# Difference between Accuracy and Precision

Precision is a
description of random errors, a measure of statistical variability.

Accuracy has
two definitions:

1. more commonly, it is a description of
systematic errors, a measure of statistical bias;

2. alternatively, ISO defines accuracy as
describing both types of observational error above (preferring the term
trueness for the common definition of accuracy).

In the fields
of science, engineering and statistics, 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 resultsAlthough 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 (non-random or directed effects caused by a factor or factors
unrelated to the independent variable) and error (random variability).

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.

Statistical
literature 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. In military terms, accuracy refers primarily to the accuracy of
fire (or "justesse de tir"), the precision of fire expressed by the
closeness of a grouping of shots at and around the centre of the target.

Quantification

See also:
False precision

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.

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: SystÃ¨me international d'unitÃ©s)
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 (the last significant place is the tenths
place), while a recording of 8,436 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 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 (hence a margin of 50 m) 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 (50 m). 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.

ISO definition
(ISO 5725)

According to
ISO 5725-1, Accuracy consists of Trueness (proximity of measurement results to
the true value) and Precision (repeatability or reproducibility of the
measurement)

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.

According to
ISO 5725-1the 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 and
precision is the closeness of agreement among a set of results.

ISO 5725-1 and
VIM also avoid the use of the term "bias", previously specified in BS
5497-1,[6] because it has different connotations outside the fields of science
and engineering, as in medicine and law.

Accuracy of a
target grouping according to BIPM and ISO 5725

Low accuracy,
poor precision, good trueness

Low accuracy,
good precision, poor trueness

In binary
classification[edit]

Main article:
Evaluation of binary classifiers

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) among the
total number of cases examined.[7] 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.

In
psychometrics and psychophysics[edit]

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.[citation needed]

**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.

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