class association scheme consists of a set X together with a partition S of X × X into n + 1 binary relations, R0, R1, ..., Rn which satisfy: R 0 = { ( x , x ) : x ∈ X } {\displaystyle R_{0}=\{(x,x):x\in X\}} ; it is called the identity relation. Defining R ∗ := { ( x , y ) : ( y , x ) ∈ R } {\displaystyle R^{*}:=\{(x,y):(y,x)\in R\}} , if R in S, then R* in S. If ( x , y ) ∈ R k {\displaystyle (x,y)\in R_{k}} , the number of z ∈ X {\displaystyle z\in X} such that ( x , z ) ∈ R i {\displaystyle (x,z)\in R_{i}} and ( z , y ) ∈ R j {\displaystyle


id: association-scheme-20260505-1
file: data/en.wikipedia.org/wiki/Association_scheme-1.md
category: reference
title: Association scheme
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Association_scheme
date_saved: 2026-05-05T09:48:58.210111+00:00
instance: kb-cron
parent: association-scheme-20260505-0
summary:
== History == The term association scheme is due to (Bose & Shimamoto 1952) but the concept is already inherent in (Bose & Nair 1939). These authors were studying what statisticians have called partially balanced incomplete block designs (PBIBDs). The subject became an object of algebraic interest with the publication of (Bose & Mesner 1959) and the introduction of the Bose–Mesner algebra. The most important contribution to the theory was the thesis of Ph. Delsarte (Delsarte 1973) who recognized and fully used the connections with coding theory and design theory. A generalization called coherent configurations has been studied by D. G. Higman. == Basic facts == p 00 0 = 1 {\displaystyle p_{00}^{0}=1} , i.e., if ( x , y ) ∈ R 0 {\displaystyle (x,y)\in R_{0}} then x = y {\displaystyle x=y} and the only z {\displaystyle z} such that ( x , z ) ∈ R 0 {\displaystyle (x,z)\in R_{0}} is z = x {\displaystyle z=x} . ∑ i = 0 k p i i 0 = | X | {\displaystyle \sum _{i=0}^{k}p_{ii}^{0}=|X|} ; this is because the R i {\displaystyle R_{i}} partition X {\displaystyle X} . == The Bose–Mesner algebra == The adjacency matrices A i {\displaystyle


id: association-scheme-20260505-2
file: data/en.wikipedia.org/wiki/Association_scheme-2.md
category: reference
title: Association scheme
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Association_scheme
date_saved: 2026-05-05T09:48:58.210111+00:00
instance: kb-cron
parent: association-scheme-20260505-0
summary:
== References == Bailey, Rosemary A. (2004), Association Schemes: Designed Experiments, Algebra and Combinatorics, Cambridge University Press, ISBN 978-0-521-82446-0, MR 2047311. (Chapters from preliminary draft are available on-line.) Bannai, Eiichi; Ito, Tatsuro (1984), Algebraic combinatorics I: Association schemes, Menlo Park, CA: Benjamin/Cummings, ISBN 0-8053-0490-8, MR 0882540 Bose, R. C.; Mesner, D. M. (1959), "On linear associative algebras corresponding to association schemes of partially balanced designs", Annals of Mathematical Statistics, 30 (1): 21–38, doi:10.1214/aoms/1177706356, JSTOR 2237117, MR 0102157 Bose, R. C.; Nair, K. R. (1939), "Partially balanced incomplete block designs", Sankhyā, 4 (3): 337–372, JSTOR 40383923 Bose, R. C.; Shimamoto, T. (1952), "Classification and analysis of partially balanced incomplete block designs with two associate classes", Journal of the American Statistical Association, 47 (258): 151–184, doi:10.1080/01621459.1952.10501161 Camion, P. (1998), "18. Codes and Association Schemes: Basic Properties of Association Schemes Relevant to Coding", in Pless, V.S.; Huffman, W.C.; Brualdi, R.A. (eds.), Handbook of Coding Theory, vol. 1, Elsevier, pp. 1441–, ISBN 978-0-444-50088-5 Delsarte, P. (1973), "An Algebraic Approach to the Association Schemes of Coding Theory", Philips Research Reports (Supplement No. 10), OCLC 641852316 Delsarte, P.; Levenshtein, V. I. (1998). "Association schemes and coding theory". IEEE Transactions on Information Theory. 44 (6): 2477–2504. doi:10.1109/18.720545.


id: bayesian-experimental-design-20260505-0
file: data/en.wikipedia.org/wiki/Bayesian_experimental_design-0.md
category: reference
title: Bayesian experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bayesian_experimental_design
date_saved: 2026-05-05T09:48:59.414261+00:00
instance: kb-cron
parent: bayesian-experimental-design-20260505-0
summary:
Bayesian experimental design provides a general probability-theoretical framework from which other theories on experimental design can be derived. It is based on Bayesian inference to interpret the observations/data acquired during the experiment. This allows accounting for both any prior knowledge on the parameters to be determined as well as uncertainties in observations. The theory of Bayesian experimental design is to a certain extent based on the theory for making optimal decisions under uncertainty. The aim when designing an experiment is to maximize the expected utility of the experiment outcome. The utility is most commonly defined in terms of a measure of the accuracy of the information provided by the experiment (e.g., the Shannon information or the negative of the variance) but may also involve factors such as the financial cost of performing the experiment. What will be the optimal experiment design depends on the particular utility criterion chosen. == Relations to more specialized optimal design theory == === Linear theory === If the model is linear, the prior probability density function (PDF) is homogeneous and observational errors are normally distributed, the theory simplifies to the classical optimal experimental design theory. === Approximate normality === In numerous publications on Bayesian experimental


id: bayesian-experimental-design-20260505-1
file: data/en.wikipedia.org/wiki/Bayesian_experimental_design-1.md
category: reference
title: Bayesian experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bayesian_experimental_design
date_saved: 2026-05-05T09:48:59.414261+00:00
instance: kb-cron
parent: bayesian-experimental-design-20260505-0
summary:
of which the latter can be evaluated without the need for evaluating individual posterior probability p ( θ ∣ y , ξ ) {\displaystyle p(\theta \mid y,\xi )} for all possible observations y {\displaystyle y} . It is worth noting that the second term on the second equation line will not depend on the design ξ {\displaystyle \xi } , as long as the observational uncertainty doesn't. On the other hand, the integral of p ( θ ) log ⁡ p ( θ ) {\displaystyle p(\theta )\log p(\theta )} in the first form is constant for all ξ {\displaystyle \xi } , so if the goal is to choose the design with the highest utility, the term need not be computed at all. Several authors have considered numerical techniques for evaluating and optimizing this criterion. Note that U ( ξ ) = I ( θ ; y ) , {\displaystyle U(\xi )=I(\theta ;y)\,,} the expected information gain being exactly the mutual information between the parameter θ and the observation y. An example of Bayesian design for linear dynamical model identification are given in . Since I ( θ ; y ) , {\displaystyle I(\theta ;y)\,,} was difficult to calculate, its


id: between-group-design-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Between-group_design_experiment-0.md
category: reference
title: Between-group design experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Between-group_design_experiment
date_saved: 2026-05-05T09:49:00.617094+00:00
instance: kb-cron
parent: between-group-design-experiment-20260505-0
summary:
In the design of experiments, a between-group design is an experiment that has two or more groups of subjects each being tested by a different testing factor simultaneously. This design is usually used in place of, or in some cases in conjunction with, the within-subject design, which applies the same variations of conditions to each subject to observe the reactions. The simplest between-group design occurs with two groups; one is generally regarded as the treatment group, which receives the ‘special’ treatment (that is, it is treated with some variable), and the control group, which receives no variable treatment and is used as a reference (prove that any deviation in results from the treatment group is, indeed, a direct result of the variable). The between-group design is widely used in psychological, economic, and sociological experiments, as well as in several other fields in the natural or social sciences. == Experimental blinds == In order to avoid experimental bias, experimental blinds are usually applied in between-group designs. The most commonly used type is the single blind, which keeps the subjects blind without identifying them as members of the treatment group or the control group. In a single-blind experiment, a placebo is usually


id: blinded-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Blinded_experiment-0.md
category: reference
title: Blinded experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blinded_experiment
date_saved: 2026-05-05T09:49:01.984530+00:00
instance: kb-cron
parent: blinded-experiment-20260505-0
summary:
In a blind or blinded experiment, information that could influence participants or investigators is withheld until the experiment is completed. Blinding is used to reduce or eliminate potential sources of bias, such as participants’ expectations, the observer-expectancy effect, observer bias, confirmation bias, and other cognitive or procedural influences. Blinding can be applied to different participants in an experiment, including study subjects, researchers, technicians, data analysts, and outcome assessors. When multiple groups are blinded simultaneously (for example, both participants and researchers), the design is referred to as a double-blind study. In some cases, blinding is desirable but impractical or unethical. For example, it is not possible to blind a participant receiving a physical therapy intervention, or a surgeon performing an operative procedure. Well-designed clinical protocols therefore aim to maximize the effectiveness of blinding within ethical and practical constraints. During the course of an experiment, a participant becomes unblinded if they deduce or otherwise obtain information that has been masked to them. For example, a patient who experiences a side effect may correctly guess their treatment, becoming unblinded. Unblinding is common in blinded experiments, particularly in pharmacological trials. In particular, trials on pain medication and antidepressants are poorly blinded. Unblinding that occurs


id: blinded-experiment-20260505-1
file: data/en.wikipedia.org/wiki/Blinded_experiment-1.md
category: reference
title: Blinded experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blinded_experiment
date_saved: 2026-05-05T09:49:01.984530+00:00
instance: kb-cron
parent: blinded-experiment-20260505-0
summary:
== Unblinding == "Unblinding" occurs in a blinded experiment when information is revealed to someone to whom it has been masked. In clinical studies, unblinding may occur unintentionally when a patient deduces their treatment group. Unblinding that occurs before the conclusion of an experiment is a source of bias. Some degree of premature unblinding is common in blinded experiments. When a blind is imperfect, its success is judged on a spectrum with no blind (or complete failure of blinding) on one end, perfect blinding on the other, and poor or good blinding between. Thus, the common view of studies as blinded or unblinded exemplifies a false dichotomy. The success of blinding is assessed by asking study participants about information that has been masked from them (e.g., whether the participant received the drug or placebo?). In a perfectly blinded experiment, the responses should be consistent with no knowledge of the masked information. However, if unblinding has occurred, the responses will indicate the degree of unblinding. Since unblinding cannot be measured directly, but must be inferred from participants' responses, its measured value will depend on the nature of the questions asked. As a result, it is not possible to objectively measure unblinding.


id: blinded-experiment-20260505-2
file: data/en.wikipedia.org/wiki/Blinded_experiment-2.md
category: reference
title: Blinded experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blinded_experiment
date_saved: 2026-05-05T09:49:01.984530+00:00
instance: kb-cron
parent: blinded-experiment-20260505-0
summary:
==== Acupuncture ==== While the possibility of blinded trials on acupuncture is controversial, a 2003 review of 47 randomized controlled trials found no fewer than four methods of blinding patients to acupuncture treatment: 1) superficial needling of true acupuncture points, 2) use of acupuncture points which are not indicated for the condition being treated, 3) insertion of needles outside of true acupuncture points, and 4) the use of placebo needles which are designed not to penetrate the skin. The authors concluded that there was "no clear association between the type of sham intervention used and the results of the trials." A 2018 study on acupuncture, which used needles that did not penetrate the skin as a sham treatment, found that 68% of patients and 83% of acupuncturists correctly identified their group allocation. The authors concluded that blinding had failed, but that more advanced placebos may someday enable well-blinded studies in acupuncture. === In physics === It is standard practice in physics to perform blinded data analysis. Once the data analysis is complete, one may unblind the data. A prior agreement to publish the data regardless of the results of the study may be made to prevent publication bias. === In


id: block-design-20260505-0
file: data/en.wikipedia.org/wiki/Block_design-0.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such that number of occurrences of each element satisfies certain conditions making the collection of blocks exhibit symmetry (balance). Block designs have applications in many areas, including experimental design, finite geometry, physical chemistry, software testing, cryptography, and algebraic geometry. Without further specifications the term block design usually refers to a balanced incomplete block design (BIBD), specifically (and also synonymously) a 2-design, which has been the most intensely studied type historically due to its application in the design of experiments. Its generalization is known as a t-design. == Overview == A design is said to be balanced (up to t) if all t-subsets of the original set occur in equally many (i.e., λ) blocks. When t is unspecified, it can usually be assumed to be 2, which means that each pair of elements is found in the same number of blocks and the design is pairwise balanced. For t = 1, each element occurs in the same number of blocks (the replication number, denoted r) and the design is said to be regular. A block design in


id: block-design-20260505-1
file: data/en.wikipedia.org/wiki/Block_design-1.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
obtained from counting for a fixed x the triples (x, y, B) where x and y are distinct points and B is a block that contains them both. This equation for every x also proves that r is constant (independent of x) even without assuming it explicitly, thus proving that the condition that any x in X is contained in r blocks is redundant and r can be computed from the other parameters. The resulting b and r must be integers, which imposes conditions on v, k, and λ. These conditions are not sufficient as, for example, a (43,7,1)-design does not exist. The order of a 2-design is defined to be n = r − λ. The complement of a 2-design is obtained by replacing each block with its complement in the point set X. It is also a 2-design and has parameters v′ = v, b′ = b, r′ = b − r, k′ = v − k, λ′ = λ + b − 2r. A 2-design and its complement have the same order. A fundamental theorem, Fisher's inequality, named after the statistician Ronald Fisher, is that b ≥ v in any 2-design. A rather surprising and not very


id: block-design-20260505-2
file: data/en.wikipedia.org/wiki/Block_design-2.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
Since k = r we can write the order of a projective plane as n = k − 1 and, from the displayed equation above, we obtain v = (n + 1)n + 1 = n2 + n + 1 points in a projective plane of order n. As a projective plane is a symmetric design, we have b = v, meaning that b = n2 + n + 1 also. The number b is the number of lines of the projective plane. There can be no repeated lines since λ = 1, so a projective plane is a simple 2-design in which the number of lines and the number of points are always the same. For a projective plane, k is the number of points on each line and it is equal to n + 1. Similarly, r = n + 1 is the number of lines with which a given point is incident. For n = 2 we get a projective plane of order 2, also called the Fano plane, with v = 4 + 2 + 1 = 7 points and 7 lines. In the Fano plane, each line has n + 1 = 3 points and


id: block-design-20260505-3
file: data/en.wikipedia.org/wiki/Block_design-3.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
== General balanced designs (t-designs) == Given any positive integer t, a t-design B is a class of k-element subsets of X, called blocks, such that every point x in X appears in exactly r blocks, and every t-element subset T appears in exactly λ blocks. The numbers v (the number of elements of X), b (the number of blocks), k, r, λ, and t are the parameters of the design. The design may be called a t-(v,k,λ)-design. Again, these four numbers determine b and r and the four numbers themselves cannot be chosen arbitrarily. The equations are λ i = λ ( v − i t − i ) / ( k − i t − i ) for i = 0 , 1 , … , t , {\displaystyle \lambda _{i}=\lambda \left.{\binom {v-i}{t-i}}\right/{\binom {k-i}{t-i}}{\text{ for }}i=0,1,\ldots ,t,} where λi is the number of blocks that contain any i-element set of points and λt = λ. Note that b = λ 0 = λ ( v t ) / ( k t ) {\displaystyle b=\lambda _{0}=\lambda {v \choose t}/{k \choose t}} and r = λ 1 = λ ( v − 1 t − 1 ) / ( k


id: block-design-20260505-4
file: data/en.wikipedia.org/wiki/Block_design-4.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
R 0 = { ( x , x ) : x ∈ X } {\displaystyle R_{0}=\{(x,x):x\in X\}} and is called the Identity relation. Defining R ∗ := { ( x , y ) ∣ ( y , x ) ∈ R } {\displaystyle R^{*}:=\{(x,y)\mid (y,x)\in R\}} , if R in S, then R* in S If ( x , y ) ∈ R k {\displaystyle (x,y)\in R_{k}} , the number of z ∈ X {\displaystyle z\in X} such that ( x , z ) ∈ R i {\displaystyle (x,z)\in R_{i}} and ( z , y ) ∈ R j {\displaystyle (z,y)\in R_{j}} is a constant p i j k {\displaystyle p_{ij}^{k}} depending on i, j, k but not on the particular choice of x and y. An association scheme is commutative if p i j k = p j i k {\displaystyle p_{ij}^{k}=p_{ji}^{k}} for all i, j and k. Most authors assume this property. A partially balanced incomplete block design with n associate classes (PBIBD(n)) is a block design based on a v-set X with b blocks each of size k and with each element appearing in r blocks, such that there is an association scheme with n classes defined


id: block-design-20260505-5
file: data/en.wikipedia.org/wiki/Block_design-5.md
category: reference
title: Block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Block_design
date_saved: 2026-05-05T09:49:03.148970+00:00
instance: kb-cron
parent: block-design-20260505-0
summary:
== References == Aschbacher, Michael (1971). "On collineation groups of symmetric block designs". Journal of Combinatorial Theory. Series A. 11 (3): 272–281. doi:10.1016/0097-3165(71)90054-9. Assmus, E.F.; Key, J.D. (1992), Designs and Their Codes, Cambridge: Cambridge University Press, ISBN 0-521-41361-3 Beth, Thomas; Jungnickel, Dieter; Lenz, Hanfried (1986), Design Theory, Cambridge University Press. 2nd ed. (1999) ISBN 978-0-521-44432-3. Bose, R. C. (1949), "A Note on Fisher's Inequality for Balanced Incomplete Block Designs", Annals of Mathematical Statistics, 20 (4): 619–620, doi:10.1214/aoms/1177729958 Bose, R. C.; Shimamoto, T. (1952), "Classification and analysis of partially balanced incomplete block designs with two associate classes", Journal of the American Statistical Association, 47 (258): 151–184, doi:10.1080/01621459.1952.10501161 Cameron, P. J.; van Lint, J. H. (1991), Designs, Graphs, Codes and their Links, Cambridge University Press, ISBN 0-521-42385-6 Colbourn, Charles J.; Dinitz, Jeffrey H. (2007), Handbook of Combinatorial Designs (2nd ed.), Boca Raton: Chapman & Hall/ CRC, ISBN 978-1-58488-506-1 Fisher, R.A. (1940), "An examination of the different possible solutions of a problem in incomplete blocks", Annals of Eugenics, 10: 52–75, doi:10.1111/j.1469-1809.1940.tb02237.x, hdl:2440/15239 Hall, Marshall Jr. (1986), Combinatorial Theory (2nd ed.), New York: Wiley-Interscience, ISBN 0-471-09138-3 Hughes, D.R.; Piper, E.C. (1985), Design theory, Cambridge: Cambridge University Press, ISBN 0-521-25754-9 Kaski, Petteri; Östergård, Patric (2008).


