Analysis of contingency tables with between-subjects variability.

When separate contingency tables are collected from each S or experimental unit, two null hypotheses concerning the association between the attributes can be tested: (a) No S shows any association, and (b) there is no mean association over the population of Ss. In almost all psychological data, the association varies among Ss, and the population hypothesis (Hypothesis b) is appropriate. Common contingency-table methods (e.g., log-linear models) test Hypothesis a and have a positive bias. To test Hypothesis b, the association should be compared with an empirical estimaztes of its variability, as in the analysis of variance, not with the multinomial sampling variability of the observations. Nine test statistics were examoned by simulation