10 
gains in geometrical quality also decrease in magnitude as the number of stars 
exceeds 4. However, the reliability of the determination of the standard error 
of unit weight is considerably improved by an increased number of stars. 
The standard error of unit weight of the image coordinates is of basic import 
ance for all photogrammetric procedures and therefore will be discussed at 
greater length. 
1.1. Determination of the standard error of unit weight of image coordinate 
measurements 
In the concept of standard error of unit weight it is assumed that an adjustment 
according to the method of least squares has been made of discrepancies in 
the measurement of known data of high reliability. The solutions of the normal 
equations give the sum of the squares of the residuals, and the variance is 
computed by dividing this sum by the number of redundant observations or 
degrees of freedom. The square root of the variance is then the standard error 
of unit weight. This is an expression for the accuracy of the basic measure 
ments while, as indicated above, the standard deviation, as determined from 
replicated or repeated observations only, is an expression for the precision. 
The standard deviation can be referred to one single observation or to the 
average. Theoretically the standard deviation of the average can be decreased 
nearly arbitrarily by increasing the replications or repetitions. 
If the procedure indicated above is used for the determination of the standard 
error of unit weight, more parameters (regular errors) can be introduced in 
the adjustment procedure according to data or estimates concerning such 
errors. Frequently affine deformations, radial and tangential distortion are 
present and call for corresponding differentials in the basic error equations. 
It may also be advantageous to compute the residuals after a preliminary 
adjustment to see if the behaviour of the residuals indicates some further 
possible regular error which may be expressed in a mathematical formula and 
then introduced in the error equation. The best indication of the significance 
of such a regular error is that the variance or the standard error of unit weight 
decreases significantly after the adjustment. The significance of the regular 
error can also be tested with the aid of its own standard error. In such a case, 
the /-test of statistical methods is the most usual one because the number of 
redundant observations in the adjustment procedure is usually limited. From 
a table of the /-distribution and for a desired significance level (usually 5 per 
cent) the factor t p can be determined for the actual degrees of freedom. If 
the determined regular error exceeds its own standard error multiplied by the 
actual / p -value, the regular error can be regarded as significant on the chosen 
level. For all such judgements the standard error of unit weight is of basic 
importance. Normal distribution tests of the residuals are also of great interest.