id: blocking-statistics-20260505-0
file: data/en.wikipedia.org/wiki/Blocking_(statistics)-0.md
category: reference
title: Blocking (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blocking_(statistics)
date_saved: 2026-05-05T09:49:20.919707+00:00
instance: kb-cron
parent: blocking-statistics-20260505-0
summary:
In the statistical theory of the design of experiments, blocking is the arranging of experimental units that are similar to one another in groups (blocks) based on one or more variables. These variables are chosen carefully to minimize the effect of their variability on the observed outcomes. There are different ways that blocking can be implemented, resulting in different confounding effects. However, the different methods share the same purpose: to control variability introduced by specific factors that could influence the outcome of an experiment. The roots of blocking originated from the statistician, Ronald Fisher, following his development of ANOVA. == History == The use of blocking in experimental design has an evolving history that spans multiple disciplines. The foundational concepts of blocking date back to the early 20th century with statisticians like Ronald A. Fisher. His work in developing analysis of variance (ANOVA) set the groundwork for grouping experimental units to control for extraneous variables. Blocking evolved over the years, leading to the formalization of randomized block designs and Latin square designs. Today, blocking still plays a pivotal role in experimental design, and in recent years, advancements in statistical software and computational capabilities have allowed researchers to explore more intricate


id: blocking-statistics-20260505-1
file: data/en.wikipedia.org/wiki/Blocking_(statistics)-1.md
category: reference
title: Blocking (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blocking_(statistics)
date_saved: 2026-05-05T09:49:20.919707+00:00
instance: kb-cron
parent: blocking-statistics-20260505-0
summary:
In our previous diet pills example, a blocking factor could be the sex of a patient. We could put individuals into one of two blocks (male or female). And within each of the two blocks, we can randomly assign the patients to either the diet pill (treatment) or placebo pill (control). By blocking on sex, this source of variability is controlled, therefore, leading to greater interpretation of how the diet pills affect weight loss. === Definition of blocking factors === A nuisance factor is used as a blocking factor if every level of the primary factor occurs the same number of times with each level of the nuisance factor. The analysis of the experiment will focus on the effect of varying levels of the primary factor within each block of the experiment. === Block a few of the most important nuisance factors === The general rule is: "Block what you can; randomize what you cannot." Blocking is used to remove the effects of a few of the most important nuisance variables. Randomization is then used to reduce the contaminating effects of the remaining nuisance variables. For important nuisance variables, blocking will yield higher significance in the variables of interest than


id: blocking-statistics-20260505-2
file: data/en.wikipedia.org/wiki/Blocking_(statistics)-2.md
category: reference
title: Blocking (statistics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Blocking_(statistics)
date_saved: 2026-05-05T09:49:20.919707+00:00
instance: kb-cron
parent: blocking-statistics-20260505-0
summary:
Yij is any observation for which X1 = i and X2 = j X1 is the primary factor X2 is the blocking factor μ is the general location parameter (i.e., the mean) Ti is the effect for being in treatment i (of factor X1) Bj is the effect for being in block j (of factor X2) === Estimates === Estimate for μ : Y ¯ {\displaystyle {\overline {Y}}} = the average of all the data Estimate for Ti : Y ¯ i ⋅ − Y ¯ {\displaystyle {\overline {Y}}_{i\cdot }-{\overline {Y}}} with Y ¯ i ⋅ {\displaystyle {\overline {Y}}_{i\cdot }} = average of all Y for which X1 = i. Estimate for Bj : Y ¯ ⋅ j − Y ¯ {\displaystyle {\overline {Y}}_{\cdot j}-{\overline {Y}}} with Y ¯ ⋅ j {\displaystyle {\overline {Y}}_{\cdot j}} = average of all Y for which X2 = j. === Generalizations === Generalized randomized block designs (GRBD) allow tests of block–treatment interaction, and has exactly one blocking factor like the RCBD. Latin squares (and other row–column designs) have two blocking factors that are believed to have no interaction. Latin hypercube sampling Graeco-Latin squares Hyper-Graeco-Latin square designs == See also == Algebraic statistics Block design


id: bose-mesner-algebra-20260505-0
file: data/en.wikipedia.org/wiki/Bose–Mesner_algebra-0.md
category: reference
title: Bose–Mesner algebra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bose–Mesner_algebra
date_saved: 2026-05-05T09:49:22.162239+00:00
instance: kb-cron
parent: bose-mesner-algebra-20260505-0
summary:
In mathematics, a Bose–Mesner algebra is a special set of matrices which arise from a combinatorial structure known as an association scheme, together with the usual set of rules for combining (forming the products of) those matrices, such that they form an associative algebra, or, more precisely, a unitary commutative algebra. Among these rules are: the result of a product is also within the set of matrices, there is an identity matrix in the set, and taking products is commutative. Bose–Mesner algebras have applications in physics to spin models, and in statistics to the design of experiments. They are named for R. C. Bose and Dale Marsh Mesner. == Definition == Let X be a set of v elements. Consider a partition of the 2-element subsets of X into n non-empty subsets, R1, ..., Rn, such that: given an x ∈ X {\displaystyle x\in X} , the number of y ∈ X {\displaystyle y\in X} such that { x , y } ∈ R i {\displaystyle \{x,y\}\in R_{i}} depends only on i (and not on x). This number will be denoted by vi, and given x , y ∈ X {\displaystyle x,y\in X} with { x , y } ∈


id: bose-mesner-algebra-20260505-1
file: data/en.wikipedia.org/wiki/Bose–Mesner_algebra-1.md
category: reference
title: Bose–Mesner algebra
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bose–Mesner_algebra
date_saved: 2026-05-05T09:49:22.162239+00:00
instance: kb-cron
parent: bose-mesner-algebra-20260505-0
summary:
∑ i = 0 n J i = I . ( 5 ) {\displaystyle \sum _{i=0}^{n}J_{i}=I.\qquad (5)} The Bose–Mesner algebra has two distinguished bases: the basis consisting of the adjacency matrices D i {\displaystyle D_{i}} , and the basis consisting of the irreducible idempotent matrices J k {\displaystyle J_{k}} . By definition, there exist well-defined complex numbers such that D i = ∑ k = 0 n p i ( k ) J k , ( 6 ) {\displaystyle D_{i}=\sum _{k=0}^{n}p_{i}(k)J_{k},\qquad (6)} and | X | J k = ∑ i = 0 n q k ( i ) D i . ( 7 ) {\displaystyle |X|J_{k}=\sum _{i=0}^{n}q_{k}\left(i\right)D_{i}.\qquad (7)} The p-numbers p i ( k ) {\displaystyle p_{i}(k)} , and the q-numbers q k ( i ) {\displaystyle q_{k}(i)} , play a prominent role in the theory. They satisfy well-defined orthogonality relations. The p-numbers are the eigenvalues of the adjacency matrix D i {\displaystyle D_{i}} . == Theorem == The eigenvalues of p i ( k ) {\displaystyle p_{i}(k)} and q k ( i ) {\displaystyle q_{k}(i)} , satisfy the orthogonality conditions: ∑ k = 0 n μ i p i ( k ) p ℓ ( k ) =


id: box-behnken-design-20260505-0
file: data/en.wikipedia.org/wiki/Box–Behnken_design-0.md
category: reference
title: Box–Behnken design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Box–Behnken_design
date_saved: 2026-05-05T09:49:23.484470+00:00
instance: kb-cron
parent: box-behnken-design-20260505-0
summary:
In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to achieve the following goals: Each factor, or independent variable, is placed at one of three equally spaced values, usually coded as −1, 0, +1. (At least three levels are needed for the following goal.) The design should be sufficient to fit a quadratic model, that is, one containing squared terms, products of two factors, linear terms and an intercept. The ratio of the number of experimental points to the number of coefficients in the quadratic model should be reasonable (in fact, their designs kept in the range of 1.5 to 2.6). The estimation variance should more or less depend only on the distance from the centre (this is achieved exactly for the designs with 4 and 7 factors), and should not vary too much inside the smallest (hyper)cube containing the experimental points. (See "rotatability" in "Comparisons of response surface designs".) Box-Behnken design is still considered to be more proficient and more powerful than other designs such as the three-level full factorial design, central composite design (CCD) and Doehlert design, despite its poor coverage of the corner of


id: bruck-ryser-chowla-theorem-20260505-0
file: data/en.wikipedia.org/wiki/Bruck–Ryser–Chowla_theorem-0.md
category: reference
title: Bruck–Ryser–Chowla theorem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bruck–Ryser–Chowla_theorem
date_saved: 2026-05-05T09:49:24.722968+00:00
instance: kb-cron
parent: bruck-ryser-chowla-theorem-20260505-0
summary:
The Bruck–Ryser–Chowla theorem is a result on the combinatorics of symmetric block designs that implies nonexistence of certain kinds of design. It states that if a (v, b, r, k, λ)-design exists with v = b (implying k = r and λ(v − 1) = k(k − 1)), then: if v is even, then k − λ is a square; if v is odd, then the following Diophantine equation has a nontrivial solution: x2 − (k − λ)y2 − (−1)(v−1)/2 λ z2 = 0. The theorem was proved in the case of projective planes by Bruck & Ryser (1949). It was extended to symmetric designs by Chowla & Ryser (1950). == Projective planes == In the special case of a symmetric design with λ = 1, that is, a projective plane, the theorem (which in this case is referred to as the Bruck–Ryser theorem) can be stated as follows: If a finite projective plane of order q exists and q is congruent to 1 or 2 (mod 4), then q must be the sum of two squares. Note that for a projective plane, the design parameters are v = b = q2 + q + 1, r = k =


id: case-control-study-20260505-0
file: data/en.wikipedia.org/wiki/Case–control_study-0.md
category: reference
title: Case–control study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Case–control_study
date_saved: 2026-05-05T09:49:25.991019+00:00
instance: kb-cron
parent: case-control-study-20260505-0
summary:
A case–control study (also known as case–referent study) is a type of observational study in which two existing groups differing in outcome are identified and compared on the basis of some supposed causal attribute. Case–control studies are often used to identify factors that may contribute to a medical condition by comparing subjects who have the condition with patients who do not have the condition but are otherwise similar. They require fewer resources but provide less evidence for causal inference than a randomized controlled trial. A case–control study is often used to produce an odds ratio. Some statistical methods make it possible to use a case–control study to also estimate relative risk, risk differences, and other quantities. == Definition == Porta's Dictionary of Epidemiology defines the case–control study as: "an observational epidemiological study of persons with the disease (or another outcome variable) of interest and a suitable control group of persons without the disease (comparison group, reference group). The potential relationship of a suspected risk factor or an attribute to the disease is examined by comparing the diseased and nondiseased subjects with regard to how frequently the factor or attribute is present (or, if quantitative, the levels of the attribute) in


id: case-control-study-20260505-1
file: data/en.wikipedia.org/wiki/Case–control_study-1.md
category: reference
title: Case–control study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Case–control_study
date_saved: 2026-05-05T09:49:25.991019+00:00
instance: kb-cron
parent: case-control-study-20260505-0
summary:
== Examples == One of the most significant triumphs of the case–control study was the demonstration of the link between tobacco smoking and lung cancer, by Richard Doll and Bradford Hill. They showed a statistically significant association in a large case–control study. Opponents argued for many years that this type of study cannot prove causation, but the eventual results of cohort studies confirmed the causal link which the case–control studies suggested, and it is now accepted that tobacco smoking is the cause of about 87% of all lung cancer mortality in the US. == Analysis == Case–control studies were initially analyzed by testing whether or not there were significant differences between the proportion of exposed subjects among cases and controls. Subsequently, Cornfield pointed out that, when the disease outcome of interest is rare, the odds ratio of exposure can be used to estimate the relative risk (see rare disease assumption). The validity of the odds ratio depends highly on the nature of the disease studied, on the sampling methodology and on the type of follow-up. Although in classical case–control studies, it remains true that the odds ratio can only approximate the relative risk in the case of rare diseases, there


id: central-composite-design-20260505-0
file: data/en.wikipedia.org/wiki/Central_composite_design-0.md
category: reference
title: Central composite design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Central_composite_design
date_saved: 2026-05-05T09:49:27.222255+00:00
instance: kb-cron
parent: central-composite-design-20260505-0
summary:
In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment. After the designed experiment is performed, linear regression is used, sometimes iteratively, to obtain results. Coded variables are often used when constructing this design. == Implementation == The design consists of three distinct sets of experimental runs: A factorial (perhaps fractional) design in the factors studied, each having two levels; A set of center points, experimental runs whose values of each factor are the medians of the values used in the factorial portion. This point is often replicated in order to improve the precision of the experiment; A set of axial points, experimental runs identical to the centre points except for one factor, which will take on values both below and above the median of the two factorial levels, and typically both outside their range. All factors are varied in this way. == Design matrix == The design matrix for a central composite design experiment involving k factors is derived from a matrix, d, containing the following three different parts corresponding to the three types


id: challenge-dechallenge-rechallenge-20260505-0
file: data/en.wikipedia.org/wiki/Challenge–dechallenge–rechallenge-0.md
category: reference
title: Challenge–dechallenge–rechallenge
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Challenge–dechallenge–rechallenge
date_saved: 2026-05-05T09:49:28.505082+00:00
instance: kb-cron
parent: challenge-dechallenge-rechallenge-20260505-0
summary:
Challenge–dechallenge–rechallenge (CDR) is a medical testing protocol in which a medicine or drug is administered, withdrawn, then re-administered, while being monitored for adverse effects at each stage. The protocol is used when statistical testing is inappropriate due to an idiosyncratic reaction by a specific individual, or a lack of sufficient test subjects and unit of analysis is the individual. During the dechallenge (withdrawal) phase, the medication is allowed to wash out of the system in order to determine what effect the medication is having on an individual. == Use in drug testing == CDR is one means of establishing the validity and benefits of medication in treating specific conditions as well as any adverse drug reactions. The Food and Drug Administration of the United States lists positive dechallenge reactions (an adverse event which disappears on withdrawal of the medication) as well as negative (an adverse event which continues after withdrawal), as well as positive rechallenge (symptoms re-occurring on re-administration) and negative rechallenge (failure of a symptom to re-occur after re-administration). It is one of the standard means of assessing adverse drug reactions in France. == Fluoxetine and suicide == Peter Breggin asserted that there was an association between fluoxetine (Prozac)


id: choice-set-20260505-0
file: data/en.wikipedia.org/wiki/Choice_set-0.md
category: reference
title: Choice set
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Choice_set
date_saved: 2026-05-05T09:49:29.753162+00:00
instance: kb-cron
parent: choice-set-20260505-0
summary:
A choice set is a finite collection of available options selected from a larger theoretical decision space. For example, a consumer has thousands of conceivable alternatives when purchasing a car, far more than they could reasonably be expected to evaluate. As such they will often narrow their search to only vehicles of a certain make, or within a specific price range. By reducing the choice set to a manageable number of alternatives, people are able to make complex decisions between theoretically infinite alternatives in a practical time frame. Choice sets are often used in psychological and market research to make data collection and evaluation more manageable, or to make direct comparisons between a specific set of choices. == Choice task == The respondent is asked a choice task. Usually this is which of the alternatives they prefer. In this example, the Choice task is 'forced'. An 'unforced' choice would allow the respondents to also select 'Neither'. The choice task is used as the dependent variable in the resulting choice model. == Example of a choice set == A choice set has the following elements: Alternatives: A number of hypothetical alternatives, Car A and Car B in this example. There may


id: civilization-s-waiting-room-20260505-0
file: data/en.wikipedia.org/wiki/Civilization's_Waiting_Room-0.md
category: reference
title: Civilization's Waiting Room
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Civilization's_Waiting_Room
date_saved: 2026-05-05T09:49:30.962781+00:00
instance: kb-cron
parent: civilization-s-waiting-room-20260505-0
summary:
Sivilisasjonens venterom (Norwegian for "Civilization's Waiting Room") was a research larp (live-action roleplaying game) held in Bergen in November 2021. It was designed to explore the potential of larps as a research methodology and as research dissemination, and was specifically intended to investigate ethical questions that arise when encountering new surveillance technologies. == Background == The project was funded by the Research Council of Norway as part of a scheme to increase the Norwegian impact of EU-funded research. The stated goal was to "create arenas where the general public can practice making ethical decisions about the use of new technologies, specifically machine vision technologies such as facial recognition, deepfakes and VR" The creative lead for the project was veteran larp developer Anita Myhre Andersen, working with Harald Misje, Jon Andreas Edland, Toril Mjelva Saatvedt, Sebastian Sjøvold and Eskil Mjelva Saatvedt. The researchers in the development team were Marianne Gunderson, Kristian A. Bjørkelo, and Jill Walker Rettberg, who had initiated the project. The larp drew upon the Nordic larp genre as well as on research on educational larping (Edu-larp) and larps as research tools. In a scholarly paper about Sivilisasjonens venterom, Malthe Stavning Erslev describes it as a research larp, which


id: clinical-study-design-20260505-0
file: data/en.wikipedia.org/wiki/Clinical_study_design-0.md
category: reference
title: Clinical study design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_study_design
date_saved: 2026-05-05T09:49:32.252147+00:00
instance: kb-cron
parent: clinical-study-design-20260505-0
summary:
Clinical study design is the formulation of clinical trials and other experiments, as well as observational studies, in medical research involving human beings and involving clinical aspects, including epidemiology . It is the design of experiments as applied to these fields. The goal of a clinical study is to assess the safety, efficacy, and / or the mechanism of action of an investigational medicinal product (IMP) or procedure, or new drug or device that is in development, but potentially not yet approved by a health authority (e.g. Food and Drug Administration). It can also be to investigate a drug, device or procedure that has already been approved but is still in need of further investigation, typically with respect to long-term effects or cost-effectiveness. Some of the considerations here are shared under the more general topic of design of experiments but there can be others, in particular related to patient confidentiality and medical ethics. == Outline of types of designs for clinical studies == === Treatment studies === Randomized controlled trial Blind trial Non-blind trial Adaptive clinical trial Platform Trials Nonrandomized trial (quasi-experiment) Interrupted time series design (measures on a sample or a series of samples from the same population are


id: clinical-trial-20260505-0
file: data/en.wikipedia.org/wiki/Clinical_trial-0.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietary choices, dietary supplements, and medical devices) and known interventions that warrant further study and comparison. Clinical trials generate data on dosage, safety and efficacy. They are conducted only after they have received health authority/ethics committee approval in the country where approval of the therapy is sought. These authorities are responsible for vetting the risk/benefit ratio of the trial—their approval does not mean the therapy is 'safe' or effective, only that the trial may be conducted. Depending on product type and development stage, investigators initially enroll volunteers or patients into small pilot studies, and subsequently conduct progressively larger scale comparative studies. Clinical trials can vary in size and cost, and they can involve a single research center or multiple centers, in one country or in multiple countries. Clinical study design aims to ensure the scientific validity and reproducibility of the results. Costs for clinical trials can range into the billions of dollars per approved drug, and the complete trial process to approval may require 7–15 years. The sponsor may be


id: clinical-trial-20260505-1
file: data/en.wikipedia.org/wiki/Clinical_trial-1.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
=== Trials of procedures === Similarly to drugs, medical or surgical procedures may be subjected to clinical trials, such as comparing different surgical approaches in treatment of fibroids for subfertility. However, when clinical trials are unethical or logistically impossible in the surgical setting, case-controlled studies will be replaced. === Patient and public involvement === Besides being participants in a clinical trial, members of the public can be actively collaborate with researchers in designing and conducting clinical research. This is known as patient and public involvement (PPI). Public involvement involves a working partnership between patients, caregivers, people with lived experience, and researchers to shape and influence what is researched and how. PPI can improve the quality of research and make it more relevant and accessible. People with current or past experience of illness can provide a different perspective than professionals and compliment their knowledge. Through their personal knowledge they can identify research topics that are relevant and important to those living with an illness or using a service. They can also help to make the research more grounded in the needs of the specific communities they are part of. Public contributors can also ensure that the research is presented in plain


id: clinical-trial-20260505-2
file: data/en.wikipedia.org/wiki/Clinical_trial-2.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
Ideas of Sir Ronald A. Fisher still play a role in clinical trials. While working for the Rothamsted experimental station in the field of agriculture, Fisher developed his Principles of experimental design in the 1920s as an accurate methodology for the proper design of experiments. Among his major ideas include the importance of randomization—the random assignment of individual elements (eg crops or patients) to different groups for the experiment; replication—to reduce uncertainty, measurements should be repeated and experiments replicated to identify sources of variation; blocking—to arrange experimental units into groups of units that are similar to each other, and thus reducing irrelevant sources of variation; use of factorial experiments—efficient at evaluating the effects and possible interactions of several independent factors. Of these, blocking and factorial design are seldom applied in clinical trials, because the experimental units are human subjects and there is typically only one independent intervention: the treatment. The British Medical Research Council officially recognized the importance of clinical trials from the 1930s. The council established the Therapeutic Trials Committee to advise and assist in the arrangement of properly controlled clinical trials on new products that seem likely on experimental grounds to have value in the treatment of disease.


id: clinical-trial-20260505-3
file: data/en.wikipedia.org/wiki/Clinical_trial-3.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
Clinical trials involving new drugs are commonly classified into five phases. Each phase of the drug approval process is treated as a separate clinical trial. The drug development process will normally proceed through phases I–IV over many years, frequently involving a decade or longer. If the drug successfully passes through phases I, II, and III, it will usually be approved by the national regulatory authority for use in the general population. Phase IV trials are performed after the newly approved drug, diagnostic or device is marketed, providing assessment about risks, benefits, or best uses. == Trial design == A fundamental distinction in evidence-based practice is between observational studies and randomized controlled trials. Types of observational studies in epidemiology, such as the cohort study and the case-control study, provide less compelling evidence than the randomized controlled trial. In observational studies, the investigators retrospectively assess associations between the treatments given to participants and their health status, with potential for considerable errors in design and interpretation. A randomized controlled trial can provide compelling evidence that the study treatment causes an effect on human health. Some phase II and most phase III drug trials are designed as randomized, double-blind, and placebo-controlled. Randomized: Each study


id: clinical-trial-20260505-4
file: data/en.wikipedia.org/wiki/Clinical_trial-4.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
==== Statistical power ==== In any clinical trial, the number of subjects, also called the sample size, has a large impact on the ability to reliably detect and measure the effects of the intervention. This ability is described as its "power", which must be calculated before initiating a study to figure out if the study is worth its costs. In general, a larger sample size increases the statistical power, also the cost. The statistical power estimates the ability of a trial to detect a difference of a particular size (or larger) between the treatment and control groups. For example, a trial of a lipid-lowering drug versus placebo with 100 patients in each group might have a power of 0.90 to detect a difference between placebo and trial groups receiving dosage of 10 mg/dL or more, but only 0.70 to detect a difference of 6 mg/dL. === Placebo groups === Merely giving a treatment can have nonspecific effects. These are controlled for by the inclusion of patients who receive only a placebo. Subjects are assigned randomly without informing them to which group they belonged. Many trials are doubled-blinded so that researchers do not know to which group a subject is assigned.


