Test Scores as Social Statistics: Comparing Distributions

Abstract

If test scores are considered ordinal but not cardinal attributes, the average test score may not be a meaningful way to summarize the scores of a group of individuals. Similarly, correlation coefficients may not form meaningful summary measures of association between test scores. Using the theory of stochastic ordering and quadrant dependence, new techniques that do not depend on any particular test scale are developed for reporting, interpreting, and comparing distributions of test scores. The use of a relevant test scale is considered also, as well as measures of distance between distributions.