When theoretical concepts in the area of social sciences are to be empirically verified, mathematical methods are used to analyse obtained data. These methods are based on certain measurement theories which relate the latent variable with the manifest one.
Measurement theories are based on specific assumptions. The conclusions possible within these theories are only valid as long as these requirements are met. Therefore, it is necessary to investigate the extent to which the mathematical assumptions are fulfilled and whether they are meaningful for a concept, e.g. the construct of achievement motive. Furthermore, the conclusions it is possible to draw on the basis of mathematical relationships must be relevant for the models within the area of the social sciences. That is, theoretical concepts and measurement theories must correspond to each other.
Lord and Novick (1968) mention in this context (p. 24):
For this reason our (i.e. test theory) models must be stated and employed with much discretion. We must resist the temptation to make assumptions simply because we desire to obtain certain results and formulas.
The most frequently used procedures for an evaluation of empirical data, for example, t-test, regression-analysis or variance analysis, are based on the so-called classical test theory. This theoretical approach has, however, quite a series of disadvantages. One of the main arguments against the classical test theory is that it is not sample-free. In particular, this means that the parameters of any two subjects can not be compared on their own virtues alone; but the group or population to which for whatever reason they may be referred, plays an essential role. This becomes evident when considering that the reliability-coefficient is a ratio of variances. The reliability of a reading-ability-test e.g. will probably be lower for a group of 13-yr old high school pupils than for a group of all 13-yr olds, because the former group is much more homogeneous. This means the ability of the high school pupil Henry Brown can be measured much more reliably when measured within the sample which is represen-