id: clinical-trial-20260505-5
file: data/en.wikipedia.org/wiki/Clinical_trial-5.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
Clinical trials designed by a local investigator, and (in the US) federally funded clinical trials, are almost always administered by the researcher who designed the study and applied for the grant. Small-scale device studies may be administered by the sponsoring company. Clinical trials of new drugs are usually administered by a contract research organization (CRO) hired by the sponsoring company. The sponsor provides the drug and medical oversight. A CRO is contracted to perform all the administrative work on a clinical trial. For phases II–IV the CRO recruits participating researchers, trains them, provides them with supplies, coordinates study administration and data collection, sets up meetings, monitors the sites for compliance with the clinical protocol, and ensures the sponsor receives data from every site. Specialist site management organizations can also be hired to coordinate with the CRO to ensure rapid IRB/IEC approval and faster site initiation and patient recruitment. Phase I clinical trials of new medicines are often conducted in a specialist clinical trial clinic, with dedicated pharmacologists, where the subjects can be observed by full-time staff. These clinics are often run by a CRO which specialises in these studies. At a participating site, one or more research assistants (often nurses)


id: clinical-trial-20260505-6
file: data/en.wikipedia.org/wiki/Clinical_trial-6.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
A clinical trial produces data that could reveal quantitative differences between two or more interventions; statistical analyses are used to determine whether such differences are true, result from chance, or are the same as no treatment (placebo). Data from a clinical trial accumulate gradually over the trial duration, extending from months to years. Accordingly, results for participants recruited early in the study become available for analysis while subjects are still being assigned to treatment groups in the trial. Early analysis may allow the emerging evidence to assist decisions about whether to stop the study, or to reassign participants to the more successful segment of the trial. Investigators may also want to stop a trial when data analysis shows no treatment effect. == Ethical aspects == Clinical trials are closely supervised by appropriate regulatory authorities. All studies involving a medical or therapeutic intervention on patients must be approved by a supervising ethics committee before permission is granted to run the trial. The local ethics committee has discretion on how it will supervise noninterventional studies (observational studies or those using already collected data). In the US, this body is called the Institutional Review Board (IRB); in the EU, they are called Ethics


id: clinical-trial-20260505-7
file: data/en.wikipedia.org/wiki/Clinical_trial-7.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
=== During public health crisis === Conducting clinical trials of vaccines during epidemics and pandemics is subject to ethical concerns. For diseases with high mortality rates like Ebola, assigning individuals to a placebo or control group can be viewed as a death sentence. In response to ethical concerns regarding clinical research during epidemics, the National Academy of Medicine authored a report identifying seven ethical and scientific considerations. These considerations are: === Pregnant women and children === Pregnant women and children are typically excluded from clinical trials as vulnerable populations, though the data to support excluding them is not robust. By excluding them from clinical trials, information about the safety and effectiveness of therapies for these populations is often lacking. During the early history of the HIV/AIDS epidemic, a scientist noted that by excluding these groups from potentially life-saving treatment, they were being "protected to death". Projects such as Research Ethics for Vaccines, Epidemics, and New Technologies (PREVENT) have advocated for the ethical inclusion of pregnant women in vaccine trials. Inclusion of children in clinical trials has additional moral considerations, as children lack decision-making autonomy. Trials in the past had been criticized for using hospitalized children or orphans; these ethical concerns


id: clinical-trial-20260505-8
file: data/en.wikipedia.org/wiki/Clinical_trial-8.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
=== Institutional review boards (IRBs) === Approval by an Institutional Review Board (IRB), or Independent Ethics Committee (IEC), is necessary before all but the most informal research can begin. In commercial clinical trials, the study protocol is not approved by an IRB before the sponsor recruits sites to conduct the trial. However, the study protocol and procedures have been tailored to fit generic IRB submission requirements. In this case, and where there is no independent sponsor, each local site investigator submits the study protocol, the consent(s), the data collection forms, and supporting documentation to the local IRB. Universities and most hospitals have in-house IRBs. Other researchers (such as in walk-in clinics) use independent IRBs. The IRB scrutinizes the study both for medical safety and for protection of the patients involved in the study, before it allows the researcher to begin the study. It may require changes in study procedures or in the explanations given to the patient. A required yearly "continuing review" report from the investigator updates the IRB on the progress of the study and any new safety information related to the study. === Regulatory agencies === In the US, the Food and Drug Administration (FDA) can audit the


id: clinical-trial-20260505-9
file: data/en.wikipedia.org/wiki/Clinical_trial-9.md
category: reference
title: Clinical trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Clinical_trial
date_saved: 2026-05-05T09:49:33.517877+00:00
instance: kb-cron
parent: clinical-trial-20260505-0
summary:
production of the drug(s) or device(s) being evaluated staff salaries for the designers and administrators of the trial payments to the contract research organization, the site management organization (if used) and any outside consultants payments to local researchers and their staff for their time and effort in recruiting test subjects and collecting data for the sponsor the cost of study materials and the charges incurred to ship them communication with the local researchers, including on-site monitoring by the CRO before and (in some cases) multiple times during the study one or more investigator training meetings expense incurred by the local researchers, such as pharmacy fees, IRB fees and postage any payments to subjects enrolled in the trial the expense of treating a test subject who develops a medical condition caused by the study drug These expenses are incurred over several years. In the US, sponsors may receive a 50 percent tax credit for clinical trials conducted on drugs being developed for the treatment of orphan diseases. National health agencies, such as the US National Institutes of Health, offer grants to investigators who design clinical trials that attempt to answer research questions of interest to the agency. In these cases, the


id: cluster-randomised-controlled-trial-20260505-0
file: data/en.wikipedia.org/wiki/Cluster-randomised_controlled_trial-0.md
category: reference
title: Cluster-randomised controlled trial
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cluster-randomised_controlled_trial
date_saved: 2026-05-05T09:49:34.771792+00:00
instance: kb-cron
parent: cluster-randomised-controlled-trial-20260505-0
summary:
A cluster-randomised controlled trial (cRCT, CRCT) is a type of randomised controlled trial in which groups of subjects (as opposed to individual subjects) are randomised. Cluster randomised controlled trials are also known as cluster-randomised trials, group-randomised trials, and place-randomized trials. Cluster-randomised controlled trials are used when there is a strong reason for randomising treatment and control groups over randomising participants. == Prevalence == A 2004 bibliometric study documented an increasing number of publications in the medical literature on cluster-randomised controlled trials since the 1980s. == Advantages == Advantages of cluster-randomised controlled trials over individually randomised controlled trials include: The ability to study interventions that cannot be directed toward selected individuals (e.g., a radio show about lifestyle changes) and the ability to control for "contamination" across individuals (e.g., one individual's changing behaviors may influence another individual to do so). Reduced cost in running a survey. For example, when wanting to survey households, it could often be cheaper to choose street blocks and survey all the houses there in order to reduce the cost of traveling for the people conducting the survey. Sometimes due to data availability, it is only possible to do cluster sampling. For example, if wanting to survey households,


id: code-break-procedure-20260505-0
file: data/en.wikipedia.org/wiki/Code-break_procedure-0.md
category: reference
title: Code-break procedure
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Code-break_procedure
date_saved: 2026-05-05T09:49:36.054406+00:00
instance: kb-cron
parent: code-break-procedure-20260505-0
summary:
A code-break procedure is a set of rules which determine when planned unblinding should occur in a blinded experiment. FDA guidelines recommend that sponsors of blinded trials include a code-break procedure in their standard operating procedure. A code-break procedure should only allow a participant to be unblinded before the conclusion of a trial in the event of an emergency. Code-break usually refers to the unmasking of treatment allocation, but can refer to any form of unblinding. Traditionally, each patient's treatment allocation data was stored in a sealed envelopes, which was to be opened to break code. However, this system is prone to abuse. Reports of researchers opening envelopes prematurely or holding the envelopes up to lights to determine their contents has led some researchers to say that the use of sealed envelopes is no longer acceptable. As of 2016, sealed envelopes were still in use in some clinical trials. Modern clinical trials usually store this information in computer files. == See also == Sealedenvelope.com – a provider of code-break services == References ==


id: combinatorial-design-20260505-0
file: data/en.wikipedia.org/wiki/Combinatorial_design-0.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids. Combinatorial design theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including finite geometry, tournament scheduling, lotteries, mathematical chemistry, mathematical biology, algorithm design and analysis, networking, group testing and cryptography. == Example == Given a certain number n of people, is it possible to assign them to sets so that each person is in at least one set, each pair of people is in exactly one set together, every two sets have exactly one person in common, and


id: combinatorial-design-20260505-1
file: data/en.wikipedia.org/wiki/Combinatorial_design-1.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
A balanced incomplete block design or BIBD (usually called for short a block design) is a collection B of b subsets (called blocks) of a finite set X of v elements, such that any element of X is contained in the same number r of blocks, every block has the same number k of elements, and each pair of distinct elements appear together in the same number λ of blocks. BIBDs are also known as 2-designs and are often denoted as 2-(v,k,λ) designs. As an example, when λ = 1 and b = v, we have a projective plane: X is the point set of the plane and the blocks are the lines. A symmetric balanced incomplete block design or SBIBD is a BIBD in which v = b (the number of points equals the number of blocks). They are the single most important and well studied subclass of BIBDs. Projective planes, biplanes and Hadamard 2-designs are all SBIBDs. They are of particular interest since they are the extremal examples of Fisher's inequality (b ≥ v). A resolvable BIBD is a BIBD whose blocks can be partitioned into sets (called parallel classes), each of which forms a partition of the


id: combinatorial-design-20260505-2
file: data/en.wikipedia.org/wiki/Combinatorial_design-2.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
== Other combinatorial designs == The Handbook of Combinatorial Designs (Colbourn & Dinitz 2007) has, amongst others, 65 chapters, each devoted to a combinatorial design other than those given above. A partial listing is given below: Association schemes A balanced ternary design BTD(V, B; ρ1, ρ2, R; K, Λ) is an arrangement of V elements into B multisets (blocks), each of cardinality K (K ≤ V), satisfying: Each element appears R = ρ1 + 2ρ2 times altogether, with multiplicity one in exactly ρ1 blocks and multiplicity two in exactly ρ2 blocks. Every pair of distinct elements appears Λ times (counted with multiplicity); that is, if mvb is the multiplicity of the element v in block b, then for every pair of distinct elements v and w, ∑ b = 1 B m v b m w b = Λ {\displaystyle \sum _{b=1}^{B}m_{vb}m_{wb}=\Lambda } . For example, one of the only two nonisomorphic BTD(4,8;2,3,8;4,6)s (blocks are columns) is: The incidence matrix of a BTD (where the entries are the multiplicities of the elements in the blocks) can be used to form a ternary error-correcting code analogous to the way binary codes are formed from the incidence matrices of BIBDs. A balanced


id: combinatorial-design-20260505-3
file: data/en.wikipedia.org/wiki/Combinatorial_design-3.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
An H(2n − 1, 2n) is a Room square of side 2n − 1, and thus the Howell designs generalize the concept of Room squares. The pairs of symbols in the cells of a Howell design can be thought of as the edges of an s regular graph on 2n vertices, called the underlying graph of the Howell design. Cyclic Howell designs are used as Howell movements in duplicate bridge tournaments. The rows of the design represent the rounds, the columns represent the boards, and the diagonals represent the tables. Linear spaces An (n,k,p,t)-lotto design is an n-set V of elements together with a set β of k-element subsets of V (blocks), so that for any p-subset P of V, there is a block B in β for which |P ∩ B | ≥ t. L(n,k,p,t) denotes the smallest number of blocks in any (n,k,p,t)-lotto design. The following is a (7,5,4,3)-lotto design with the smallest possible number of blocks: {1,2,3,4,7} {1,2,5,6,7} {3,4,5,6,7}. Lotto designs model any lottery that is run in the following way: Individuals purchase tickets consisting of k numbers chosen from a set of n numbers. At a certain point the sale of tickets is stopped and a


id: combinatorial-design-20260505-4
file: data/en.wikipedia.org/wiki/Combinatorial_design-4.md
category: reference
title: Combinatorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorial_design
date_saved: 2026-05-05T09:49:37.423591+00:00
instance: kb-cron
parent: combinatorial-design-20260505-0
summary:
A tuscan square on n symbols is equivalent to a decomposition of the complete graph with n vertices into n hamiltonian directed paths. In a sequence of visual impressions, one flash card may have some effect on the impression given by the next. This bias can be cancelled by using n sequences corresponding to the rows of an n × n tuscan-1 square. A t-wise balanced design (or t BD) of type t − (v,K,λ) is a v-set X together with a family of subsets of X (called blocks) whose sizes are in the set K, such that every t-subset of distinct elements of X is contained in exactly λ blocks. If K is a set of positive integers strictly between t and v, then the t BD is proper. If all the k-subsets of X for some k are blocks, the t BD is a trivial design. Notice that in the following example of a 3-{12,{4,6},1) design based on the set X = {1,2,...,12}, some pairs appear four times (such as 1,2) while others appear five times (6,12 for instance). 1 2 3 4 5 6 1 2 7 8 1 2 9 11 1 2 10 12 3


id: combinatorics-of-experimental-design-20260505-0
file: data/en.wikipedia.org/wiki/Combinatorics_of_Experimental_Design-0.md
category: reference
title: Combinatorics of Experimental Design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Combinatorics_of_Experimental_Design
date_saved: 2026-05-05T09:49:38.636786+00:00
instance: kb-cron
parent: combinatorics-of-experimental-design-20260505-0
summary:
Combinatorics of Experimental Design is a textbook on the design of experiments, a subject that connects applications in statistics to the theory of combinatorial mathematics. It was written by mathematician Anne Penfold Street and her daughter, statistician Deborah Street, and published in 1987 by the Oxford University Press under their Clarendon Press imprint. == Topics == The book has 15 chapters. Its introductory chapter covers the history and applications of experimental designs, it has five chapters on balanced incomplete block designs and their existence, and three on Latin squares and mutually orthogonal Latin squares. Other chapters cover resolvable block designs, finite geometry, symmetric and asymmetric factorial designs, and partially balanced incomplete block designs. After this standard material, the remaining two chapters cover less-standard material. The penultimate chapter covers miscellaneous types of designs including circular block designs, incomplete Latin squares, and serially balanced sequences. The final chapter describes specialized designs for agricultural applications. The coverage of the topics in the book includes examples, clearly written proofs, historical references, and exercises for students. == Audience and reception == Although intended as an advanced undergraduate textbook, this book can also be used as a graduate text, or as a reference for researchers. Its


id: completely-randomized-design-20260505-0
file: data/en.wikipedia.org/wiki/Completely_randomized_design-0.md
category: reference
title: Completely randomized design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Completely_randomized_design
date_saved: 2026-05-05T09:49:39.957288+00:00
instance: kb-cron
parent: completely-randomized-design-20260505-0
summary:
In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account. This article describes completely randomized designs that have one primary factor. The experiment compares the values of a response variable based on the different levels of that primary factor. For completely randomized designs, the levels of the primary factor are randomly assigned to the experimental units. == Randomization == To randomize is to determine the run sequence of the experimental units randomly. For example, if there are 3 levels of the primary factor with each level to be run 2 times, then there are 6! (where ! denotes factorial) possible run sequences (or ways to order the experimental trials). Because of the replication, the number of unique orderings is 90 (since 90 = 6!/(2!*2!*2!)). An example of an unrandomized design would be to always run 2 replications for the first level, then 2 for the second level, and finally 2 for the third level. To randomize the runs, one way would be to put 6 slips of paper in a box with 2 having level 1, 2 having level 2, and 2 having


id: computer-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Computer_experiment-0.md
category: reference
title: Computer experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Computer_experiment
date_saved: 2026-05-05T09:49:41.205376+00:00
instance: kb-cron
parent: computer-experiment-20260505-0
summary:
A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other similar disciplines. == Background == Computer simulations are constructed to emulate a physical system. Because these are meant to replicate some aspect of a system in detail, they often do not yield an analytic solution. Therefore, methods such as discrete event simulation or finite element solvers are used. A computer model is used to make inferences about the system it replicates. For example, climate models are often used because experimentation on an earth sized object is impossible. == Objectives == Computer experiments have been employed with many purposes in mind. Some of those include: Uncertainty quantification: Characterize the uncertainty present in a computer simulation arising from unknowns during the computer simulation's construction. Inverse problems: Discover the underlying properties of the system from the physical data. Bias correction: Use physical data to correct for bias in the simulation. Data assimilation: Combine multiple simulations and physical data sources into a complete predictive model. Systems design: Find inputs that result in optimal system performance measures. == Computer simulation modeling


id: confirmation-bias-20260505-0
file: data/en.wikipedia.org/wiki/Confirmation_bias-0.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Confirmation bias (also confirmatory bias, myside bias, or congeniality bias) is the tendency to search for, interpret, favor and recall information in a way that confirms or supports one's prior beliefs, values, or decisions. People display this bias when they select information that supports their views, ignoring contrary information or when they interpret ambiguous evidence as supporting their existing attitudes. The effect is strongest for desired outcomes, emotionally charged issues and deeply entrenched beliefs. Biased search for information, biased interpretation of this information and biased memory recall have been invoked to explain four specific effects: attitude polarization (when a disagreement becomes more extreme despite the different parties being exposed to the same evidence) belief perseverance (when beliefs persist after the evidence for them is shown to be false) the irrational primacy effect (a greater reliance on information encountered early in a series) illusory correlation (when people falsely perceive an association between two events or situations). A series of psychological experiments in the 1960s suggested that people are biased toward confirming their existing beliefs. Later work reinterpreted these results as a tendency to test ideas in a one-sided way, focusing on one possibility and ignoring alternatives. Explanations for the observed biases


id: confirmation-bias-20260505-1
file: data/en.wikipedia.org/wiki/Confirmation_bias-1.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Experiments have found repeatedly that people tend to test hypotheses in a one-sided way, by searching for evidence consistent with their current hypothesis. Rather than searching through all the relevant evidence, they phrase questions to receive an affirmative answer that supports their theory. They look for the consequences that they would expect if their hypothesis were true, rather than what would happen if it were false. For example, someone using yes/no questions to find a number they suspect to be the number 3 might ask, "Is it an odd number?" People prefer this type of question, called a "positive test", even when a negative test such as "Is it an even number?" would yield exactly the same information. However, this does not mean that people seek tests that guarantee a positive answer. In studies where subjects could select either such pseudo-tests or genuinely diagnostic ones, they favored the genuinely diagnostic. The preference for positive tests in itself is not a bias, since positive tests can be highly informative. However, in combination with other effects, this strategy can confirm existing beliefs or assumptions, independently of whether they are true. In real-world situations, evidence is often complex and mixed. For example, various


id: confirmation-bias-20260505-2
file: data/en.wikipedia.org/wiki/Confirmation_bias-2.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Confirmation biases are not limited to the collection of evidence. Even if two individuals have the same information, the way they interpret it can be biased. A team at Stanford University conducted an experiment involving participants who felt strongly about capital punishment, with half in favor and half against it. Each participant read descriptions of two studies: a comparison of U.S. states with and without the death penalty, and a comparison of murder rates in a state before and after the introduction of the death penalty. After reading a quick description of each study, the participants were asked whether their opinions had changed. Then, they read a more detailed account of each study's procedure and had to rate whether the research was well-conducted and convincing. In fact, the studies were fictional. Half the participants were told that one kind of study supported the deterrent effect and the other undermined it, while for other participants the conclusions were swapped. The participants, whether supporters or opponents, reported shifting their attitudes slightly in the direction of the first study they read. Once they read the more detailed descriptions of the two studies, they almost all returned to their original belief regardless of the


id: confirmation-bias-20260505-3
file: data/en.wikipedia.org/wiki/Confirmation_bias-3.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
=== Biased recall of information === People may remember evidence selectively to reinforce their expectations, even if they gather and interpret evidence in a neutral manner. This effect is called "selective recall", "confirmatory memory", or "access-biased memory". Psychological theories differ in their predictions about selective recall. Schema theory predicts that information matching prior expectations will be more easily stored and recalled than information that does not match. Some alternative approaches say that surprising information stands out and so is memorable. Predictions from both these theories have been confirmed in different experimental contexts, with no theory winning outright. In one study, participants read a profile of a woman which described a mix of introverted and extroverted behaviors. They later had to recall examples of her introversion and extroversion. One group was told this was to assess the woman for a job as a librarian, while a second group were told it was for a job in real estate sales. There was a significant difference between what these two groups recalled, with the "librarian" group recalling more examples of introversion and the "sales" groups recalling more extroverted behavior. A selective memory effect has also been shown in experiments that manipulate the desirability


id: confirmation-bias-20260505-4
file: data/en.wikipedia.org/wiki/Confirmation_bias-4.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Before psychological research on confirmation bias, the phenomenon had been observed throughout history. Beginning with the Greek historian Thucydides (c. 460 BC – c. 395 BC), who wrote of misguided reason in The Peloponnesian War; "... for it is a habit of mankind to entrust to careless hope what they long for, and to use sovereign reason to thrust aside what they do not fancy". Italian poet Dante Alighieri (1265–1321) noted it in the Divine Comedy, in which St. Thomas Aquinas cautions Dante upon meeting in Paradise, "opinion—hasty—often can incline to the wrong side, and then affection for one's own opinion binds, confines the mind". Ibn Khaldun noticed the same effect in his Muqaddimah: Untruth naturally afflicts historical information. There are various reasons that make this unavoidable. One of them is partisanship for opinions and schools. ... if the soul is infected with partisanship for a particular opinion or sect, it accepts without a moment's hesitation the information that is agreeable to it. Prejudice and partisanship obscure the critical faculty and preclude critical investigation. The result is that falsehoods are accepted and transmitted. In the Novum Organum, English philosopher and scientist Francis Bacon (1561–1626) noted that biased assessment of evidence


