Residuals for two-way contingency tables, especially those computed for multiresponces

Abstract

The problem of testing statistical hypotheses of independence of two multiresponse variables is considered. This is a specific inferential environment to analyze certain patterns, particularly for the questionnaire data. Data analyst normally looks for certain combination of responses being more frequently chosen by responders than the other ones. A formalism that is adequate for the considerations of such a kind is connected with calculation of p-values within the so-called posthoc analysis. Since this analysis is often connected with one cell of an appropriate contingency table only, we consider residual (or deviate) of this cell. As a result of theoretical and experimental study we consider algorithms that can be effective for the problem. We consider the case of 2 × 3 tables. Some aspects are relevant also for classical i.e. uniresponsive contingency tables. © 2006 Springer.