7 
Projectors of photogrammetric stereoscopic projection instruments have 
also been tested in this manner; see the international tests as reported in 
Hallert-Ottoson-Ternryd 1960. 
1.2 Tolerances 
The basic geometrical quality of the instrument can be expressed by the stand 
ard error of unit weight after the determination of possible regular sources of 
error as parameters in the adjustment procedure. It is of fundamental impor 
tance for the tolerance tests described here, that the individual errors or 
residuals, from which the standard error of unit weight is computed, belong 
to a normal distribution or, more completely expressed, that the distribution 
of the population from which the group of residuals is a sample, is normal. 
Therefore, normal distribution tests should be applied to the residuals after 
test adjustments. This requires a sufficient number of residuals, preferably 
more than 100. In principle, the residuals should be independent. 
The tolerances can be established for the basic accuracy of the instrument 
(the standard error of unit weight), for the parameters of the adjustment (the 
regular errors) and for arbitrary functions thereof. 
1.21 The Standard Error of Unit Weight 
The problem is to decide when the standard error of unit weight of an instru 
ment being tested has reached such a level that it must be regarded as signifi 
cantly different from the corresponding value which is characteristic for that 
type of instrument. From a statistical point of view this latter value may be 
regarded as a very carefully determined characteristic of the distribution of the 
error population of the instrument. According to the central limit theorem 
the actual distribution can generally be regarded, at least approximately, as 
normal, see Cramer 1946. 
This characteristic can be a standard error of unit weight s 0 , determined 
with infinite degrees of freedom. 
From a determination of whether the corresponding value 5 0 from a test 
(sample) with limited degrees of freedom deviates significantly from s 0 the 
M 2 
F-test of statistics is applied. First the ratio I — I is formed. This ratio should 
not exceed a specified number F which is based on the degrees of freedom m 
and n in the determination of s 0 and s 0 in addition to a percent value of F. 
For given values of the degrees of freedom and the percent (usually 5) the F 
value is tabulated in references such as Cramer 1954. 1 
x ) Several comprehensive and detailed tables are available.