id: confirmation-bias-20260505-5
file: data/en.wikipedia.org/wiki/Confirmation_bias-5.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
== Information processing explanations == There are currently three main information processing explanations of confirmation bias, plus a recent addition. === Cognitive versus motivational === According to Robert MacCoun, most biased evidence processing occurs through a combination of "cold" (cognitive) and "hot" (motivated) mechanisms. Cognitive explanations for confirmation bias are based on limitations in people's ability to handle complex tasks, and the shortcuts, called heuristics, that they use. For example, people may judge the reliability of evidence by using the availability heuristic that is, how readily a particular idea comes to mind. It is also possible that people can only focus on one thought at a time, so find it difficult to test alternative hypotheses in parallel. Another heuristic is the positive test strategy identified by Klayman and Ha, in which people test a hypothesis by examining cases where they expect a property or event to occur. This heuristic avoids the difficult or impossible task of working out how diagnostic each possible question will be. However, it is not universally reliable, so people can overlook challenges to their existing beliefs. Motivational explanations involve an effect of desire on belief. It is known that people prefer positive thoughts over negative ones


id: confirmation-bias-20260505-6
file: data/en.wikipedia.org/wiki/Confirmation_bias-6.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
=== Optimal information acquisition === Recent research in economics has challenged the traditional view of confirmation bias as purely a cognitive flaw. Under conditions where acquiring and processing information is costly, seeking confirmatory evidence can actually be an optimal strategy. Instead of pursuing contrarian or disconfirming evidence, it may be more efficient to focus on sources likely to align with one's existing beliefs, given the constraints on time and resources. Economist Weijie Zhong has developed a model demonstrating that individuals who must make decisions under time pressure, and who face costs for obtaining more information, will often prefer confirmatory signals. According to this model, when individuals believe strongly in a certain hypothesis, they optimally seek information that confirms it, allowing them to build confidence more efficiently. If the expected confirmatory signals are not received, their confidence in the initial hypothesis will gradually decline, leading to belief updating. This approach shows that seeking confirmation is not necessarily biased but may be a rational allocation of limited attention and resources. == Real-world effects == === Social media === In social media, confirmation bias is amplified by the use of filter bubbles and echo chambers (or "algorithmic editing"), which displays to individuals only


id: confirmation-bias-20260505-7
file: data/en.wikipedia.org/wiki/Confirmation_bias-7.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
=== Medicine and health === Cognitive biases are important variables in clinical decision-making by medical general practitioners (GPs) and medical specialists. Two important ones are confirmation bias and the overlapping availability bias. A GP may make a diagnosis early on during an examination, and then seek confirming evidence rather than falsifying evidence. This cognitive error is partly caused by the availability of evidence about the supposed disorder being diagnosed. For example, the client may have mentioned the disorder, or the GP may have recently read a much-discussed paper about the disorder. The basis of this cognitive shortcut or heuristic (termed anchoring) is that the doctor does not consider multiple possibilities based on evidence, but prematurely latches on (or anchors to) a single cause. In emergency medicine, because of time pressure, there is a high density of decision-making, and shortcuts are frequently applied. The potential failure rate of these cognitive decisions needs to be managed by education about the 30 or more cognitive biases that can occur, so as to set in place proper debiasing strategies. Confirmation bias may also cause doctors to perform unnecessary medical procedures due to pressure from adamant patients. Mental disorders may be prone to misdiagnosis in


id: confirmation-bias-20260505-8
file: data/en.wikipedia.org/wiki/Confirmation_bias-8.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
=== Paranormal beliefs === One factor in the appeal of alleged psychic readings is that listeners apply a confirmation bias which fits the psychic's statements to their own lives. By making a large number of ambiguous statements in each sitting, the psychic gives the client more opportunities to find a match. This is one of the techniques of cold reading, with which a psychic can deliver a subjectively impressive reading without any prior information about the client. Investigator James Randi compared the transcript of a reading to the client's report of what the psychic had said, and found that the client showed a strong selective recall of the "hits". As a striking illustration of confirmation bias in the real world, Nickerson mentions numerological pyramidology: the practice of finding meaning in the proportions of the Egyptian pyramids. There are many different length measurements that can be made of, for example, the Great Pyramid of Giza and many ways to combine or manipulate them. Hence it is almost inevitable that people who look at these numbers selectively will find superficially impressive correspondences, for example with the dimensions of the Earth. === Recruitment and selection === Unconscious cognitive bias (including confirmation bias) in


id: confirmation-bias-20260505-9
file: data/en.wikipedia.org/wiki/Confirmation_bias-9.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
Confirmation biases provide one plausible explanation for the persistence of beliefs when the initial evidence for them is removed or when they have been sharply contradicted. This belief perseverance effect has been first demonstrated experimentally by Festinger, Riecken, and Schachter. These psychologists spent time with a cult whose members were convinced that the world would end on 21 December 1954. After the prediction failed, most believers still clung to their faith. Their book describing this research is aptly named When Prophecy Fails. The term belief perseverance, however, was coined in a series of experiments using what is called the "debriefing paradigm": participants read fake evidence for a hypothesis, their attitude change is measured, then the fakery is exposed in detail. Their attitudes are then measured once more to see if their belief returns to its previous level. A common finding is that at least some of the initial belief remains even after a full debriefing. In one experiment, participants had to distinguish between real and fake suicide notes. The feedback was random: some were told they had done well while others were told they had performed badly. Even after being fully debriefed, participants were still influenced by the feedback. They


id: confirmation-bias-20260505-10
file: data/en.wikipedia.org/wiki/Confirmation_bias-10.md
category: reference
title: Confirmation bias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confirmation_bias
date_saved: 2026-05-05T09:49:42.474584+00:00
instance: kb-cron
parent: confirmation-bias-20260505-0
summary:
== Further reading == Leavitt, Fred (2015), Dancing with absurdity: Your most cherished beliefs (and all your others) are probably wrong, Peter Lang Publishers, ISBN 978-1-4539-1490-8, OCLC 908685982 Stanovich, Keith (2009), What intelligence tests miss: The psychology of rational thought (Lay), New Haven (Connecticut): Yale University Press, ISBN 978-0-300-12385-2 Westen, Drew (2007), The political brain: The role of emotion in deciding the fate of the nation, PublicAffairs, ISBN 978-1-58648-425-5, OCLC 86117725 Meppelink, Corine S., Edith G. Smit, Marieke L. Fransen, and Nicola Diviani. "'I Was Right about Vaccination': Confirmation Bias and Health Literacy in Online Health Information Seeking." Journal of Health Communication 24, no. 2 (2019): 129–40. https://doi.org/10.1080/10810730.2019.1583701. Pearson, George David Hooke, and Silvia Knobloch-Westerwick. "Is the Confirmation Bias Bubble Larger Online? Pre-Election Confirmation Bias in Selective Exposure to Online versus Print Political Information." Mass Communication & Society 22, no. 4 (2019): 466–86. https://doi.org/10.1080/15205436.2019.1599956. == External links == Skeptic's Dictionary: confirmation bias – Robert T. Carroll Teaching about confirmation bias – class handout and instructor's notes by K.H. Grobman Confirmation bias at You Are Not So Smart Confirmation bias learning object – interactive number triples exercise by Rod McFarland for Simon Fraser University Brief summary of the 1979 Stanford assimilation


id: confounding-20260505-0
file: data/en.wikipedia.org/wiki/Confounding-0.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
In causal inference, confounding is a form of systematic error (or bias) that can distort estimates of causal effects in observational studies. A confounder is traditionally understood to be a variable that (1) independently predicts the outcome (or dependent variable), (2) is associated with the exposure (or independent variable), and (3) is not on the causal pathway between the exposure and the outcome. Failure to control for a confounder results in a spurious association between exposure and outcome. Confounding is a causal concept rather than a purely statistical one, and therefore cannot be fully described by correlations or associations alone. The presence of confounders helps explain why correlation does not imply causation, and why careful study design and analytical methods (such as randomization, statistical adjustment, or causal diagrams) are required to distinguish causal effects from spurious associations. Several notation systems and formal frameworks, such as causal directed acyclic graphs (DAGs), have been developed to represent and detect confounding, making it possible to identify when a variable must be controlled for in order to obtain an unbiased estimate of a causal effect. Confounders are threats to internal validity. == Definition == Confounding is defined in terms of the data generating model.


id: confounding-20260505-1
file: data/en.wikipedia.org/wiki/Confounding-1.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
because the observational quantity contains information about the correlation between X and Z, and the interventional quantity does not (since X is not correlated with Z in a randomized experiment). It can be shown that, in cases where only observational data is available, an unbiased estimate of the desired quantity P ( y ∣ do ( x ) ) {\displaystyle P(y\mid {\text{do}}(x))} , can be obtained by "adjusting" for all confounding factors, namely, conditioning on their various values and averaging the result. In the case of a single confounder Z, this leads to the "adjustment formula": which gives an unbiased estimate for the causal effect of X on Y. The same adjustment formula works when there are multiple confounders except, in this case, the choice of a set Z of variables that would guarantee unbiased estimates must be done with caution. The criterion for a proper choice of variables is called the Back-Door and requires that the chosen set Z "blocks" (or intercepts) every path between X and Y that contains an arrow into X. Such sets are called "Back-Door admissible" and may include variables which are not common causes of X and Y, but merely proxies thereof. Returning to


id: confounding-20260505-2
file: data/en.wikipedia.org/wiki/Confounding-2.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
== Decreasing the potential for confounding == A reduction in the potential for the occurrence and effect of confounding factors can be obtained by increasing the types and numbers of comparisons performed in an analysis. If measures or manipulations of core constructs are confounded (i.e. operational or procedural confounds exist), subgroup analysis may not reveal problems in the analysis. Additionally, increasing the number of comparisons can create other problems (see multiple comparisons). Peer review is a process that can assist in reducing instances of confounding, either before study implementation or after analysis has occurred. Peer review relies on collective expertise within a discipline to identify potential weaknesses in study design and analysis, including ways in which results may depend on confounding. Similarly, replication can test for the robustness of findings from one study under alternative study conditions or alternative analyses (e.g., controlling for potential confounds not identified in the initial study). Confounding effects may be less likely to occur and act similarly at multiple times and locations. In selecting study sites, the environment can be characterized in detail at the study sites to ensure sites are ecologically similar and therefore less likely to have confounding variables. Lastly, the relationship between


id: confounding-20260505-3
file: data/en.wikipedia.org/wiki/Confounding-3.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
Case-control studies assign confounders to both groups, cases and controls, equally. For example, if somebody wanted to study the cause of myocardial infarct and thinks that the age is a probable confounding variable, each 67-year-old infarct patient will be matched with a healthy 67-year-old "control" person. In case-control studies, matched variables most often are the age and sex. Drawback: Case-control studies are feasible only when it is easy to find controls, i.e. persons whose status vis-à-vis all known potential confounding factors is the same as that of the case's patient: Suppose a case-control study attempts to find the cause of a given disease in a person who is 1) 45 years old, 2) African-American, 3) from Alaska, 4) an avid football player, 5) vegetarian, and 6) working in education. A theoretically perfect control would be a person who, in addition to not having the disease being investigated, matches all these characteristics and has no diseases that the patient does not also have—but finding such a control would be an enormous task. Cohort studies: A degree of matching is also possible and it is often done by only admitting certain age groups or a certain sex into the study population, creating


id: confounding-20260505-4
file: data/en.wikipedia.org/wiki/Confounding-4.md
category: reference
title: Confounding
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Confounding
date_saved: 2026-05-05T09:49:43.772485+00:00
instance: kb-cron
parent: confounding-20260505-0
summary:
== Criticism == Concerns have been raised that confounding in medical research can product false null results due to decreasing exposure reliability and increasing sibling-correlations. == Artifacts == Artifacts are variables that should have been systematically varied, either within or across studies, but that were accidentally held constant. Artifacts are thus threats to external validity. Artifacts are factors that covary with the treatment and the outcome. Campbell and Stanley identify several artifacts. The major threats to internal validity are history, maturation, testing, instrumentation, statistical regression, selection, experimental mortality, and selection-history interactions. One way to minimize the influence of artifacts is to use a pretest-posttest control group design. Within this design, "groups of people who are initially equivalent (at the pretest phase) are randomly assigned to receive the experimental treatment or a control condition and then assessed again after this differential experience (posttest phase)". Thus, any effects of artifacts are (ideally) equally distributed in participants in both the treatment and control conditions. == See also == Observational interpretation fallacy Anecdotal evidence – Evidence relying on personal testimony Causal inference – Branch of statistics Epidemiological method – Scientific method in the specific field Simpson's paradox – Error in statistical reasoning with groups


id: consecutive-case-series-20260505-0
file: data/en.wikipedia.org/wiki/Consecutive_case_series-0.md
category: reference
title: Consecutive case series
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Consecutive_case_series
date_saved: 2026-05-05T09:49:45.006467+00:00
instance: kb-cron
parent: consecutive-case-series-20260505-0
summary:
A consecutive case series is a type of case series clinical study that includes all eligible patients identified by the researchers during the study registration period. The patients are treated in the order in which they are identified. This type of study usually does not have a control group. For example, in Sugrue, et al. (2016), a consecutive case series design was used to determine trends in hand surgery research. == References == == External links == Consecutive case series entry in the public domain NCI Dictionary of Cancer Terms This article incorporates public domain material from Dictionary of Cancer Terms. U.S. National Cancer Institute.


id: consolidated-standards-of-reporting-trials-20260505-0
file: data/en.wikipedia.org/wiki/Consolidated_Standards_of_Reporting_Trials-0.md
category: reference
title: Consolidated Standards of Reporting Trials
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Consolidated_Standards_of_Reporting_Trials
date_saved: 2026-05-05T09:49:46.314658+00:00
instance: kb-cron
parent: consolidated-standards-of-reporting-trials-20260505-0
summary:
Consolidated Standards of Reporting Trials (CONSORT) encompasses various initiatives developed by the CONSORT Group to alleviate the problems arising from inadequate reporting of randomized controlled trials. It is part of the larger EQUATOR Network initiative to enhance the transparency and accuracy of reporting in research. == CONSORT Statement == The main product of the CONSORT Group is the CONSORT Statement, which is an evidence-based, minimum set of recommendations for reporting randomized trials. It offers a standard way for authors to prepare reports of trial findings, facilitating their complete and transparent reporting, reducing the influence of bias on their results, and aiding their critical appraisal and interpretation. The most recent version of the Statement—the CONSORT 2010 Statement—consists of a 25-item checklist and a participant flow diagram, along with some brief descriptive text. The checklist items focus on reporting how the trial was designed, analyzed, and interpreted; the flow diagram displays the progress of all participants through the trial. The Statement has been translated into several languages. The CONSORT "Explanation and Elaboration" document explains and illustrates the principles underlying the CONSORT Statement. It is strongly recommended that it be used in conjunction with the CONSORT Statement. Considered an evolving document, the CONSORT


id: controlling-for-a-variable-20260505-0
file: data/en.wikipedia.org/wiki/Controlling_for_a_variable-0.md
category: reference
title: Controlling for a variable
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Controlling_for_a_variable
date_saved: 2026-05-05T09:49:47.524084+00:00
instance: kb-cron
parent: controlling-for-a-variable-20260505-0
summary:
In causal models, controlling for a variable means binning data according to measured values of the variable. This is typically done so that the variable can no longer act as a confounder in, for example, an observational study or experiment. When estimating the effect of explanatory variables on an outcome by regression, controlled-for variables are included as inputs in order to separate their effects from the explanatory variables. A limitation of controlling for variables is that a causal model is needed to identify important confounders (backdoor criterion is used for the identification). Without having one, a possible confounder might remain unnoticed. Another associated problem is that if a variable which is not a real confounder is controlled for, it may in fact make other variables (possibly not taken into account) become confounders while they were not confounders before. In other cases, controlling for a non-confounding variable may cause underestimation of the true causal effect of the explanatory variables on an outcome (e.g. when controlling for a mediator or its descendant). Counterfactual reasoning mitigates the influence of confounders without this drawback. == Experiments == Experiments attempt to assess the effect of manipulating one or more independent variables on one or more


id: cooperative-pulling-paradigm-20260505-0
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-0.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
The cooperative pulling paradigm is an experimental design in which two or more animals pull rewards toward themselves via an apparatus that they cannot successfully operate alone. Researchers (ethologists, comparative psychologists, and evolutionary psychologists) use cooperative pulling experiments to try to understand how cooperation works and how and when it may have evolved. The type of apparatus used in cooperative pulling experiments can vary. Researcher Meredith Crawford, who invented the experimental paradigm in 1937, used a mechanism consisting of two ropes attached to a rolling platform that was too heavy to be pulled by a single chimpanzee. The standard apparatus is one in which a single string or rope is threaded through loops on a movable platform. If only one participant pulls the string, it comes loose and the platform can no longer be retrieved. Only by pulling together in coordination can the participants be successful; success by chance is highly unlikely. Some researchers have designed apparatus that involve handles instead of ropes. Although many animals retrieve rewards in their cooperative pulling tasks, the conclusions regarding cooperation are mixed and complex. Chimpanzees, bonobos, orangutans, capuchins, tamarins, wolves, elephants, ravens, and kea appear to understand the requirements of the task. For


id: cooperative-pulling-paradigm-20260505-1
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-1.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
=== Subjects === So far, fewer than twenty species have participated in cooperative pulling experiments: chimpanzees, bonobos, orangutans, capuchin monkeys, tamarins, macaques, humans, hyenas, wolves, dogs, elephants, otters, dolphins, rooks, ravens, parrots, and kea. Researchers have picked species that cooperate in the wild (e.g., capuchins), live in social structures (e.g., wolves), or have known cognitive abilities (e.g., orangutans). Most of the participating animals have been in human care at an animal research center; some lived semi-free at a sanctuary in their natural habitat. One study involved free animals (Barbary macaques) in the wild. === Conditions === To arrive at conclusions regarding cooperation, researchers have designed experiments with various conditions. ==== Delay ==== The first animal has access to the apparatus before the other one. If the animal does not wait for its partner this suggests a lack of understanding of the requirements for successful cooperation. === Recruitment === The subject recruits the partner (for example by opening a door) when the task requires cooperation. ==== Partner choice ==== The first animal gets to choose which animal from a pair it wants as a partner. In some cases individual animals from within a group can decide to join an animal already


id: cooperative-pulling-paradigm-20260505-2
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-2.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
=== Overview === Although many animals retrieve rewards in their cooperative pulling tasks, the conclusions regarding cooperation are mixed and complex. Some researchers have attributed successful cooperation to random simultaneous action, or to the simple reactive behavior of pulling the rope when it moves. Many trials with capuchins, hyenas, parrots and rooks led to failure because one partner pulled without the other present, suggesting a lack of understanding of cooperation. A few researchers have offered the possible explanation that animals may understand cooperation to some extent but simply can not suppress the desire to have food they see. But there is evidence that some species do have an understanding of cooperation and perform intentional coordination to achieve a goal. Specifically, chimpanzees, bonobos, orangutans, tamarins, capuchins, elephants, wolves, ravens, and kea appear to understand how cooperation works. Chimpanzees not only wait for a partner, but will actively solicit help when needed. They appear to recall previous outcomes to recruit the most effective partner. In a group setting, chimpanzees punish initial competitive behavior (taking food without pulling, displacing animals) such that eventually, after many trials, successful cooperation becomes the norm. Bonobos, which are social animals with higher tolerance levels, can outperform chimpanzees


id: cooperative-pulling-paradigm-20260505-3
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-3.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Similar mixed results, not matching the cooperative abilities observed in chimpanzees in the wild, were obtained in later studies by other researchers using a variety of experimental set-ups, including the loose-string task pioneered by Hirata. Povinelli and O'Neill, for example, found that trained chimpanzees were unable to teach naive chimpanzees to cooperate on a Crawford-like box-pulling task. The naive animals did not imitate the experts. Chalmeau and Gallo found only two chimpanzees consistently cooperating in their handle-pulling task, and this involved one ape holding his own handle and waiting for the other to pull his. They concluded that social factors and not limited cognitive abilities were the reason for lack of widespread success, as they observed dominant chimpanzees controlling the apparatus and preventing others from interacting. Melis, Hare, and Tomasello set up an experiment to control for such social factors. In a loose-string cooperative task without training they compared the ability of pairs of captive chimpanzees who in a non-cooperative setting were willing to share food with each other to pairs who were less inclined to do so. The results showed that food sharing was a good predictor for success in the cooperative pulling task. Melis, Hare, and Tomasello concluded


id: cooperative-pulling-paradigm-20260505-4
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-4.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Orangutans (Pongo pygmaeus) are tool-using apes that are mostly solitary. Chalmeau, Lardeux, Brandibas, and Gallo tested the cooperative capabilities of a pair of orangutans, using a device with handles. Only through simultaneous pulling could the pair retrieve a food reward. Without any training the orangutans succeeded in the first session. Over the course of 30 sessions, the apes succeeded more quickly, having learned to coordinate. Across trials the researchers found an increase in a sequence of actions that suggested understanding of cooperation: first looking at the partner; then if the partner holds or pulls the handle, starting to pull. The researchers also concluded that the orangutans learned a partner had to be present for success. For example, they observed that time spent alone at the apparatus decreased as the trials progressed. In some instances one orangutan pushed the other towards the free handle, soliciting cooperation. The researchers observed an asymmetry: one ape did all the monitoring and coordinating, the other one seemed to simply pull if the first one was present. Rewards did not have to be shared equally for success to appear, as one orangutan took 92% of all food. This ape anticipated the falling of food and stuck


