Tests for Equality of Correlated Proportions in a Polychotomous Response Design

Abstract

This paper surveys available techniques and introduces an explicit statement of a new statistic to test for equality of correlated proportions in a polychotomous response design. The statistic does not require use of general linear models methodology, but it is an explicit, special case of methodology implicit in Bhapkar (1966), Grizzle, Starmer, and Koch (1969) and Koch and Reinfurt (1971). The large-sample distribution for the test statistic is derived as well as computational formulas for calculating the statistic. Associated post hoc procedures are also developed. A conservative, modified form of the statistic is constructed, and an empirical investigation of the small sample behavior of both statistics is carried out via Monte Carlo sampling. A set of guidelines for the potential user of the techniques is provided.