2.1. The Concepts and Terms Precision and
Accuracy.
So far, among the many terms and expressions for geo
metrical quality in use, the two words precision and
accuracy seem to be most common. They are frequently
used without distinction and expressions of the following
type can often be found in the literature:
the precision (accuracy) is e.g. 1 micrometer (or 5 per
cent)
the results are precise (accurate) to . ..
First of all it could be said that there is a certain illogical
tendency in such expressions. The terms “inaccuracy” and
“imprecision” would doubtless be better but are certainly
very difficult to introduce into the traditional language.
Moreover, see Eisenhart, Ref. 2: 2.
The interpretation of the terms precision and accuracy
in statistically well defined concepts and terms is generally
more or less difficult. An investigation among a limited
number of scientists in the field of measurement as to the
interpretation of the expressions “precision (accuracy) of
1 micrometer” or “precise (accurate) to,...” has given a
number of different answers.
Among those are:
root mean square error (deviation), (sometimes maxi
mum values thereof)
standard error (standard deviation), (sometimes maxi
mum values thereof)
standard error (deviation) of unit weight, (sometimes
maximum values thereof)
mean error (deviation), (sometimes maximum values
thereof)
average error (deviation), (sometimes maximum values
thereof)
probable error (deviation),
maximum error (deviation),
confidence limit (on a certain confidence level)
tolerance
It is evidently not easy to decide in a certain case even
among specialists what precision and accuracy really mean
as they are used today. It is in many cases necessary to ask
the author, and sometimes it has been found that he does
not know either.
In “Glossary of some terms and expressions, used in
the theory of errors of photogrammetry” presented within
Commission VI, I.S.P. at the Lisbon Congress in 1964,
Ref. 2: 1, the committee tried to find clear definitions of
precision and accuracy. The definitions, existing in statis
tics, were used as basic expressions and were then some
what modified after proposals from national societies of
photogrammetry, individual experts from photogrammetric
and geodetic theory of errors and statistics.
Dr. Churchill Eisenhart, National Bureau of Standards,
Washington, D.C., U.S.A., has given a very concentrated
definition in a paper from 1963, Ref. 2: 2.
Accuracy has to do with closeness to the truth;
Precision, only with closeness together.
Further can be quoted:
“The precision, or more correctly, the imprecision of a
measurement process is ordinarily summarized by the
standard deviation of the process, which expresses the
characteristic disagreement of repeated measurements of
a single quantity by the process concerned, and thus serves
to indicate by how much a particular measurement is
likely to differ from other values that the same measure
ment process might have provided in this instance, or
might yield on remeasurement of the same quantity on
another occasion .. .
To characterize the accuracy of a measurement process
it is necessary, therefore, to indicate (a) its systematic
error or bias, (b) its precision (or /^precision)—and strictly
speaking, also (c) the form of the distribution of the indi
vidual measurements about the process average.”
In fact, to estimate possible systematic (or regular) errors
of a measurement instrument is the main purpose of calibra
tion procedures. The better such errors can be determined,
the closer will the residual errors of irregular nature
approach the deviations which characterize the precision
(or rather imprecision) and which usually are expressed as
the concept standard deviation as determined from repeated
or replicated measurements only. The standard deviation
can refer to one measurement or to the average of several
repetitions or replications. It is well known from statistics
that the standard deviation of the average of repeated
measurements decreases with the square root of the number
of repetitions and that consequently the standard deviation
of the average can be arbitrarily decreased by repetitions
and averaging only. This means that the precision of the
results of measurements can be arbitrarily increased from
repetitions only. The accuracy cannot be increased in the
same easy way because the measurements can be and
usually are physically correlated, i.e. affected with errors
of systematic nature. These errors have to be determined
as far as possible through the calibration procedure which
shall be applied also under real operational conditions.
But a complete determination of all systematic errors is
simply not possible because of the limitations of the
measurement procedure, by which the systematic errors
are to be determined. Therefore the residuals from a
calibration procedure are composed of an undetermined
mixture of small systematic errors and what usually are
called random or accidental errors.
If the systematic errors are significant they can be cor
rected for but never exactly because they are always
affected with irregular errors from the calibration proce
dure, where the systematic errors (to be used as correc
tions) were determined. Realistic estimations of statistical
values of these irregular errors in the calibration procedure
also belong to the tasks of the calibration. Because every
calibration procedure as a principle requires data of so