Abstract

Much of the criticism of Stevens's criterion for permissible statistics as applied to measurement data results from a lack of clarity in Stevens's position. In this paper set-theoretical notions have been used to clarify that position. We define a sig-function as a function defined on numerical assignments. If A and R are empirical and numerical relational systems, respectively, then a sig-function F is constant on A with respect to R if, and only if, the value of F is the same for all numerical assignments for A with respect to R. Using these notions we prove rigorously certain generalizations of Stevens's results