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