id: cooperative-pulling-paradigm-20260505-5
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-5.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Molesti and Majolo tested a group of wild Barbary macaques (Macaca sylvanus) in Morocco to see if they would cooperate, and if so, what determined their partner choice. Macaques live in complex social environments and are relatively tolerant socially. After solo training, the researchers presented a loose-string apparatus for the cooperative task, which the animals were free to use. Most animals that passed solo training were successful in spontaneously cooperating to obtain food (22 out of 26). More than half the pairs that chose to cooperate were juvenile-adult pairs. More than two monkeys pulling was never observed; stealing food from a partner was rare. After a first successful cooperation, they were more likely to pull when a partner was directly available, but this was not always the case. Molesti and Majolo did not rule out that pulling while no one held or pulled the other end of the rope was simply a signal to actively recruit a potential partner. The researchers randomly introduced control trials in which the solo apparatus was set up as well. The macaques preferred to get the food alone when a partner was not needed during the control. The extent to which a monkey tolerated another


id: cooperative-pulling-paradigm-20260505-6
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-6.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Ostojić and Clayton administered the loose-string cooperation task to domestic dogs (Canis familiaris). Pet dogs first were given a solo task in which the string ends were close enough for one dog to pull at both. Then they were given a transfer test to assess if they could generalize their newly learned rule to novel situations. Finally, the joint task was administered. Dog pairs always came from the same household. In half of the joint tasks one of the pair of dogs was shortly delayed by an obstacle course. All dogs that learned to master the solo task solved the joint task within 60 trials. In the delayed condition, the not-delayed dog waited before pulling most of the time, but only for a few seconds. The researchers also tested dog–human pairs, again in delayed and not-delayed conditions. Dogs were equally successful when working with humans in the non-delayed condition, but far less successful when they had to wait for the human, who on average arrived with a 13-seconds longer delay than the delayed dog in the dog–dog trials. Ostojić and Clayton concluded that inhibiting the necessary action was not easy for dogs. They ruled out that dogs simply went for


id: cooperative-pulling-paradigm-20260505-7
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-7.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Elephants have a complex social structure and large brains that enable them to solve many problems. Their size and strength do not make them easy candidates for experiments. Researchers Plotnik, Lair, Suphachoksahakun, and de Waal adapted the apparatus and task to elephant requirements. They trained captive Asian elephants (Elephas maximus) to use a rope to pull a sliding platform with food on it towards themselves. Once the elephants managed this solo task, the researchers introduced a loose-string apparatus by threading the rope around the platform. At first, two elephants were released simultaneously to walk side by side in two lanes to the two loose ends of the rope. Using their trunks the animals coordinated their actions and retrieved the food. At this stage they could simply be applying a 'see the rope, pull the rope' strategy. To see whether they understood the requirements of the task the researchers introduced a delay for one elephant, initially of 5 seconds and ultimately of 45 seconds. At first the lead elephant failed to retrieve the food but was soon seen to wait for a partner. Across 60 trials the first elephant waited for the second one before pulling in most cases. In a


id: cooperative-pulling-paradigm-20260505-8
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-8.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Rooks (Corvus frugilegus) are large-brained members of the bird family Corvidae. They live in big groups and have a high level of social tolerance. Researchers Seed, Clayton, and Emery set up a loose-string experiment with eight captive rooks. They were first trained in a solo task, with the string ends placed at 1 cm, 3 cm and ultimately 6 cm apart (0.4, 1.2, and 2.4 inch respectively). A pair's willingness to share food was then tested, and was found to differ somewhat between pairs, although food was rarely monopolized by a dominant bird. In the cooperative task, all pairs were able to solve the cooperation problem and retrieve food; two pairs managed this in their first session. Food sharing was a good predictor for successful cooperation. In a subsequent delay test, where one partner had access to the apparatus first, all rooks pulled the string without waiting for their partner to enter the test area in the majority of trials. In a second variant, birds were given a choice between a platform they could operate successfully alone and one that required a pulling partner. When tested alone, four of the six rooks showed no significant preference for either platform. Seed,


id: cooperative-pulling-paradigm-20260505-9
file: data/en.wikipedia.org/wiki/Cooperative_pulling_paradigm-9.md
category: reference
title: Cooperative pulling paradigm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cooperative_pulling_paradigm
date_saved: 2026-05-05T09:49:48.882099+00:00
instance: kb-cron
parent: cooperative-pulling-paradigm-20260505-0
summary:
Kea (Nestor notabilis), parrots native to New Zealand, are a distant relative of the grey parrot. They live in complex social groups and do well on cognitive tests. Heaney, Gray, and Taylor gave four captive kea a series of cooperative loose-string tasks. After solo training and shaping with string ends increasingly further apart, two birds were released simultaneously in a joint loose-string task. Both pairs did very well, one pair failing only 5 in 60 trials. Shaping was then used in a delay task, with the partner released after one second, then two, and gradually up to 25 seconds later than the first bird. The birds managed to wait for a partner between 74% and 91% of test trials, including success at 65 seconds delay, longer than any other animal of any species had been tested for. To assess if this success could be explained by the learning of a combination of cues, such as seeing a partner while feeling tension on the string, or by a proper understanding of cooperation, the researchers randomly gave the kea a set-up they could solve alone or one in which they needed to cooperate with a delayed partner. Three of the four kea


id: crossover-study-20260505-0
file: data/en.wikipedia.org/wiki/Crossover_study-0.md
category: reference
title: Crossover study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Crossover_study
date_saved: 2026-05-05T09:49:50.139679+00:00
instance: kb-cron
parent: crossover-study-20260505-0
summary:
In medicine, a crossover study or crossover trial is a longitudinal study in which subjects receive a sequence of different treatments (or exposures). While crossover studies can be observational studies, many important crossover studies are controlled experiments, which are discussed in this article. Crossover designs are common for experiments in many scientific disciplines, for example psychology, pharmaceutical science, and medicine. Randomized, controlled crossover experiments are especially important in health care. In a randomized clinical trial, the subjects are randomly assigned to different arms of the study which receive different treatments. When the trial has a repeated measures design, the same measures are collected multiple times for each subject. A crossover trial has a repeated measures design in which each patient is assigned to a sequence of two or more treatments, of which one may be a standard treatment or a placebo. Nearly all crossover are designed to have "balance", whereby all subjects receive the same number of treatments and participate for the same number of periods. In most crossover trials each subject receives all treatments, in a random order. Statisticians suggest that designs should have four periods, which is more efficient than the two-period design, even if the study must


id: data-collection-20260505-0
file: data/en.wikipedia.org/wiki/Data_collection-0.md
category: reference
title: Data collection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Data_collection
date_saved: 2026-05-05T09:49:51.362272+00:00
instance: kb-cron
parent: data-collection-20260505-0
summary:
Data collection or data gathering is the process of gathering and measuring information on targeted variables in an established system, which then enables one to answer relevant questions and evaluate outcomes. Data collection is a research component in all study fields, including physical and social sciences, humanities, and business. While methods vary by discipline, the emphasis on ensuring accurate and honest collection remains the same. The goal for all data collection is to capture evidence that allows data analysis to lead to the formulation of credible answers to the questions that have been posed. Regardless of the field of or preference for defining data (quantitative or qualitative), accurate data collection is essential to maintain research integrity. The selection of appropriate data collection instruments (existing, modified, or newly developed) and delineated instructions for their correct use reduce the likelihood of errors. == Methodology == Data collection and validation consist of four steps when it involves taking a census and seven steps when it involves sampling. A formal data collection process is necessary, as it ensures that the data gathered are both defined and accurate. This way, subsequent decisions based on arguments embodied in the findings are made using valid data. The


id: data-dredging-20260505-0
file: data/en.wikipedia.org/wiki/Data_dredging-0.md
category: reference
title: Data dredging
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Data_dredging
date_saved: 2026-05-05T09:49:52.727198+00:00
instance: kb-cron
parent: data-dredging-20260505-0
summary:
Data dredging, also known as data snooping or p-hacking, is the misuse of data analysis to find patterns in data that can be presented as statistically significant, thus dramatically increasing and understating the risk of false positives. This is done by performing many statistical tests on the data and only reporting those that come back with significant results. Thus data dredging is also often a misused or misapplied form of data mining. The process of data dredging involves testing multiple hypotheses using a single data set by exhaustively searching—perhaps for combinations of variables that might show a correlation, and perhaps for groups of cases or observations that show differences in their mean or in their breakdown by some other variable. Conventional tests of statistical significance are based on the probability that a particular result would arise if chance alone were at work, and necessarily accept some risk of mistaken conclusions of a certain type (mistaken rejections of the null hypothesis). This level of risk is called the significance. When large numbers of tests are performed, some produce false results of this type; hence 5% of randomly chosen hypotheses might be (erroneously) reported to be statistically significant at the 5% significance


id: data-dredging-20260505-1
file: data/en.wikipedia.org/wiki/Data_dredging-1.md
category: reference
title: Data dredging
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Data_dredging
date_saved: 2026-05-05T09:49:52.727198+00:00
instance: kb-cron
parent: data-dredging-20260505-0
summary:
=== Post-hoc grouping === If a dataset contains multiple features, then one or more of the features can be used as grouping, and potentially create a statistically significant result. For example, if a dataset of patients records their age and sex, then a researcher can consider grouping them by age and check if the illness recovery rate is correlated with age. If it does not work, then the researcher might check if it correlates with sex. If not, then perhaps it correlates with age after controlling for sex, etc. The number of possible groupings grows exponentially with the number of features. === Hypothesis suggested by non-representative data === Suppose that a study of a random sample of people includes exactly two people with a birthday of August 7: Mary and John. Someone engaged in data dredging might try to find additional similarities between Mary and John. By going through hundreds or thousands of potential similarities between the two, each having a low probability of being true, an unusual similarity can almost certainly be found. Perhaps John and Mary are the only two people in the study who switched minors three times in college. A hypothesis, biased by data dredging, could


id: data-dredging-20260505-2
file: data/en.wikipedia.org/wiki/Data_dredging-2.md
category: reference
title: Data dredging
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Data_dredging
date_saved: 2026-05-05T09:49:52.727198+00:00
instance: kb-cron
parent: data-dredging-20260505-0
summary:
== Appearance in media == One example is the chocolate weight loss hoax study conducted by journalist John Bohannon, who explained publicly in a Gizmodo article that the study was deliberately conducted fraudulently as a social experiment. This study was widespread in many media outlets around 2015, with many people believing the claim that eating a chocolate bar every day would cause them to lose weight, against their better judgement. This study was published in the Institute of Diet and Health. According to Bohannon, to reduce the p-value to below 0.05, taking 18 different variables into consideration when testing was crucial. == Remedies == While looking for patterns in data is legitimate, applying a statistical test of significance or hypothesis test to the same data until a pattern emerges is prone to abuse. One way to construct hypotheses while avoiding data dredging is to conduct randomized out-of-sample tests. The researcher collects a data set, then randomly partitions it into two subsets, A and B. Only one subset—say, subset A—is examined for creating hypotheses. Once a hypothesis is formulated, it must be tested on subset B, which was not used to construct the hypothesis. Only where B also supports such a


id: dependent-and-independent-variables-20260505-0
file: data/en.wikipedia.org/wiki/Dependent_and_independent_variables-0.md
category: reference
title: Dependent and independent variables
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Dependent_and_independent_variables
date_saved: 2026-05-05T09:49:55.288751+00:00
instance: kb-cron
parent: dependent-and-independent-variables-20260505-0
summary:
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are the outcome of the test they depend on, by some law or rule (e.g., by a mathematical function). Independent variables, on the other hand, are not seen as depending on any other variable in the scope of the experiment in question. Rather, they are controlled by the experimenter. == In pure mathematics == In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number or set of numbers). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is x, and the most common symbol for the output is y; the function itself is commonly written y = f(x). It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and


id: dependent-and-independent-variables-20260505-1
file: data/en.wikipedia.org/wiki/Dependent_and_independent_variables-1.md
category: reference
title: Dependent and independent variables
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Dependent_and_independent_variables
date_saved: 2026-05-05T09:49:55.288751+00:00
instance: kb-cron
parent: dependent-and-independent-variables-20260505-0
summary:
== Other variables == A variable may be thought to alter the dependent or independent variables, but may not actually be the focus of the experiment. So that the variable will be kept constant or monitored to try to minimize its effect on the experiment. Such variables may be designated as either a "controlled variable", "control variable", or "fixed variable". Extraneous variables are candidate independent variables which may be included in a regression analysis to aid a researcher with accurate response parameter estimation, prediction, and goodness of fit, but are not of substantive interest to the hypothesis under examination. For example, in a study examining the effect of post-secondary education on lifetime earnings, some extraneous variables might be gender, ethnicity, social class, genetics, intelligence, age, and so forth. A variable is extraneous only when it can be assumed (or shown) to influence the dependent variable. If included in a regression, it can improve the fit of the model. If it is excluded from the regression and if it has a non-zero covariance with one or more of the independent variables of interest, its omission will bias the regression's result for the effect of that independent variable of interest. This effect


id: design-effect-20260505-0
file: data/en.wikipedia.org/wiki/Design_effect-0.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
In survey research, the design effect is a number that shows how well a sample of people may represent a larger group of people for a specific measure of interest (such as the mean). This is important when the sample comes from a sampling method that is different than just picking people using a simple random sample. The design effect is a positive real number, represented by the symbol Deff {\displaystyle {\text{Deff}}} . If Deff = 1 {\displaystyle {\text{Deff}}=1} , then the sample was selected in a way that is just as good as if people were picked randomly. When Deff > 1 {\displaystyle {\text{Deff}}>1} , then inference from the data collected is not as accurate as it could have been if people were picked randomly. When researchers use complicated methods to pick their sample, they use the design effect to check and adjust their results. It may also be used when planning a study in order to determine the sample size. == Introduction == In survey methodology, the design effect (generally denoted as Deff {\displaystyle {\text{Deff}}} , D eff {\displaystyle D_{\text{eff}}} , or D eft 2 {\displaystyle D_{\text{eft}}^{2}} ) is a measure of the expected impact of a sampling


id: design-effect-20260505-1
file: data/en.wikipedia.org/wiki/Design_effect-1.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
The numerator represents the actual variance for an estimator of a parameter ( θ ^ w {\displaystyle {\hat {\theta }}_{w}} ) under a given sampling design p {\displaystyle p} ; The denominator represents the variance assuming the same sample size, but if the sample were obtained using the estimator for simple random sampling without replacement ( θ ^ S R S W O R {\displaystyle {\hat {\theta }}_{SRSWOR}} ). So that: Deff p ( θ ^ ) = v a r ( θ ^ w ) v a r ( θ ^ S R S W O R ) {\displaystyle {\text{Deff}}_{p}({\hat {\theta }})={\frac {var({\hat {\theta }}_{w})}{var({\hat {\theta }}_{SRSWOR})}}} In other words, Deff {\displaystyle {\text{Deff}}} measures the extent to which the variance has increased (or, in some cases, decreased) because the sample was drawn and adjusted to a specific sampling design (e.g., using weights or other measures) compared to if the sample was from a simple random sample (without replacement). Notice how the definition of Deff {\displaystyle {\text{Deff}}} is based on parameters of the population that are often unknown, and that are hard to estimate directly. Specifically, the definition involves the variances of estimators under two different sampling designs, even though


id: design-effect-20260505-2
file: data/en.wikipedia.org/wiki/Design_effect-2.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
This quantity reflects what would be the sample size that is needed to achieve the current variance of the estimator (for some parameter) with the existing design, if the sample design (and its relevant parameter estimator) were based on a simple random sample. A related quantity is the effective sample size ratio (ESSR), which can be calculated by simply taking the inverse of Deff {\displaystyle {\text{Deff}}} (i.e., n eff n = 1 Deff {\displaystyle {\frac {n_{\text{eff}}}{n}}={\frac {1}{\text{Deff}}}} ). For example, let the design effect, for estimating the population mean based on some sampling design, be 2. If the sample size is 1,000, then the effective sample size will be 500. It means that the variance of the weighted mean based on 1,000 samples will be the same as that of a simple mean based on 500 samples obtained using a simple random sample. == The design effect for well-known sampling designs == === The design effect depends on sampling design and statistical adjustments === Different sampling designs and statistical adjustments may have substantially different impact on the bias and variance of estimators (such as the mean). An example of a design which can lead to estimation efficiency, compared to simple


id: design-effect-20260505-3
file: data/en.wikipedia.org/wiki/Design_effect-3.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
Disproportional sampling due to selection frame or procedure. This happens when a researcher deliberately over- or under-samples specific sub-populations or clusters. For example: In stratified sampling when units from some strata are known to have a larger variance than other strata. In such cases, the intention of the researcher may be to use this prior knowledge about the variance between strata in order to reduce the overall variance of an estimator of some population level parameter of interest (e.g., the mean). This can be achieved by a strategy known as optimum allocation, in which a stratum h {\displaystyle h} is over sampled proportional to higher standard deviation and lower sampling cost (i.e., f h ∝ S h C h {\displaystyle f_{h}\propto {\frac {S_{h}}{\sqrt {C_{h}}}}} , where S h {\displaystyle S_{h}} is the standard deviation of the outcome in h {\displaystyle h} , and C h {\displaystyle C_{h}} relates to the cost of recruiting one element from h {\displaystyle h} ). An example of an optimum allocation is Neyman's optimal allocation which, when cost is fixed for recruiting people from each stratum, the sample size is: n h = n W h S U h ∑ h W h S U


id: design-effect-20260505-4
file: data/en.wikipedia.org/wiki/Design_effect-4.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
Alternatively, when the sampling design is fully known (leading to some p h {\displaystyle p_{h}} probability of selection for some element from stratum h), and the non-response is measurable (i.e., we know that only r h {\displaystyle r_{h}} observations answered in stratum h), then an exactly known inverse probability weight can be calculated for each element i from stratum h using: w i = 1 p h r h {\displaystyle w_{i}={\frac {1}{p_{h}r_{h}}}} . Sometimes a statistical adjustment, such as post-stratification or raking, is used for estimating the selection probability. E.g., when comparing the sample we have with same target population, also known as matching to controls. The estimation process may be focused only on adjusting the existing population to an alternative population (for example, if trying to extrapolate from a panel drawn from several regions to an entire country). In such a case, the adjustment might be focused on some calibration factor c i {\displaystyle c_{i}} and the weights be calculated as w i = c i p h r h {\displaystyle w_{i}={\frac {c_{i}}{p_{h}r_{h}}}} . However, in other cases, both the under-coverage and non-response are all modeled as part of the statistical adjustment, which leads to an estimation of the


id: design-effect-20260505-5
file: data/en.wikipedia.org/wiki/Design_effect-5.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
==== "Design based" vs "model based" for describing properties of estimators ==== Adjusting for unequal probability selection through "individual case weights" (e.g. inverse probability weighting), yields various types of estimators for quantities of interest. Estimators such as Horvitz–Thompson estimator yield unbiased estimators (if the selection probabilities are indeed known, or approximately known), for total and the mean of the population. Deville and Särndal (1992) coined the term "calibration estimator" for estimators using weights such that they satisfy some condition, such as having the sum of weights equal the population size. And more generally, that the weighted sum of weights is equal some quantity of an auxiliary variable: ∑ w i x i = X {\displaystyle \sum w_{i}x_{i}=X} (e.g., that the sum of weighted ages of the respondents is equal to the population size in each age group). The two primary ways to argue about the properties of calibration estimators are: randomization based (or, sampling design based) - in this case, the weights ( w i {\displaystyle w_{i}} ) and values of the outcome of interest y i {\displaystyle y_{i}} that are measured in the sample are all treated as known. In this framework, there is variability in the (known) values


id: design-effect-20260505-6
file: data/en.wikipedia.org/wiki/Design_effect-6.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
Frequency weights are a basic type of weighting presented in introductory statistics courses. With these, each weight is an integer number that indicates the absolute frequency of an item in the sample. These are also sometimes termed repeat (or occurrence) weights. The specific value has an absolute meaning that is lost if the weights are transformed, such as when scaling. For example: if we have the numbers 10 and 20 with the frequency weights values of 2 and 3, then when "spreading" our data it is: 10,10, 20, 20, 20 (with weights of 1 to each of these items). Frequency weights includes the amount of information contained in a dataset, and thus allows things like creating unbiased weighted variance estimation using Bessel's correction. Notice that such weights are often random variables, since the specific number of items we will see from each value in the dataset is random. inverse-variance weighting, also known as analytic weights, is when each element is assigned a weight that is the inverse of its (known) variance. When all elements have the same expectancy, using such weights for calculating weighted averages has the least variance among all weighted averages. In the common formulation, these weights are


id: design-effect-20260505-7
file: data/en.wikipedia.org/wiki/Design_effect-7.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
Deff = n ∑ i = 1 n w i 2 ( ∑ i = 1 n w i ) 2 = 1 n ∑ i = 1 n w i 2 ( 1 n ∑ i = 1 n w i ) 2 = w 2 ¯ w ¯ 2 {\displaystyle {\text{Deff}}={\frac {n\sum _{i=1}^{n}w_{i}^{2}}{(\sum _{i=1}^{n}w_{i})^{2}}}={\frac {{\frac {1}{n}}\sum _{i=1}^{n}w_{i}^{2}}{\left({\frac {1}{n}}\sum _{i=1}^{n}w_{i}\right)^{2}}}={\frac {\overline {w^{2}}}{{\overline {w}}^{2}}}} This version of the formula is valid when one stratum had several observations taken from it (i.e., each having the same weight), or when there are just many strata were each one had one observation taken from it, but several of them had the same probability of selection. While the interpretation is slightly different, the calculation of the two scenarios comes out to be the same. When using Kish's design effect for unequal weights, you may use the following simplified formula for "Kish's Effective Sample Size" n eff = ( ∑ i = 1 n w i ) 2 ∑ i = 1 n w i 2 {\displaystyle n_{\text{eff}}={\frac {(\sum _{i=1}^{n}w_{i})^{2}}{\sum _{i=1}^{n}w_{i}^{2}}}} ===== Assumptions and proofs ===== The above formula, by Kish, gives the increase in the variance of the weighted mean based on "haphazard" weights.


