kb/data/en.wikipedia.org/wiki/Accuracy_and_precision-1.md

title	chunk	source	category	tags	date_saved	instance
Accuracy and precision	2/3	https://en.wikipedia.org/wiki/Accuracy_and_precision	reference	science, encyclopedia	2026-05-05T14:27:21.980356+00:00	kb-cron

the difference between the mean of the measurements and the reference value, the bias. Establishing and correcting for bias is necessary for calibration. the combined effect of that and precision. A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures. Where not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m (the last significant place is the tenths place), while a recording of 843 m would imply a margin of error of 0.5 m (the last significant digits are the units). A reading of 8,000 m, with trailing zeros and no decimal point, is ambiguous; the trailing zeros may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: 8.0 × 103 m indicates that the first zero is significant (hence a margin of 50 m) while 8.000 × 103 m indicates that all three zeros are significant, giving a margin of 0.5 m. Similarly, one can use a multiple of the basic measurement unit: 8.0 km is equivalent to 8.0 × 103 m. It indicates a margin of 0.05 km (50 m). However, reliance on this convention can lead to false precision errors when accepting data from sources that do not obey it. For example, a source reporting a number like 153,753 with precision +/- 5,000 looks like it has precision +/- 0.5. Under the convention it would have been rounded to 150,000. Alternatively, in a scientific context, if it is desired to indicate the margin of error with more precision, one can use a notation such as 7.54398(23) × 10−10 m, meaning a range of between 7.54375 and 7.54421 × 10−10 m. Precision includes:

repeatability — the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repeating during a short time period; and reproducibility — the variation arising using the same measurement process among different instruments and operators, and over longer time periods. In engineering, precision is often taken as three times Standard Deviation of measurements taken, representing the range that 99.73% of measurements can occur within. For example, an ergonomist measuring the human body can be confident that 99.73% of their extracted measurements fall within ± 0.7 cm - if using the GRYPHON processing system - or ± 13 cm - if using unprocessed data.

== In classification ==

=== In binary classification ===

Accuracy is also used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition. That is, the accuracy is the proportion of correct predictions (both true positives and true negatives) among the total number of cases examined. As such, it compares estimates of pre- and post-test probability. To make the context clear by the semantics, it is often referred to as the "Rand accuracy" or "Rand index". It is a parameter of the test. The formula for quantifying binary accuracy is:

      Accuracy
    
    =
    
      
        
          T
          P
          +
          T
          N
        
        
          T
          P
          +
          T
          N
          +
          F
          P
          +
          F
          N
        
      
    
  

{\displaystyle {\text{Accuracy}}={\frac {TP+TN}{TP+TN+FP+FN}}}

where TP = True positive; FP = False positive; TN = True negative; FN = False negative In this context, the concepts of trueness and precision as defined by ISO 5725-1 are not applicable. One reason is that there is not a single “true value” of a quantity, but rather two possible true values for every case, while accuracy is an average across all cases and therefore takes into account both values. However, the term precision is used in this context to mean a different metric originating from the field of information retrieval (see § In information systems).

=== In multiclass classification === When computing accuracy in multiclass classification, accuracy is simply the fraction of correct classifications:

      Accuracy
    
    =
    
      
        correct classifications
        all classifications
      
    
  

{\displaystyle {\text{Accuracy}}={\frac {\text{correct classifications}}{\text{all classifications}}}}

This is usually expressed as a percentage. For example, if a classifier makes ten predictions and nine of them are correct, the accuracy is 90%. Accuracy is sometimes also viewed as a micro metric, to underline that it tends to be greatly affected by the particular class prevalence in a dataset and the classifier's biases. Furthermore, it is also called top-1 accuracy to distinguish it from top-5 accuracy, common in convolutional neural network evaluation. To evaluate top-5 accuracy, the classifier must provide relative likelihoods for each class. When these are sorted, a classification is considered correct if the correct classification falls anywhere within the top 5 predictions made by the network. Top-5 accuracy was popularized by the ImageNet challenge. It is usually higher than top-1 accuracy, as any correct predictions in the 2nd through 5th positions will not improve the top-1 score, but do improve the top-5 score.

== In psychometrics and psychophysics == In psychometrics and psychophysics, the term accuracy is interchangeably used with validity and constant error. Precision is a synonym for reliability and variable error. The validity of a measurement instrument or psychological test is established through experiment or correlation with behavior. Reliability is established with a variety of statistical techniques, classically through an internal consistency test like Cronbach's alpha to ensure sets of related questions have related responses, and then comparison of those related question between reference and target population.

== In logic simulation ==

In logic simulation, a common mistake in evaluation of accurate models is to compare a logic simulation model to a transistor circuit simulation model. This is a comparison of differences in precision, not accuracy. Precision is measured with respect to detail and accuracy is measured with respect to reality.

== In information systems ==