Shrinkage Formulas for two Nominal Level Measures of Association

Abstract

To assess the degree of association extant in an r × c contingency table, analysts are likely to use two compound least-squares measures, Crameér's [Formula: see text] or Light and Margolin's [Formula: see text] Sample specific by, definition, both coefficients are positively biased. To estimate the degree to which two nominally scaled variables are related in a population, simple adjustments to reduce this bias can and should be made when the sample size is not large. Accordingly, the adjusted coefficients [Formula: see text] and [Formula: see text] are proposed. As shown, these generalized second-moment chance-corrected measures correspond with their multiple regression and point multiserial correlation counterparts, [Formula: see text] and [Formula: see text]