id: design-effect-20260505-8
file: data/en.wikipedia.org/wiki/Design_effect-8.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
===== Relation to disproportionate stratified sampling ===== Kish's original definition compared the variance under some sampling design to the variance achieved through a simple random sample. Some literature provide the following alternative definition for Kish's design effect: "the ratio of the variance of the weighted survey mean under disproportionate stratified sampling to the variance under proportionate stratified sampling when all stratum unit variances are equal". Reflecting on this, Park and Lee (2006) stated that "The rationale behind [...][Kish's] derivation is that the loss in precision of [the weighted mean] due to haphazard unequal weighting can be approximated by the ratio of the variance under disproportionate stratified sampling to that under the proportionate stratified sampling". Note that this alternative definition only approximated since if the denominator is based on "proportionate stratified sampling" (achieved via stratified sampling) then such a selection will yield a reduced variance as compared with simple random sample. This is since stratified sampling removes some of the variability in the specific number of elements per stratum, as occurs under SRS. Relatedly, Cochran (1977) provides a formula for the proportional increase in variance due to deviation from optimum allocation (what, in Kish's formulas, would be called L). ===== Alternative


id: design-effect-20260505-9
file: data/en.wikipedia.org/wiki/Design_effect-9.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
σ ^ y {\displaystyle {\hat {\sigma }}_{y}} estimates the population variance σ y {\displaystyle \sigma _{y}} , and L is the relvariance of the weights, as defined in Kish's formula: L = c v w 2 = relvar ( w ) = V ( w ) w ¯ 2 {\displaystyle L=cv_{w}^{2}={\text{relvar}}(w)={\frac {V(w)}{{\bar {w}}^{2}}}} . This assumes that the regression model fits well so that the probability of selection and the residuals are independent, since it leads to the residuals, and the square residuals, to be uncorrelated with the weights, i.e., that ρ ϵ , W = 0 {\displaystyle \rho _{\epsilon ,W}=0} and also ρ ϵ 2 , W = 0 {\displaystyle \rho _{\epsilon ^{2},W}=0} . When the population size (N) is very large, the formula can be written as: Deff S p e n c e r = ( 1 − ρ ^ y , P 2 ) ( 1 + c v w 2 ) + ( 1 c v Y 2 ) 2 c v w 2 {\displaystyle {\text{Deff}}_{Spencer}=(1-{\hat {\rho }}_{y,P}^{2})(1+cv_{w}^{2})+\left({\frac {1}{cv_{Y}^{2}}}\right)^{2}cv_{w}^{2}} (since α = Y ¯ − β × P ¯ = Y ¯ − β × 1 N ≈ Y ¯ {\displaystyle \alpha ={\bar {Y}}-\beta \times


id: design-effect-20260505-10
file: data/en.wikipedia.org/wiki/Design_effect-10.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
=== The design effect for complex designs === ==== Unequal selection probabilities times Cluster sampling ==== In a 1987 paper, Kish proposed a combined design effect that incorporates both the effects due to weighting that accounts for unequal selection probabilities and cluster sampling: Deff Kish = n ∑ h = 1 H ( n h w h 2 ) ( ∑ h = 1 H n h w h ) 2 ( 1 + ( n ∗ − 1 ) ρ ) = Deff k × Deff C {\displaystyle {\text{Deff}}_{\text{Kish}}={\frac {n\sum \limits _{h=1}^{H}(n_{h}w_{h}^{2})}{\left(\sum \limits _{h=1}^{H}n_{h}w_{h}\right)^{2}}}\left(1+(n^{*}-1)\rho \right)={\text{Deff}}_{k}\times {\text{Deff}}_{C}} The above uses notations similar to what is used in this article (the original 1987 publication used different notation). A model based justification for this formula was provided by Gabler et al. ==== Stratified sampling times unequal selection probabilities times Cluster sampling ==== In 2000, Liu and Aragon proposed a decomposition of unequal selection probabilities design effect for different strata in stratified sampling. In 2002, Liu et al. extended that work to account for stratified samples, where within each stratum is a set of unequal selection probability weights. The cluster sampling is either global or per stratum. Similar work was done also by


id: design-effect-20260505-11
file: data/en.wikipedia.org/wiki/Design_effect-11.md
category: reference
title: Design effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_effect
date_saved: 2026-05-05T09:49:56.844427+00:00
instance: kb-cron
parent: design-effect-20260505-0
summary:
When planning a future data collection - D e f f {\displaystyle Deff} may be used to evaluate the sampling efficiency. E.g. if there is potentially "too much" increase in variance due to some sampling design decision, or if some alternative (economically feasible) design is more efficient. This also influences the sample size (overall, per stratum, per cluster, etc.). When planning the sample size, work may be done to correct the design effect so as to separate the interviewer effect (measurement error) from the effects of the sampling design on the sampling variance. As a diagnostic tool - D e f f {\displaystyle Deff} may help in evaluating potential problems with a post-hoc weighting analysis (e.g. from non-response adjustments). For example, if the D e f f {\displaystyle Deff} value is especially high, then it might indicate an issue with the sampling or weighting scheme. This can also assist when performing some manipulation on the weights (e.g., weight trimming), the design effect could be used to evaluate the influence of the manipulation on the effective sample size. And also in identifying glaring issues with the data or its analysis (e.g., ranging from mistakes to the presence of Outliers). Although some


id: design-matrix-20260505-0
file: data/en.wikipedia.org/wiki/Design_matrix-0.md
category: reference
title: Design matrix
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_matrix
date_saved: 2026-05-05T09:49:58.034133+00:00
instance: kb-cron
parent: design-matrix-20260505-0
summary:
In statistics and in particular in regression analysis, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix of values of explanatory variables of a set of objects. Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for that object. The design matrix is used in certain statistical models, e.g., the general linear model. It can contain indicator variables (ones and zeros) that indicate group membership in an ANOVA, or it can contain values of continuous variables. The design matrix contains data on the independent variables (also called explanatory variables), in a statistical model that is intended to explain observed data on a response variable (often called a dependent variable). The theory relating to such models uses the design matrix as input to some linear algebra : see for example linear regression. A notable feature of the concept of a design matrix is that it is able to represent a number of different experimental designs and statistical models, e.g., ANOVA, ANCOVA, and linear regression. == Definition == The design matrix is defined to be a matrix X {\displaystyle X} such that X


id: design-matrix-20260505-1
file: data/en.wikipedia.org/wiki/Design_matrix-1.md
category: reference
title: Design matrix
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_matrix
date_saved: 2026-05-05T09:49:58.034133+00:00
instance: kb-cron
parent: design-matrix-20260505-0
summary:
[ y 1 y 2 y 3 y 4 y 5 y 6 y 7 ] = [ 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 ] [ μ 1 μ 2 μ 3 ] + [ ε 1 ε 2 ε 3 ε 4 ε 5 ε 6 ε 7 ] {\displaystyle {\begin{bmatrix}y_{1}\\y_{2}\\y_{3}\\y_{4}\\y_{5}\\y_{6}\\y_{7}\end{bmatrix}}={\begin{bmatrix}1&0&0\\1&0&0\\1&0&0\\0&1&0\\0&1&0\\0&0&1\\0&0&1\end{bmatrix}}{\begin{bmatrix}\mu _{1}\\\mu _{2}\\\mu _{3}\end{bmatrix}}+{\begin{bmatrix}\varepsilon _{1}\\\varepsilon _{2}\\\varepsilon _{3}\\\varepsilon _{4}\\\varepsilon _{5}\\\varepsilon _{6}\\\varepsilon _{7}\end{bmatrix}}} In this model μ i {\displaystyle \mu _{i}} represents the mean of the i {\displaystyle i} th group. === One-way ANOVA (offset from reference group) === The ANOVA model could be equivalently written as each group parameter τ i {\displaystyle \tau _{i}} being an offset from some overall reference. Typically this reference point is taken to be one of the groups under consideration. This makes sense in the context of comparing multiple treatment groups to a control group and the control group is considered the "reference". In this example, group 1 was chosen to be the reference group. As such the model to be fit is y i j = μ + τ i + ε i j {\displaystyle y_{ij}=\mu +\tau _{i}+\varepsilon _{ij}}


id: design-space-exploration-20260505-0
file: data/en.wikipedia.org/wiki/Design_space_exploration-0.md
category: reference
title: Design space exploration
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design_space_exploration
date_saved: 2026-05-05T09:49:59.275013+00:00
instance: kb-cron
parent: design-space-exploration-20260505-0
summary:
Design Space Exploration (DSE) refers to systematic analysis and pruning of unwanted design points based on parameters of interest. While the term DSE can apply to any kind of system, we refer to electronic and embedded system design in this article. Given the complex specification of electronic systems and the plethora of design choices ranging from the choice of components, number of components, operating modes of each of the components, connections between the components, choice of algorithm, etc.; design decisions need to be based on a systematic exploration process. However, the exploration process is complex because of a variety of ways in which the same functionality can be implemented. A tradeoff analysis between each of the implementation options based on a certain parameter of interest forms the basis of DSE. The parameter of interest could vary across systems, but the commonly used parameters are power, performance, and cost. Additional factors like size, shape, weight, etc. can be important for some handheld systems like cellphone and tablets. With growing usage of mobile devices, energy is also becoming a mainstream optimization parameter along with power and performance. Owing to the complexity of the exploration process, researchers have proposed automated DSE where the


id: design-expert-20260505-0
file: data/en.wikipedia.org/wiki/Design–Expert-0.md
category: reference
title: Design–Expert
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Design–Expert
date_saved: 2026-05-05T09:50:00.505639+00:00
instance: kb-cron
parent: design-expert-20260505-0
summary:
Design–Expert is a statistical software package from Stat-Ease Inc. that is specifically dedicated to performing design of experiments (DOE). Design–Expert offers comparative tests, screening, characterization, optimization, robust parameter design, mixture designs and combined designs. Design–Expert provides test matrices for screening up to 50 factors. Statistical significance of these factors is established with analysis of variance (ANOVA). Graphical tools help identify the impact of each factor on the desired outcomes and reveal abnormalities in the data. == History == Stat-Ease released its first version of Design–Expert in 1988. In 1996 the firm released version 5 which was the first version of the software designed for Microsoft Windows. Version 6.0 moved to a full 32-bit architecture and fuller compliance with Windows visual convention and also allowed up to 256 runs for two-level blocked designs. Version 7.0 added 3D surface plots for category factors and a t-value effects Pareto chart among many other functional additions. This version also includes the ability to type in variable constraints directly to the design in ratio form. Version 9 incorporates split-plot factorial designs including two-level full and fractional factorials, general factorials and optimal factorials. == Features == Design–Expert offers test matrices for screening up to 50 factors.


id: designated-member-review-20260505-0
file: data/en.wikipedia.org/wiki/Designated_Member_Review-0.md
category: reference
title: Designated Member Review
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Designated_Member_Review
date_saved: 2026-05-05T09:50:01.851591+00:00
instance: kb-cron
parent: designated-member-review-20260505-0
summary:
A Designated Member Review (DMR) or Designated Subcommittee Review (DSR), also known as Designated Review, is a review of a protocol where a committee designates one or more members of the committee to review a decisionmaking process or a protocol or procedure, a review which would ordinarily require the full committee's review. Typically this pertains to IACUCs. In protocols of the National Institutes of Health (NIH) in the United States, 'Correct Conduct of Full-Committee and Designated-Member Protocol Reviews', there are two ways a procedure or protocol can be reviewed, according to PHS policy. Sometimes a protocol or amendment to policies is submitted, which may not need to be considered at a full meeting. If everyone on the committee agrees, then the chair or the committee can assign a person of knowledge and selected other member(s) to review the protocol and approve it or send it back to the full committee for discussion. A first step in such a process is for the chair to poll committee members to determine agreement for the DMR. If they agree, the DMR proceeds; if they do not agree, the DMR does not occur and it should be considered at a convened meeting by the


id: difference-in-differences-20260505-0
file: data/en.wikipedia.org/wiki/Difference_in_differences-0.md
category: reference
title: Difference in differences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Difference_in_differences
date_saved: 2026-05-05T09:50:03.034225+00:00
instance: kb-cron
parent: difference-in-differences-20260505-0
summary:
Difference in differences (DID or DD) is a quasi-experimental statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a "treatment group" versus a "control group" in a natural experiment. It calculates the effect of a treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average change over time in the outcome variable for the treatment group to the average change over time for the control group. Although it is intended to mitigate the effects of extraneous factors and selection bias, depending on how the treatment group is chosen, this method may still be subject to certain biases (e.g., mean regression, reverse causality and omitted variable bias). In contrast to a time-series estimate of the treatment effect on subjects (which analyzes differences over time) or a cross-section estimate of the treatment effect (which measures the difference between treatment and control groups), the difference in differences uses panel data to measure the differences, between the treatment and control group, of the changes in the outcome


id: difference-in-differences-20260505-1
file: data/en.wikipedia.org/wiki/Difference_in_differences-1.md
category: reference
title: Difference in differences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Difference_in_differences
date_saved: 2026-05-05T09:50:03.034225+00:00
instance: kb-cron
parent: difference-in-differences-20260505-0
summary:
δ ( D 11 − D 12 ) + δ ( D 22 − D 21 ) + ε ¯ 11 − ε ¯ 12 + ε ¯ 22 − ε ¯ 21 . {\displaystyle {\begin{aligned}&({\overline {y}}_{11}-{\overline {y}}_{12})-({\overline {y}}_{21}-{\overline {y}}_{22})\\[6pt]={}&{\big [}(\gamma _{1}+\lambda _{1}+\delta D_{11}+{\overline {\varepsilon }}_{11})-(\gamma _{1}+\lambda _{2}+\delta D_{12}+{\overline {\varepsilon }}_{12}){\big ]}\\&\qquad {}-{\big [}(\gamma _{2}+\lambda _{1}+\delta D_{21}+{\overline {\varepsilon }}_{21})-(\gamma _{2}+\lambda _{2}+\delta D_{22}+{\overline {\varepsilon }}_{22}){\big ]}\\[6pt]={}&\delta (D_{11}-D_{12})+\delta (D_{22}-D_{21})+{\overline {\varepsilon }}_{11}-{\overline {\varepsilon }}_{12}+{\overline {\varepsilon }}_{22}-{\overline {\varepsilon }}_{21}.\end{aligned}}} The strict exogeneity assumption then implies that E ⁡ [ ( y ¯ 11 − y ¯ 12 ) − ( y ¯ 21 − y ¯ 22 ) ] = δ ( D 11 − D 12 ) + δ ( D 22 − D 21 ) . {\displaystyle \operatorname {E} \left[({\overline {y}}_{11}-{\overline {y}}_{12})-({\overline {y}}_{21}-{\overline {y}}_{22})\right]~=~\delta (D_{11}-D_{12})+\delta (D_{22}-D_{21}).} Without loss of generality, assume that s = 2 {\displaystyle s=2} is the treatment group, and t = 2 {\displaystyle t=2} is the after period, then D 22 = 1 {\displaystyle D_{22}=1} and D 11 = D 12 = D 21 = 0 {\displaystyle D_{11}=D_{12}=D_{21}=0} , giving the DID estimator δ ^ = ( y ¯ 11 − y ¯ 12 ) − ( y ¯


id: difference-in-differences-20260505-2
file: data/en.wikipedia.org/wiki/Difference_in_differences-2.md
category: reference
title: Difference in differences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Difference_in_differences
date_saved: 2026-05-05T09:50:03.034225+00:00
instance: kb-cron
parent: difference-in-differences-20260505-0
summary:
where E ^ ( ⋯ ∣ … ) {\displaystyle {\widehat {E}}(\dots \mid \dots )} stands for conditional averages computed on the sample, for example, T = 1 {\displaystyle T=1} is the indicator for the after period, S = 0 {\displaystyle S=0} is an indicator for the control group. Note that β ^ 1 {\displaystyle {\hat {\beta }}_{1}} is an estimate of the counterfactual rather than the impact of the control group. The control group is often used as a proxy for the counterfactual (see, Synthetic control method for a deeper understanding of this point). Thereby, β ^ 1 {\displaystyle {\hat {\beta }}_{1}} can be interpreted as the impact of both the control group and the intervention's (treatment's) counterfactual. Similarly, β ^ 2 {\displaystyle {\hat {\beta }}_{2}} , due to the parallel trend assumption, is also the same differential between the treatment and control group in T = 1 {\displaystyle T=1} . The above descriptions should not be construed to imply the (average) effect of only the control group, for β ^ 1 {\displaystyle {\hat {\beta }}_{1}} , or only the difference of the treatment and control groups in the pre-period, for β ^ 2 {\displaystyle {\hat {\beta }}_{2}} . As


id: difference-in-differences-20260505-3
file: data/en.wikipedia.org/wiki/Difference_in_differences-3.md
category: reference
title: Difference in differences
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Difference_in_differences
date_saved: 2026-05-05T09:50:03.034225+00:00
instance: kb-cron
parent: difference-in-differences-20260505-0
summary:
=== In economic history === Difference-in-differences has also been applied to the study of historical events, particularly in the field of economic history, where researchers rely on natural experiments to investigate long-run outcomes. By comparing regions or groups that were differentially exposed to shocks such as disease, institutional change, or wartime destruction, scholars have used the method to identify causal effects that cannot be observed directly. In 2021, Elena Esposito used DID to examine how the arrival of malaria influenced the expansion of African slavery in the United States. She compared counties that were more ecologically suitable for malaria transmission with those that were less suitable, before and after the introduction of the disease in the late seventeenth century. Results showed that malaria-prone counties experienced a much greater increase in the share of enslaved Africans after the disease became endemic. In addition, enslaved individuals from parts of Africa with high malaria prevalence sold at higher prices in Louisiana slave markets, suggesting that buyers placed a premium on resistance to malaria. This application demonstrated how DID can be used to link environmental shocks with institutional development over the long run. González, Marshall, and Naidu in 2017 used DID to analyze how


id: drug-design-20260505-0
file: data/en.wikipedia.org/wiki/Drug_design-0.md
category: reference
title: Drug design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Drug_design
date_saved: 2026-05-05T09:50:04.282020+00:00
instance: kb-cron
parent: drug-design-20260505-0
summary:
Drug design, often referred to as rational drug design or simply rational design, is the inventive process of finding new medications based on the knowledge of a biological target. The drug is most commonly an organic small molecule that activates or inhibits the function of a biomolecule such as a protein, which in turn results in a therapeutic benefit to the patient. In the most basic sense, drug design involves the design of molecules that are complementary in shape and charge to the biomolecular target with which they interact and therefore will bind to it. Drug design frequently but not necessarily relies on computer modeling techniques. This type of modeling is sometimes referred to as computer-aided drug design. Finally, drug design that relies on the knowledge of the three-dimensional structure of the biomolecular target is known as structure-based drug design. In addition to small molecules, biopharmaceuticals including peptides and especially therapeutic antibodies are an increasingly important class of drugs and computational methods for improving the affinity, selectivity, and stability of these protein-based therapeutics have also been developed. == Definition == The phrase "drug design" is similar to ligand design (i.e., design of a molecule that will bind tightly to its


id: drug-design-20260505-1
file: data/en.wikipedia.org/wiki/Drug_design-1.md
category: reference
title: Drug design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Drug_design
date_saved: 2026-05-05T09:50:04.282020+00:00
instance: kb-cron
parent: drug-design-20260505-0
summary:
==== Rational drug discovery ==== Rational drug design (also called reverse pharmacology) begins with a hypothesis that modulation of a specific biological target may have therapeutic value. In order for a biomolecule to be selected as a drug target, two essential pieces of information are required. The first is evidence that modulation of the target will be disease modifying. This knowledge may come from, for example, disease linkage studies that show an association between mutations in the biological target and certain disease states. The second is that the target is capable of binding to a small molecule and that its activity can be modulated by the small molecule. Once a suitable target has been identified, the target is normally cloned and produced and purified. The purified protein is then used to establish a screening assay. In addition, the three-dimensional structure of the target may be determined. The search for small molecules that bind to the target is begun by screening libraries of potential drug compounds. This may be done by using the screening assay (a "wet screen"). In addition, if the structure of the target is available, a virtual screen may be performed of candidate drugs. Ideally, the candidate drug


