In the fields of science, engineering, industry, and statistics, the accuracy of a measurement
system is the degree of closeness of measurements of a quantity to that quantity's actual 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.
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.
A measurement system is considered valid if it is both accurate and precise. Related terms
include bias and error. The terminology is also applied to indirect
measurements—that is, values obtained by a computational procedure from observed data.
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.
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.
Quantification
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, according to the book of industrial instrumentation
Antonio Creus. Ideally a measurement device is both accurate
and precise, with measurements all close to and tightly clustered around the known 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 and maintained by national standards organizations such as the National
Institute of Standards and Technology in the United States.
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, while a recording of 8,436 m would imply a margin of error
of 0.5 m. A reading of 8,000 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 × 103 m indicates that the first zero is significant while 8.000 × 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 × 103 m.
In fact, it indicates a margin of 0.05 km. However, reliance on this convention can lead
to false precision errors when accepting data from sources that do not obey it.
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.
Terminology of ISO 5725
A shift in the meaning of these terms appeared with the publication of the ISO 5725 series
of standards, which is also reflected in the 2008 issue of the "BIPM International Vocabulary
of Metrology", items 2.13 and 2.14. According to ISO 5725-1, the terms trueness
and precision are both used to describe the accuracy of a measurement. Trueness refers
to the closeness of the mean of the measurement results to the actual value and precision
refers to the closeness of agreement within individual results. Therefore, according to
the ISO standard, the term "accuracy" refers to both trueness and precision.
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. 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 in the population. To make the
context clear by the semantics, it is often referred to as the "Rand Accuracy". It is
a parameter of the test.
On the other hand, precision or positive predictive value is defined as the proportion of the
true positives against all the positive results
An accuracy of 100% means that the measured values are exactly the same as the given values.
Also see Sensitivity and specificity. Accuracy may be determined from Sensitivity
and Specificity, provided Prevalence is known, using the equation:
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. In situations where the minority class is more important, F-measure may be
more appropriate, especially in situations with very skewed class imbalance.
Another useful performance measure is the balanced accuracy which avoids inflated performance
estimates on imbalanced datasets. It is defined as the arithmetic mean of sensitivity and
specificity, or the average accuracy obtained on either class:
If the classifier performs equally well on either class, this term reduces to the conventional
accuracy. In contrast, if the conventional accuracy is above chance only because the
classifier takes advantage of an imbalanced test set, then the balanced accuracy, as appropriate,
will drop to chance. A closely related chance corrected measure is:
A direct approach to debiasing and renormalizing Accuracy is Cohen's kappa, whilst Informedness
has been shown to be a Kappa-family debiased renormalization of Recall. Informedness and
Kappa have the advantage that chance level is defined to be 0, and they have the form
of a probability. Informedness has the stronger property that it is the probability that an
informed decision is made, when positive. When negative this is still true for the absolutely
value of Informedness, but the information has been used to force an incorrect response.
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 The concepts of accuracy and precision have
also been studied in the context of data bases, information systems and their sociotechnical
context. The necessary extension of these two concepts on the basis of theory of science
suggests that they should be centered on accuracy defined as the closeness to the true value
seen as the degree of agreement of readings or of calculated values of one same conceived
entity, measured or calculated by different methods, in the context of maximum possible
disagreement.
See also Accepted and experimental value
Engineering tolerance Exactness
Experimental uncertainty analysis F-score
Measurement uncertainty Precision
Probability Sensitivity and specificity
Significant figures Statistical significance
References
External links BIPM - Guides in metrology - Guide to the
Expression of Uncertainty in Measurement and International Vocabulary of Metrology
"Beyond NIST Traceability: What really creates accuracy" - Controlled Environments magazine
Precision and Accuracy with Three Psychophysical Methods
Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, Appendix
D.1: Terminology Accuracy and Precision
Accuracy vs Precision — a brief, clear video by Matt Parker