42 lines
6.0 KiB
Markdown
42 lines
6.0 KiB
Markdown
---
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title: "Accuracy and precision"
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chunk: 1/3
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source: "https://en.wikipedia.org/wiki/Accuracy_and_precision"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T14:27:21.980356+00:00"
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instance: "kb-cron"
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---
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Accuracy and precision are measures of observational error; accuracy is how close a given set of measurements is to the true value and precision is how close the measurements are to each other.
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The International Organization for Standardization (ISO) defines a related measure:
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trueness, "the closeness of agreement between the arithmetic mean of a large number of test results and the true or accepted reference value."
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While precision is a description of random errors (a measure of statistical variability),
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accuracy has two different definitions:
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More commonly, a description of systematic errors (a measure of statistical bias of a given measure of central tendency, such as the mean). In this definition of "accuracy", the concept is independent of "precision", so a particular set of data can be said to be accurate, precise, both, or neither. This concept corresponds to ISO's trueness.
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A combination of both precision and trueness, accounting for the two types of observational error (random and systematic), so that high accuracy requires both high precision and high trueness. This usage corresponds to ISO's definition of accuracy (trueness and precision).
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== Common technical definition ==
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In simpler terms, given a statistical sample or set of data points from repeated measurements of the same quantity, the sample or set can be said to be accurate if their average is close to the true value of the quantity being measured, while the set can be said to be precise if their standard deviation is relatively small.
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In the fields of science and engineering, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's true value. The precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. Although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method.
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The field of statistics, where the interpretation of measurements plays a central role, prefers to use the terms bias and variability instead of accuracy and precision: bias is the amount of inaccuracy and variability is the amount of imprecision.
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A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from the flawed experiment. Eliminating the systematic error improves accuracy but does not change precision.
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A measurement system is considered valid if it is both accurate and precise. Related terms include bias (non-random or directed effects caused by a factor or factors unrelated to the independent variable) and error (random variability).
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The terminology is also applied to indirect measurements—that is, values obtained by a computational procedure from observed data.
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In addition to accuracy and precision, measurements may also have a measurement resolution, which is the smallest change in the underlying physical quantity that produces a response in the measurement.
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In numerical analysis, accuracy is also the nearness of a calculation to the true value; while precision is the resolution of the representation, typically defined by the number of decimal or binary digits.
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In military terms, accuracy refers primarily to the accuracy of fire (justesse de tir), the precision of fire expressed by the closeness of a grouping of shots at and around the centre of the target.
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== ISO definition (ISO 5725) ==
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A shift in the meaning of these terms appeared with the publication of the ISO 5725 series of standards in 1994, which is also reflected in the 2008 issue of the BIPM International Vocabulary of Metrology (VIM), items 2.13 and 2.14.
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According to ISO 5725-1, the general term "accuracy" is used to describe the closeness of a measurement to the true value. When the term is applied to sets of measurements of the same measurand, it involves a component of random error and a component of systematic error. In this case trueness is the closeness of the mean of a set of measurement results to the actual (true) value, that is the systematic error, and precision is the closeness of agreement among a set of results, that is the random error.
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ISO 5725-1 and VIM also avoid the use of the term "bias", previously specified in BS 5497-1, because it has different connotations outside the fields of science and engineering, as in medicine and law.
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== Quantification and applications ==
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In industrial instrumentation, accuracy is the measurement tolerance, or transmission of the instrument and defines the limits of the errors made when the instrument is used in normal operating conditions.
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Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the true value. The accuracy and precision of a measurement process is usually established by repeatedly measuring some traceable reference standard. Such standards are defined in the International System of Units (abbreviated SI from French: Système international d'unités) and maintained by national standards organizations such as the National Institute of Standards and Technology in the United States.
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This also applies when measurements are repeated and averaged. In that case, the term standard error is properly applied: the precision of the average is equal to the known standard deviation of the process divided by the square root of the number of measurements averaged. Further, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal distribution than that of individual measurements.
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With regard to accuracy we can distinguish: |