id: drug-design-20260505-2
file: data/en.wikipedia.org/wiki/Drug_design-2.md
category: reference
title: Drug design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Drug_design
date_saved: 2026-05-05T09:50:04.282020+00:00
instance: kb-cron
parent: drug-design-20260505-0
summary:
=== Structure-based === Structure-based drug design (or direct drug design) relies on knowledge of the three dimensional structure of the biological target obtained through methods such as x-ray crystallography or NMR spectroscopy. If an experimental structure of a target is not available, it may be possible to create a homology model of the target based on the experimental structure of a related protein. Using the structure of the biological target, candidate drugs that are predicted to bind with high affinity and selectivity to the target may be designed using interactive graphics and the intuition of a medicinal chemist. Alternatively, various automated computational procedures may be used to suggest new drug candidates. Current methods for structure-based drug design can be divided roughly into three main categories. The first method is identification of new ligands for a given receptor by searching large databases of 3D structures of small molecules to find those fitting the binding pocket of the receptor using fast approximate docking programs. This method is known as virtual screening. A second category is de novo design of new ligands. In this method, ligand molecules are built up within the constraints of the binding pocket by assembling small pieces in a


id: drug-design-20260505-3
file: data/en.wikipedia.org/wiki/Drug_design-3.md
category: reference
title: Drug design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Drug_design
date_saved: 2026-05-05T09:50:04.282020+00:00
instance: kb-cron
parent: drug-design-20260505-0
summary:
== Examples == A particular example of rational drug design involves the use of three-dimensional information about biomolecules obtained from such techniques as X-ray crystallography and NMR spectroscopy. Computer-aided drug design in particular becomes much more tractable when there is a high-resolution structure of a target protein bound to a potent ligand. This approach to drug discovery is sometimes referred to as structure-based drug design. The first unequivocal example of the application of structure-based drug design leading to an approved drug is the carbonic anhydrase inhibitor dorzolamide, which was approved in 1995. Another case study in rational drug design is imatinib, a tyrosine kinase inhibitor designed specifically for the bcr-abl fusion protein that is characteristic for Philadelphia chromosome-positive leukemias (chronic myelogenous leukemia and occasionally acute lymphocytic leukemia). Imatinib is substantially different from previous drugs for cancer, as most agents of chemotherapy simply target rapidly dividing cells, not differentiating between cancer cells and other tissues. Additional examples include: == Drug screening == Types of drug screening include phenotypic screening, high-throughput screening, and virtual screening. Phenotypic screening is characterized by the process of screening drugs using cellular or animal disease models to identify compounds that alter the phenotype and produce beneficial disease-related


id: ecological-study-20260505-0
file: data/en.wikipedia.org/wiki/Ecological_study-0.md
category: reference
title: Ecological study
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ecological_study
date_saved: 2026-05-05T09:50:05.530567+00:00
instance: kb-cron
parent: ecological-study-20260505-0
summary:
In epidemiology, ecological studies are used to understand the relationship between outcome and exposure at a population level, where 'population' represents a group of individuals with a shared characteristic such as geography, ethnicity, socio-economic status of employment. What differentiates ecological studies from other studies is that the unit analysis being studied is the group, therefore inferences cannot be made about individual study participants. On the other hand, details of outcome and exposure can be generalized to the population being studied. Examples of such studies include investigating associations between units of grouped data, such as electoral wards, regions, or even whole countries. == Study design == Generally, three different designs can be used to conduct ecological studies depending on the situation. Such studies may compare populations or groups using a multiple-group design, periods of time using a time-trend design, or groups and time using a mixed design. == Notable examples == === Cholera study === The study by John Snow regarding a cholera outbreak in London is considered the first ecological study to solve a health issue. He used a map of deaths from cholera to determine that the source of the cholera was a pump on Broad Street. He had


id: experimental-factor-ontology-20260505-0
file: data/en.wikipedia.org/wiki/Experimental_factor_ontology-0.md
category: reference
title: Experimental factor ontology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Experimental_factor_ontology
date_saved: 2026-05-05T09:50:06.784380+00:00
instance: kb-cron
parent: experimental-factor-ontology-20260505-0
summary:
Experimental factor ontology, also known as EFO, is an open-access ontology of experimental variables particularly those used in molecular biology. The ontology covers variables which include aspects of disease, anatomy, cell type, cell lines, chemical compounds and assay information. EFO is developed and maintained at the EMBL-EBI as a cross-cutting resource for the purposes of curation, querying and data integration in resources such as Ensembl, ChEMBL and Expression Atlas. == Scope and access == The original aim of EFO was to describe experimental variables in the EBI's Expression Atlas resource. This consisted primarily of disease, anatomical regions and cell types. By December 2013 the scope had grown to include several other EMBL-EBI resources and several external projects including CellFinder, cell lines from the ENCODE project and phenotype to SNP information in the NHGRI's Catalog of Published Genome-Wide Association Studies. EFO makes use of existing biomedical ontologies from the Open Biomedical Ontologies collection in order to improve interoperability with other resources which may also use these same ontologies, such as ChEBI and the Ontology for Biomedical Investigations. All data in the database is non-proprietary or is derived from a non-proprietary source. It is thus freely accessible and available to anyone. In


id: ethics-committee-20260505-0
file: data/en.wikipedia.org/wiki/Ethics_committee-0.md
category: reference
title: Ethics committee
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ethics_committee
date_saved: 2026-05-05T09:50:08.036049+00:00
instance: kb-cron
parent: ethics-committee-20260505-0
summary:
An ethics committee is a body responsible for ensuring that medical experimentation and human subject research are carried out in an ethical manner in accordance with national and international law. == By jurisdiction == === European Union === An ethics committee in the European Union is a body responsible for oversight of medical or human research studies in EU member states. Local terms for a European ethics committee include: A Research Ethics Committee (REC) in the United Kingdom A Medical Research Ethics Committee (MREC) in the Netherlands. A Comité de Protection des Personnes (CPP) in France. === United States === In the United States, an ethics committee is usually known as an institutional review board (IRB) or research ethics board (REB) and is dedicated to overseeing the rights and well-being of research subjects participating in scientific studies in the US. Similarly in Canada, the committee is called a Research Ethics Board (REB). === Australia === In Australia, an ethics committee in medical research refers to a Human Research Ethics Committee (HREC). === New Zealand === Aotearoa New Zealand's ethics committee is Kāhui Matatika o te Motu, also known as the National Ethics Advisory Committee (NEAC). They outline the standards for


id: experimental-benchmarking-20260505-0
file: data/en.wikipedia.org/wiki/Experimental_benchmarking-0.md
category: reference
title: Experimental benchmarking
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Experimental_benchmarking
date_saved: 2026-05-05T09:50:10.509258+00:00
instance: kb-cron
parent: experimental-benchmarking-20260505-0
summary:
Experimental benchmarking allows researchers to learn about the accuracy of non-experimental research designs. Specifically, one can compare observational results to experimental findings to calibrate bias. Under ordinary conditions, carrying out an experiment gives the researchers an unbiased estimate of their parameter of interest. This estimate can then be compared to the findings of observational research. Note that benchmarking is an attempt to calibrate non-statistical uncertainty (flaws in underlying assumptions). When combined with meta-analysis this method can be used to understand the scope of bias associated with a specific area of research. == History == The start of experimental benchmarking in social science is often attributed to Robert LaLonde. In 1986 he found that findings of econometric procedures assessing the effect of an employment program on trainee earnings did not recover the experimental findings. Experimental benchmarking is often conducted in medical research, such as Schnell‐Inderst et al. (2017) and Burden et al. (2017). == Procedural Considerations == The most instructive experimental benchmarking designs are done on a large scale. They also compare experimental and non-experimental work that looks at the same outcome and the same population. == Observational Designs That Can Be Assessed with Benchmarking == Non-experimental, or observational, research designs


id: exploratory-thought-20260505-0
file: data/en.wikipedia.org/wiki/Exploratory_thought-0.md
category: reference
title: Exploratory thought
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Exploratory_thought
date_saved: 2026-05-05T09:50:11.728800+00:00
instance: kb-cron
parent: exploratory-thought-20260505-0
summary:
Exploratory thought is an academic term used in the field of psychology to describe reasoning that neutrally considers multiple points of view and tries to anticipate all possible objections to, or flaws in, a particular position, with the goal of seeking truth. The opposite of exploratory thought is confirmatory thought, which is reasoning designed to construct justification supporting a specific point of view. Both terms were coined by social psychologist Jennifer Lerner and psychology professor Philip Tetlock in the 2002 book Emerging Perspectives in Judgment and Decision Making. The authors argue that most people, most of the time, make decisions based on gut feelings and poor logic, and reason through issues primarily to provide justification, to themselves and to others, of what they already believe. Lerner and Tetlock say that when people expect to need to justify their position to external parties, and they already know those parties' views, they will tend to adopt a similar position to theirs, and then engage in confirmatory thought with the goal of bolstering their own credibility rather than reaching a good conclusion. However, if the external parties are overly aggressive or critical, people will disengage from thought altogether, and simply assert their personal


id: factorial-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Factorial_experiment-0.md
category: reference
title: Factorial experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Factorial_experiment
date_saved: 2026-05-05T09:50:13.140941+00:00
instance: kb-cron
parent: factorial-experiment-20260505-0
summary:
In statistics, a factorial experiment (also known as full factorial experiment) investigates how multiple factors influence a specific outcome, called the response variable. Each factor is tested at distinct values, or levels, and the experiment includes every possible combination of these levels across all factors. This comprehensive approach lets researchers see not only how each factor individually affects the response, but also how the factors interact and influence each other. Often, factorial experiments simplify things by using just two levels for each factor. A 2x2 factorial design, for instance, has two factors, each with two levels, leading to four unique combinations to test. The interaction between these factors is often the most crucial finding, even when the individual factors also have an effect. If a full factorial design becomes too complex due to the sheer number of combinations, researchers can use a fractional factorial design. This method strategically omits some combinations (usually at least half) to make the experiment more manageable. These combinations of factor levels are sometimes called runs (of an experiment), points (viewing the combinations as vertices of a graph), and cells (arising as intersections of rows and columns). == History == Factorial designs were used in the


id: factorial-experiment-20260505-1
file: data/en.wikipedia.org/wiki/Factorial_experiment-1.md
category: reference
title: Factorial experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Factorial_experiment
date_saved: 2026-05-05T09:50:13.140941+00:00
instance: kb-cron
parent: factorial-experiment-20260505-0
summary:
== Example == The simplest factorial experiment contains two levels for each of two factors. Suppose an engineer wishes to study the total power used by each of two different motors, A and B, running at each of two different speeds, 2000 or 3000 RPM. The factorial experiment would consist of four experimental units: motor A at 2000 RPM, motor B at 2000 RPM, motor A at 3000 RPM, and motor B at 3000 RPM. Each combination of a single level selected from every factor is present once. This experiment is an example of a 22 (or 2×2) factorial experiment, so named because it considers two levels (the base) for each of two factors (the power or superscript), or #levels#factors, producing 22=4 factorial points. Designs can involve many independent variables. As a further example, the effects of three input variables can be evaluated in eight experimental conditions shown as the corners of a cube. This can be conducted with or without replication, depending on its intended purpose and available resources. It will provide the effects of the three independent variables on the dependent variable and possible interactions. == Notation == Factorial experiments are described by two things: the number of


id: factorial-experiment-20260505-2
file: data/en.wikipedia.org/wiki/Factorial_experiment-2.md
category: reference
title: Factorial experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Factorial_experiment
date_saved: 2026-05-05T09:50:13.140941+00:00
instance: kb-cron
parent: factorial-experiment-20260505-0
summary:
A contrast vector belongs to the main effect of a particular factor if the values of its components depend only on the level of that factor. A contrast vector belongs to the interaction of two factors, say A and B, if (i) the values of its components depend only on the levels of A and B, and (ii) it is orthogonal (perpendicular) to the contrast vectors representing the main effects of A and B. Similar definitions hold for interactions of more than two factors. In the 2 × 3 example, for instance, the pattern of the A column follows the pattern of the levels of factor A, indicated by the first component of each cell. Similarly, the pattern of the B columns follows the levels of factor B (sorting on B makes this easier to see). The number of columns needed to specify each effect is the degrees of freedom for the effect, and is an essential quantity in the analysis of variance. The formula is as follows: A main effect for a factor with s levels has s−1 degrees of freedom. The interaction of two factors with s1 and s2 levels, respectively, has (s1−1)(s2−1) degrees of freedom. The formula


id: factorial-experiment-20260505-3
file: data/en.wikipedia.org/wiki/Factorial_experiment-3.md
category: reference
title: Factorial experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Factorial_experiment
date_saved: 2026-05-05T09:50:13.140941+00:00
instance: kb-cron
parent: factorial-experiment-20260505-0
summary:
== Implementation == For more than two factors, a 2k factorial experiment can usually be recursively designed from a 2k−1 factorial experiment by replicating the 2k−1 experiment, assigning the first replicate to the first (or low) level of the new factor, and the second replicate to the second (or high) level. This framework can be generalized to, e.g., designing three replicates for three level factors, etc. A factorial experiment allows for estimation of experimental error in two ways. The experiment can be replicated, or the sparsity-of-effects principle can often be exploited. Replication is more common for small experiments and is a very reliable way of assessing experimental error. When the number of factors is large (typically more than about 5 factors, but this does vary by application), replication of the design can become operationally difficult. In these cases, it is common to only run a single replicate of the design, and to assume that factor interactions of more than a certain order (say, between three or more factors) are negligible. Under this assumption, estimates of such high order interactions are estimates of an exact zero, thus really an estimate of experimental error. When there are many factors, many experimental runs


id: field-experiment-20260505-0
file: data/en.wikipedia.org/wiki/Field_experiment-0.md
category: reference
title: Field experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Field_experiment
date_saved: 2026-05-05T09:50:14.421917+00:00
instance: kb-cron
parent: field-experiment-20260505-0
summary:
Field experiments are experiments carried out outside of laboratory settings. They are different from others in that they are conducted in real-world settings often unobtrusively and control not only the subject pool but selection and overtness, as defined by leaders such as John A. List. This is in contrast to laboratory experiments, which enforce scientific control by testing a hypothesis in the artificial and highly controlled setting of a laboratory. Field experiments have some contextual differences as well from naturally occurring experiments and quasi-experiments. While naturally occurring experiments rely on an external force (e.g. a government, nonprofit, etc.) controlling the randomization treatment assignment and implementation, field experiments require researchers to retain control over randomization and implementation. Quasi-experiments occur when treatments are administered as-if randomly (e.g. U.S. Congressional districts where candidates win with slim margins, weather patterns, natural disasters, etc.). In a field experiment, researchers randomly assign subjects (or other sampling units) to either treatment or control groups to test claims of causal relationships. Random assignment helps establish the comparability of the treatment and control group so that any differences between them that emerge after the treatment has been administered plausibly reflect the influence of the treatment rather than preexisting differences


id: field-experiment-20260505-1
file: data/en.wikipedia.org/wiki/Field_experiment-1.md
category: reference
title: Field experiment
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Field_experiment
date_saved: 2026-05-05T09:50:14.421917+00:00
instance: kb-cron
parent: field-experiment-20260505-0
summary:
== Limitations == There are limitations of and arguments against using field experiments in place of other research designs (e.g. lab experiments, survey experiments, observational studies, etc.). Given that field experiments necessarily take place in a specific geographic and political setting, there is a concern about extrapolating outcomes to formulate a general theory regarding the population of interest. However, researchers have begun to find strategies to effectively generalize causal effects outside of the sample by comparing the environments of the treated population and external population, accessing information from larger sample size, and accounting and modeling for treatment effects heterogeneity within the sample. Others have used covariate blocking techniques to generalize from field experiment populations to external populations. Noncompliance issues affecting field experiments (both one-sided and two-sided noncompliance) can occur when subjects who are assigned to a certain group never receive their assigned intervention. Other problems to data collection include attrition (where subjects who are treated do not provide outcome data) which, under certain conditions, will bias the collected data. These problems can lead to imprecise data analysis; however, researchers who use field experiments can use statistical methods in calculating useful information even when these difficulties occur. Using field experiments can


id: fisher-information-20260505-0
file: data/en.wikipedia.org/wiki/Fisher_information-0.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
In mathematical statistics, the Fisher information is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized and explored by the statistician Sir Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys' rule. It also appears as the large-sample covariance of the posterior distribution, provided that the prior is sufficiently smooth (a result known as Bernstein–von Mises theorem, which was anticipated by Laplace for exponential families). The same result is used when approximating the posterior with Laplace's approximation, where the Fisher information appears as the covariance of the fitted Gaussian. Statistical systems of a scientific nature (physical, biological, etc.) whose likelihood functions


id: fisher-information-20260505-1
file: data/en.wikipedia.org/wiki/Fisher_information-1.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
The partial derivative of f(X; θ) with respect to θ exists almost everywhere. (It can fail to exist on a null set, as long as this set does not depend on θ.) The integral of f(X; θ) can be differentiated under the integral sign with respect to θ. The support of f(X; θ) does not depend on θ. If θ is a vector then the regularity conditions must hold for every component of θ. It is easy to find an example of a density that does not satisfy the regularity conditions: The density of a Uniform(0, θ) variable fails to satisfy conditions 1 and 3. In this case, even though the Fisher information can be computed from the definition, it will not have the properties it is typically assumed to have. === In terms of likelihood === Because the likelihood of θ given X is always proportional to the probability f(X; θ), their logarithms necessarily differ by a constant that is independent of θ, and the derivatives of these logarithms with respect to θ are necessarily equal. Thus one can substitute in a log-likelihood l(θ; X) instead of log f(X; θ) in the definitions of Fisher Information. === Samples of


id: fisher-information-20260505-2
file: data/en.wikipedia.org/wiki/Fisher_information-2.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
In other words, the precision to which we can estimate θ is fundamentally limited by the Fisher information of the likelihood function. Alternatively, the same conclusion can be obtained directly from the Cauchy–Schwarz inequality for random variables, | Cov ⁡ ( A , B ) | 2 ≤ Var ⁡ ( A ) Var ⁡ ( B ) {\displaystyle |\operatorname {Cov} (A,B)|^{2}\leq \operatorname {Var} (A)\operatorname {Var} (B)} , applied to the random variables θ ^ ( X ) {\displaystyle {\hat {\theta }}(X)} and ∂ θ log ⁡ f ( X ; θ ) {\displaystyle \partial _{\theta }\log f(X;\theta )} , and observing that for unbiased estimators we have Cov ⁡ [ θ ^ ( X ) , ∂ θ log ⁡ f ( X ; θ ) ] = ∫ θ ^ ( x ) ∂ θ f ( x ; θ ) d x = ∂ θ E ⁡ [ θ ^ ] = 1. {\displaystyle \operatorname {Cov} [{\hat {\theta }}(X),\partial _{\theta }\log f(X;\theta )]=\int {\hat {\theta }}(x)\,\partial _{\theta }f(x;\theta )\,dx=\partial _{\theta }\operatorname {E} [{\hat {\theta }}]=1.} == Examples == === Single-parameter Bernoulli experiment === A Bernoulli trial is a random variable with two possible outcomes, 0 and 1,


id: fisher-information-20260505-3
file: data/en.wikipedia.org/wiki/Fisher_information-3.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
=== Estimate θ from X ~ Bern (√θ) === As another toy example consider a random variable X {\displaystyle X} with possible outcomes 0 and 1, with probabilities p 0 = 1 − θ {\displaystyle p_{0}=1-{\sqrt {\theta }}} and p 1 = θ {\displaystyle p_{1}={\sqrt {\theta }}} , respectively, for some θ ∈ [ 0 , 1 ] {\displaystyle \theta \in [0,1]} . Our goal is estimating θ {\displaystyle \theta } from observations of X {\displaystyle X} . The Fisher information reads in this case I ( θ ) = E [ ( ∂ ∂ θ log ⁡ f ( X ; θ ) ) 2 | θ ] = ( 1 − θ ) ( − 1 2 θ ( 1 − θ ) ) 2 + θ ( 1 2 θ ) 2 = 1 4 θ ( 1 1 − θ + 1 θ ) . {\displaystyle {\begin{aligned}{\mathcal {I}}(\theta )&=\mathrm {E} \left[\left({\frac {\partial }{\partial \theta }}\log f(X;\theta )\right)^{2}{\Bigg |}\,\theta \right]\\&=(1-{\sqrt {\theta }})\left({\frac {-1}{2{\sqrt {\theta }}(1-{\sqrt {\theta }})}}\right)^{2}+{\sqrt {\theta }}\left({\frac {1}{2\theta }}\right)^{2}\\&={\frac {1}{4\theta }}\left({\frac {1}{1-{\sqrt {\theta }}}}+{\frac {1}{\sqrt {\theta }}}\right)\end{aligned}}.} This expression can also be derived directly from the change of reparametrization formula given below. More generally, for


