accuracy

1 the quality of nearness to the truth or the true value; "he was beginning to doubt the accuracy of his compass"; "the lawyer questioned the truth of my account" [syn: truth] [ant: inaccuracy]

2 (mathematics) the number of significant figures given in a number; "the atomic clock enabled scientists to measure time with much greater accuracy"

English

Etymology

From accurate and -cy suffix.

Pronunciation

Noun

1. The state of being accurate; freedom from mistakes, this exemption arising from carefulness; exact conformity to truth, or to a rule or model; precision; exactness; nicety; correctness

   The value of testimony depends on its accuracy.

   • Reid

     The professed end [of logic] is to teach men to think, to judge, and to reason, with precision and accuracy.

   • Lardner

     The accuracy with which the piston fits the sides.

Translations

In the fields of science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual (true) value. Accuracy is closely related to precision, also called reproducibility or repeatability, the degree to which further measurements or calculations show the same or similar results. The results of calculations or a measurement can be accurate but not precise; precise but not accurate; neither; or both. A result is called valid if it is both accurate and precise. The related terms in surveying are error (random variability in research) and bias (non-random or directed effects caused by a factor or factors unrelated by the independent variable).

Accuracy vs precision - the target analogy

In many cases precision can be characterised in terms of the standard deviation of the measurements, sometimes incorrectly called the measurement process's standard error. The smaller the standard deviation, the higher the precision. In some literature, precision is defined as the reciprocal of variance, while many others still confuse precision with the confidence interval. The interval defined by the standard deviation is the 68.3% ("one sigma") confidence interval of the measurements. If enough measurements have been made to accurately estimate the standard deviation of the process, and if the measurement process produces normally distributed errors, then it is likely that 68.3% of the time, the true value of the measured property will lie within one standard deviation, 95.4% of the time it will lie within two standard deviations, and 99.7% of the time it will lie within three standard deviations of the measured value.

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.

With regard to accuracy we can distinguish:

• 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. Here, when 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 8436 m would imply a margin of error of 0.5 m (the last significant digits are the units).

A reading of 8000 m, with trailing zeroes and no decimal point, is ambiguous; the trailing zeroes may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: '8.0 x 10³ m' indicates that the first zero is significant (hence a margin of 50 m) while '8.000 x 10³ m' indicates that all three zeroes are significant, giving a margin of 0.5 m. Similarly, it is possible to use a multiple of the basic measurement unit: '8.0 km' is equivalent to '8.0 x 10³ m'. In fact, 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.

Looking at this in another way, a value of 8 would mean that the measurement has been made with a precision of '1' (the measuring instrument was able to measure only up to 1's place) whereas a value of 8.0 (though mathematically equal to 8) would mean that the value at the first decimal place was measured and was found to be zero. (The measuring instrument was able to measure the first decimal place.) The second value is more precise. Neither of the measured values may be accurate (the actual value could be 9.5 but measured inaccurately as 8 in both instances). Thus, accuracy can be said to be the 'correctness' of a measurement, while precision could be identified as the ability to resolve smaller differences.

Precision is sometimes stratified into:

• 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.

A common way to statistically measure precision is a Six Sigma tool called ANOVA Gage R&R. As stated before, you can be both accurate and precise. For instance, if all your arrows hit the bull's eye of the target, they are all both near the "true value" (accurate) and near one another (precise).

Something to think about: In the NFL, a place kicker makes 9 of 10 field goals, and another makes 6 of 10. Even if the 6 that the second kicker made were straight down the middle and the first kicker just made his in, he is still less accurate and less precise than the first kicker. This differs from the darts example because either you make it or you do not; there are not different levels of points that can be scored.

Accuracy 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 true results (both true positives and true negatives) in the population. It is a parameter of the test.

=\frac

An accuracy of 100% means that the test identifies all sick and well people correctly.

Also see Specificity (tests) and Sensitivity (tests).

Accuracy may be determined from Sensitivity and Specificity, provided Prevalence is known, using the equation:

=()() + ()(1-)

The accuracy paradox for predictive analytics states that predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. It may be better to avoid the accuracy metric in favor of other metrics such as precision and recall.

Accuracy and precision in psychometrics

In psychometrics the terms accuracy and precision are interchangeably used with validity and reliability respectively. Validity of a measurement instrument or psychological test is established through experiment or correlation with behavior. Reliability is established with a variety of statistical technique (classically Cronbach's alpha).

See also

• Calculation of glass properties - Decreasing accuracy of experimental data in modern scientific publications for some glass properties

References

• Accuracy and Precision

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