SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

A new nonparametric two-way ANOVA model for ordinal dependent variables

Andras Vargha
ELTE Institute of Psychology

Brunner, Dette, and Munk (1997), and Brunner and Puri (2001) introduced the concept of Pi relative treatment effects, by means of which the value levels of several samples can be compared even if the dependent variable is only ordinally scaled. Kulle (1999) derived asymptotically exact procedures for testing the null hypothesis H0: P1 = P2 = ¼  = Ph (h > 2) in the one-way independent samples layout. Kulle (1999) formulated also a two-way linear model for the main and interaction effects of the relative treatment effects.

In the present paper it will be shown that Kulle's two-way model may in certain cases be inconsistent with the corresponding parametric two-way ANOVA model, even if the dependent variable is normal and the assumption of variance homogeneity holds. Based on the concept of conditional relative treatment effects, a new nonparametric two-way ANOVA model will be introduced. This is a generalization of Kulle’s one-way model but does not suffer from the above mentioned deficiency of Kulle's two-way model of relative treatment effects.