id: fisher-information-20260505-4
file: data/en.wikipedia.org/wiki/Fisher_information-4.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
=== Multivariate normal distribution === The FIM for a N-variate multivariate normal distribution, X ∼ N ( μ ( θ ) , Σ ( θ ) ) {\displaystyle \,X\sim N\left(\mu (\theta ),\,\Sigma (\theta )\right)} has a special form. Let the K-dimensional vector of parameters be θ = [ θ 1 … θ K ] T {\displaystyle \theta ={\begin{bmatrix}\theta _{1}&\dots &\theta _{K}\end{bmatrix}}^{\textsf {T}}} and the vector of normal random variables be X = [ X 1 … X N ] T {\displaystyle X={\begin{bmatrix}X_{1}&\dots &X_{N}\end{bmatrix}}^{\textsf {T}}} . Assume that the mean values of these random variables are μ ( θ ) = [ μ 1 ( θ ) … μ N ( θ ) ] T {\displaystyle \,\mu (\theta )={\begin{bmatrix}\mu _{1}(\theta )&\dots &\mu _{N}(\theta )\end{bmatrix}}^{\textsf {T}}} , and let Σ ( θ ) {\displaystyle \,\Sigma (\theta )} be the covariance matrix. Then, for 1 ≤ m , n ≤ K {\displaystyle 1\leq m,\,n\leq K} , the (m, n) entry of the FIM is: I m , n = ∂ μ T ∂ θ m Σ − 1 ∂ μ ∂ θ n + 1 2 tr ⁡ ( Σ − 1 ∂ Σ ∂ θ m Σ − 1 ∂ Σ ∂


id: fisher-information-20260505-5
file: data/en.wikipedia.org/wiki/Fisher_information-5.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
Given a convex function f : [ 0 , ∞ ) → ( − ∞ , ∞ ] {\displaystyle f:[0,\infty )\to (-\infty ,\infty ]} that f ( x ) {\displaystyle f(x)} is finite for all x > 0 {\displaystyle x>0} , f ( 1 ) = 0 {\displaystyle f(1)=0} , and f ( 0 ) = lim t → 0 + f ( t ) {\displaystyle f(0)=\lim _{t\to 0^{+}}f(t)} , (which could be infinite), it defines an f-divergence D f {\displaystyle D_{f}} . Then if f {\displaystyle f} is strictly convex at 1 {\displaystyle 1} , then locally at θ ∈ Θ {\displaystyle \theta \in \Theta } , the Fisher information matrix is a metric, in the sense that ( δ θ ) T I ( θ ) ( δ θ ) = 1 f ″ ( 1 ) D f ( P θ + δ θ ∥ P θ ) {\displaystyle (\delta \theta )^{T}I(\theta )(\delta \theta )={\frac {1}{f''(1)}}D_{f}(P_{\theta +\delta \theta }\parallel P_{\theta })} where P θ {\displaystyle P_{\theta }} is the distribution parametrized by θ {\displaystyle \theta } . That is, it's the distribution with pdf f ( x ; θ ) {\displaystyle f(x;\theta )} . In this form,


id: fisher-information-20260505-6
file: data/en.wikipedia.org/wiki/Fisher_information-6.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
where Z ε {\displaystyle Z_{\varepsilon }} is a Gaussian variable with covariance matrix ε I {\displaystyle \varepsilon I} . The name "surface area" is apt because the entropy power e H ( X ) {\displaystyle e^{H(X)}} is the volume of the "effective support set", so S ( X ) {\displaystyle S(X)} is the "derivative" of the volume of the effective support set, much like the Minkowski-Steiner formula. The remainder of the proof uses the entropy power inequality, which is like the Brunn–Minkowski inequality. The trace of the Fisher information matrix is found to be a factor of S ( X ) {\displaystyle S(X)} . == Applications == === Optimal design of experiments === Fisher information is widely used in optimal experimental design. Because of the reciprocity of estimator-variance and Fisher information, minimizing the variance corresponds to maximizing the information. When the linear (or linearized) statistical model has several parameters, the mean of the parameter estimator is a vector and its variance is a matrix. The inverse of the variance matrix is called the "information matrix". Because the variance of the estimator of a parameter vector is a matrix, the problem of "minimizing the variance" is complicated. Using statistical theory, statisticians


id: fisher-information-20260505-7
file: data/en.wikipedia.org/wiki/Fisher_information-7.md
category: reference
title: Fisher information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher_information
date_saved: 2026-05-05T09:50:15.726073+00:00
instance: kb-cron
parent: fisher-information-20260505-0
summary:
Thus the Fisher information represents the curvature of the relative entropy of a conditional distribution with respect to its parameters. == History == The Fisher information was discussed by several early statisticians, notably F. Y. Edgeworth. For example, Savage says: "In it [Fisher information], he [Fisher] was to some extent anticipated (Edgeworth 1908–9 esp. 502, 507–8, 662, 677–8, 82–5 and references he [Edgeworth] cites including Pearson and Filon 1898 [. . .])." There are a number of early historical sources and a number of reviews of this early work. == See also == Efficiency (statistics) Observed information Fisher information metric Formation matrix Information geometry Jeffreys prior Cramér–Rao bound Minimum Fisher information Quantum Fisher information White information matrix test Other measures employed in information theory: Entropy (information theory) Kullback–Leibler divergence Self-information == Notes == == References == Cramér, Harald (1946). Mathematical methods of statistics. Princeton mathematical series. Princeton: Princeton University Press. ISBN 0-691-08004-6. {{cite book}}: ISBN / Date incompatibility (help) Edgeworth, F. Y. (Jun 1908). "On the Probable Errors of Frequency-Constants". Journal of the Royal Statistical Society. 71 (2): 381–397. doi:10.2307/2339461. JSTOR 2339461. Edgeworth, F. Y. (Sep 1908). "On the Probable Errors of Frequency-Constants (Contd.)". Journal of the Royal Statistical Society.


id: fisher-s-inequality-20260505-0
file: data/en.wikipedia.org/wiki/Fisher's_inequality-0.md
category: reference
title: Fisher's inequality
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fisher's_inequality
date_saved: 2026-05-05T09:50:16.972104+00:00
instance: kb-cron
parent: fisher-s-inequality-20260505-0
summary:
Fisher's inequality is a necessary condition for the existence of a balanced incomplete block design, that is, a system of subsets that satisfy certain prescribed conditions in combinatorial mathematics. Outlined by Ronald Fisher, a population geneticist and statistician, who was concerned with the design of experiments such as studying the differences among several different varieties of plants, under each of a number of different growing conditions, called blocks. Let: v be the number of varieties of plants; b be the number of blocks. To be a balanced incomplete block design it is required that: k different varieties are in each block, 1 ≤ k < v; no variety occurs twice in any one block; any two varieties occur together in exactly λ blocks; each variety occurs in exactly r blocks. Fisher's inequality states simply that b ≥ v. == Proof == Let the incidence matrix M be a v × b matrix defined so that Mi,j is 1 if element i is in block j and 0 otherwise. Then B = MMT is a v × v matrix such that Bi,i = r and Bi,j = λ for i ≠ j. Since r ≠ λ, det(B) ≠ 0, so rank(B)


id: fractional-factorial-design-20260505-0
file: data/en.wikipedia.org/wiki/Fractional_factorial_design-0.md
category: reference
title: Fractional factorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fractional_factorial_design
date_saved: 2026-05-05T09:50:18.197962+00:00
instance: kb-cron
parent: fractional-factorial-design-20260505-0
summary:
In statistics, a fractional factorial design is a way to conduct experiments with fewer experimental runs than a full factorial design. Instead of testing every single combination of factors, it tests only a carefully selected portion. This "fraction" of the full design is chosen to reveal the most important information about the system being studied (sparsity-of-effects principle), while significantly reducing the number of runs required. It is based on the idea that many tests in a full factorial design can be redundant. However, this reduction in runs comes at the cost of potentially more complex analysis, as some effects can become intertwined, making it impossible to isolate their individual influences. Therefore, choosing which combinations to test in a fractional factorial design must be done carefully. == History == Fractional factorial design was introduced by British statistician David John Finney in 1945, extending previous work by Ronald Fisher on the full factorial experiment at Rothamsted Experimental Station. Developed originally for agricultural applications, it has since been applied to other areas of engineering, science, and business. == Basic working principle == Similar to a full factorial experiment, a fractional factorial experiment investigates the effects of independent variables, known as factors, on a


id: fractional-factorial-design-20260505-1
file: data/en.wikipedia.org/wiki/Fractional_factorial_design-1.md
category: reference
title: Fractional factorial design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fractional_factorial_design
date_saved: 2026-05-05T09:50:18.197962+00:00
instance: kb-cron
parent: fractional-factorial-design-20260505-0
summary:
== Generation == In practice, experimenters typically rely on statistical reference books to supply the "standard" fractional factorial designs, consisting of the principal fraction. The principal fraction is the set of treatment combinations for which the generators evaluate to + under the treatment combination algebra. However, in some situations, experimenters may take it upon themselves to generate their own fractional design. A fractional factorial experiment is generated from a full factorial experiment by choosing an alias structure. The alias structure determines which effects are confounded with each other. For example, the five-factor 25 − 2 can be generated by using a full three-factor factorial experiment involving three factors (say A, B, and C) and then choosing to confound the two remaining factors D and E with interactions generated by D = A*B and E = A*C. These two expressions are called the generators of the design. So for example, when the experiment is run and the experimenter estimates the effects for factor D, what is really being estimated is a combination of the main effect of D and the two-factor interaction involving A and B. An important characteristic of a fractional design is the defining relation, which gives the set


id: generalized-randomized-block-design-20260505-0
file: data/en.wikipedia.org/wiki/Generalized_randomized_block_design-0.md
category: reference
title: Generalized randomized block design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Generalized_randomized_block_design
date_saved: 2026-05-05T09:50:19.398918+00:00
instance: kb-cron
parent: generalized-randomized-block-design-20260505-0
summary:
In randomized statistical experiments, generalized randomized block designs (GRBDs) are used to study the interaction between blocks and treatments. For a GRBD, each treatment is replicated at least two times in each block; this replication allows the estimation and testing of an interaction term in the linear model (without making parametric assumptions about a normal distribution for the error). == Univariate response == === GRBDs versus RCBDs: Replication and interaction === Like a randomized complete block design (RCBD), a GRBD is randomized. Within each block, treatments are randomly assigned to experimental units: this randomization is also independent between blocks. In a (classic) RCBD, however, there is no replication of treatments within blocks. === Two-way linear model: Blocks and treatments === The experimental design guides the formulation of an appropriate linear model. Without replication, the (classic) RCBD has a two-way linear-model with treatment- and block-effects but without a block-treatment interaction. Without replicates, this two-way linear-model that may be estimated and tested without making parametric assumptions (by using the randomization distribution, without using a normal distribution for the error). In the RCBD, the block-treatment interaction cannot be estimated using the randomization distribution; a fortiori there exists no "valid" (i.e. randomization-based) test for


id: gittins-index-20260505-0
file: data/en.wikipedia.org/wiki/Gittins_index-0.md
category: reference
title: Gittins index
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gittins_index
date_saved: 2026-05-05T09:50:20.644914+00:00
instance: kb-cron
parent: gittins-index-20260505-0
summary:
The Gittins index is a measure of the reward that can be achieved through a given stochastic process with certain properties, namely: the process has an ultimate termination state and evolves with an option, at each intermediate state, of terminating. Upon terminating at a given state, the reward achieved is the sum of the probabilistic expected rewards associated with every state from the actual terminating state to the ultimate terminal state, inclusive. The index is a real scalar. == Terminology == To illustrate the theory we can take two examples from a developing sector, such as from electricity generating technologies: wind power and wave power. If we are presented with the two technologies when they are both proposed as ideas we cannot say which will be better in the long run as we have no data, as yet, to base our judgments on. It would be easy to say that wave power would be too problematic to develop as it seems easier to put up many wind turbines than to make the long floating generators, tow them out to sea and lay the cables necessary. If we were to make a judgment call at that early time in development we


id: gittins-index-20260505-1
file: data/en.wikipedia.org/wiki/Gittins_index-1.md
category: reference
title: Gittins index
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gittins_index
date_saved: 2026-05-05T09:50:20.644914+00:00
instance: kb-cron
parent: gittins-index-20260505-0
summary:
== History == Questions about the optimal stopping policies in the context of clinical trials have been open from the 1940s and in the 1960s a few authors analyzed simple models leading to optimal index policies, but it was only in the 1970s that Gittins and his collaborators demonstrated in a Markovian framework that the optimal solution of the general case is an index policy whose "dynamic allocation index" is computable in principle for every state of each project as a function of the single project's dynamics. In parallel to Gittins, Martin Weitzman established the same result in the economics literature. Soon after the seminal paper of Gittins, Peter Whittle demonstrated that the index emerges as a Lagrange multiplier from a dynamic programming formulation of the problem called retirement process and conjectured that the same index would be a good heuristic in a more general setup named Restless bandit. The question of how to actually calculate the index for Markov chains was first addressed by Varaiya and his collaborators with an algorithm that computes the indexes from the largest first down to the smallest and by Chen and Katehakis who showed that standard LP could be used to calculate the


id: gittins-index-20260505-2
file: data/en.wikipedia.org/wiki/Gittins_index-2.md
category: reference
title: Gittins index
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gittins_index
date_saved: 2026-05-05T09:50:20.644914+00:00
instance: kb-cron
parent: gittins-index-20260505-0
summary:
=== Generalized index === If the probability of survival β ( i ) {\displaystyle \beta (i)} depends on the state i {\displaystyle i} , a generalization introduced by Sonin (2008) defines the Gittins index α ( i ) {\displaystyle \alpha (i)} as the maximum discounted total reward per chance of termination. α ( i ) = sup τ > 0 R τ ( i ) Q τ ( i ) {\displaystyle \alpha (i)=\sup _{\tau >0}{\frac {R^{\tau }(i)}{Q^{\tau }(i)}}} where R τ ( i ) = ⟨ ∑ t = 0 τ − 1 R [ Z ( t ) ] ⟩ Z ( 0 ) = i {\displaystyle R^{\tau }(i)=\left\langle \sum _{t=0}^{\tau -1}R[Z(t)]\right\rangle _{Z(0)=i}} Q τ ( i ) = ⟨ 1 − ∏ t = 0 τ − 1 β [ Z ( t ) ] ⟩ Z ( 0 ) = i {\displaystyle Q^{\tau }(i)=\left\langle 1-\prod _{t=0}^{\tau -1}\beta [Z(t)]\right\rangle _{Z(0)=i}} If β t {\displaystyle \beta ^{t}} is replaced by ∏ j = 0 t − 1 β [ Z ( j ) ] {\displaystyle \prod _{j=0}^{t-1}\beta [Z(j)]} in the definitions of ν ( i ) {\displaystyle \nu (i)} , w ( i ) {\displaystyle w(i)} and h (


id: glossary-of-experimental-design-20260505-0
file: data/en.wikipedia.org/wiki/Glossary_of_experimental_design-0.md
category: reference
title: Glossary of experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Glossary_of_experimental_design
date_saved: 2026-05-05T09:50:21.948791+00:00
instance: kb-cron
parent: glossary-of-experimental-design-20260505-0
summary:
A glossary of terms used in experimental research. == Concerned fields == Statistics Experimental design Estimation theory


id: glossary-of-experimental-design-20260505-1
file: data/en.wikipedia.org/wiki/Glossary_of_experimental_design-1.md
category: reference
title: Glossary of experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Glossary_of_experimental_design
date_saved: 2026-05-05T09:50:21.948791+00:00
instance: kb-cron
parent: glossary-of-experimental-design-20260505-0
summary:
== Glossary == Alias: When the estimate of an effect also includes the influence of one or more other effects (usually high order interactions) the effects are said to be aliased (see confounding). For example, if the estimate of effect D in a four factor experiment actually estimates (D + ABC), then the main effect D is aliased with the 3-way interaction ABC. Note: This causes no difficulty when the higher order interaction is either non-existent or insignificant. Analysis of variance (ANOVA): A mathematical process for separating the variability of a group of observations into assignable causes and setting up various significance tests. Balanced design: An experimental design where all cells (i.e. treatment combinations) have the same number of observations. Blocking: A schedule for conducting treatment combinations in an experimental study such that any effects on the experimental results due to a known change in raw materials, operators, machines, etc., become concentrated in the levels of the blocking variable. Note: the reason for blocking is to isolate a systematic effect and prevent it from obscuring the main effects. Blocking is achieved by restricting randomization. Center Points: Points at the center value of all factor ranges. Coding Factor Levels: Transforming the


id: glossary-of-experimental-design-20260505-2
file: data/en.wikipedia.org/wiki/Glossary_of_experimental_design-2.md
category: reference
title: Glossary of experimental design
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Glossary_of_experimental_design
date_saved: 2026-05-05T09:50:21.948791+00:00
instance: kb-cron
parent: glossary-of-experimental-design-20260505-0
summary:
Lack of fit error: Error that occurs when the analysis omits one or more important terms or factors from the process model. Note: Including replication in a designed experiment allows separation of experimental error into its components: lack of fit and random (pure) error. Model: Mathematical relationship which relates changes in a given response to changes in one or more factors. Nested Factors: See factors above. Orthogonality: Two vectors of the same length are orthogonal if the sum of the products of their corresponding elements is 0. Note: An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors. Paradigm: a model created given the basic design, the hypothesis and the particular conditions for the experiment. Random effect: An effect associated with input variables chosen at random from a population having a large or infinite number of possible values. Random error: Error that occurs due to natural variation in the process. Note: Random error is typically assumed to be normally distributed with zero mean and a constant variance. Note: Random error is also called experimental error. Randomization: A schedule for allocating treatment material and for conducting treatment combinations


id: group-testing-20260505-0
file: data/en.wikipedia.org/wiki/Group_testing-0.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
In statistics and combinatorial mathematics, group testing is any procedure that breaks up the task of identifying objects into tests on groups of items, rather than testing each item individually. First studied by Robert Dorfman in 1943, group testing is a relatively new field of mathematics that can be applied to a wide range of practical applications and is an active area of research today. A familiar example of group testing involves a string of light bulbs connected in series, where exactly one of the bulbs is known to be broken. The objective is to find the broken bulb using the smallest number of tests (where a test is when some of the bulbs are connected to a power supply). A simple approach is to test each bulb individually. However, when there are a large number of bulbs it would be much more efficient to pool the bulbs into groups. For example, by connecting the first half of the bulbs at once, it can be determined which half the broken bulb is in, ruling out half of the bulbs in just one test. Schemes for carrying out group testing can be simple or complex and the tests involved at each


id: group-testing-20260505-1
file: data/en.wikipedia.org/wiki/Group_testing-1.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
=== Variations and extensions === There are many ways to extend the problem of group testing. One of the most important is called noisy group testing, and deals with a big assumption of the original problem: that testing is error-free. A group-testing problem is called noisy when there is some chance that the result of a group test is erroneous (e.g. comes out positive when the test contained no defectives). The Bernoulli noise model assumes this probability is some constant, q {\displaystyle q} , but in general it can depend on the true number of defectives in the test and the number of items tested. For example, the effect of dilution can be modelled by saying a positive result is more likely when there are more defectives (or more defectives as a fraction of the number tested), present in the test. A noisy algorithm will always have a non-zero probability of making an error (that is, mislabeling an item). Group testing can be extended by considering scenarios in which there are more than two possible outcomes of a test. For example, a test may have the outcomes 0 , 1 {\displaystyle 0,1} and 2 + {\displaystyle 2^{+}} , corresponding to


id: group-testing-20260505-2
file: data/en.wikipedia.org/wiki/Group_testing-2.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
=== Combinatorial group testing === Group testing was first studied in the combinatorial context by Li in 1962, with the introduction of Li’s s {\displaystyle s} -stage algorithm. Li proposed an extension of Dorfman's '2-stage algorithm' to an arbitrary number of stages that required no more than t = e log 2 ⁡ ( e ) d log 2 ⁡ ( n ) {\textstyle t={\frac {e}{\log _{2}(e)}}d\log _{2}(n)} tests to be guaranteed to find d {\displaystyle d} or fewer defectives among n {\displaystyle n} items. The idea was to remove all the items in negative tests, and divide the remaining items into groups as was done with the initial pool. This was to be done s − 1 {\displaystyle s-1} times before performing individual testing. Combinatorial group testing in general was later studied more fully by Katona in 1973. Katona introduced the matrix representation of non-adaptive group-testing and produced a procedure for finding the defective in the non-adaptive 1-defective case in no more than t = ⌈ log 2 ⁡ ( n ) ⌉ {\displaystyle t=\lceil \log _{2}(n)\rceil } tests, which he also proved to be optimal. In general, finding optimal algorithms for adaptive combinatorial group testing is difficult, and


id: group-testing-20260505-3
file: data/en.wikipedia.org/wiki/Group_testing-3.md
category: reference
title: Group testing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group_testing
date_saved: 2026-05-05T09:50:23.496143+00:00
instance: kb-cron
parent: group-testing-20260505-0
summary:
x {\displaystyle \mathbf {x} } is intended to describe the (unknown) set of defective items. The key property of x {\displaystyle \mathbf {x} } is that it is an implicit input. That is to say, there is no direct knowledge of what the entries of x {\displaystyle \mathbf {x} } are, other than that which can be inferred via some series of 'tests'. This leads on to the next definition. Let x {\displaystyle \mathbf {x} } be an input vector. A set, S ⊆ { 1 , 2 , … , n } {\displaystyle S\subseteq \{1,2,\dots ,n\}} is called a test. When testing is noiseless, the result of a test is positive when there exists j ∈ S {\displaystyle j\in S} such that x j = 1 {\displaystyle x_{j}=1} , and the result is negative otherwise. Therefore, the goal of group testing is to come up with a method for choosing a 'short' series of tests that allow x {\displaystyle \mathbf {x} } to be determined, either exactly or with a high degree of certainty. A group-testing algorithm is said to make an error if it incorrectly labels an item (that is, labels any defective item as non-defective or vice


