Exemplifying natural science measurement in the social sciences with Rasch measurement theory

This paper presents a social science example of measurement in which the integer count from a convenient origin is shown to be in equal units. This feature is identical to direct measurement in the natural sciences. The example rests on applying the probabilistic Rasch measurement model to two assessments of the same persons which (i) realises measurement as a real valued comparison between persons invariant with respect to instruments; (ii) characterises random variation of replicated measurements by the Gaussian distribution; (iii) shows that the variance of the replications is the inverse of the size of the unit.