Nominal analysis of "variance"

Nominal responses are the natural way for people to report actions or opinions. Because nominal responses do not generate numerical data, they have been underutilized in behavioral research. On those occasions in which nominal responses are elicited, the responses are customarily aggregated over people or trials so that large-sample statistics can be employed. A new analysis is proposed that directly associates differences among responses with particular sources in factorial designs. A pair of nominal responses either matches or does not; when responses do not match, they vary. That analogue to variance is incorporated in the nominal analysis of "variance" (NANOVA) procedure, wherein the proportions of matches associated with sources play the same role as do sums of squares in an ANOVA. The NANOVA table is structured like an ANOVA table. The significance levels of the N ratios formed by comparing proportions are determined by resampling. Fictitious behavioral examples featuring independent groups and repeated measures designs are presented. A Windows program for the analysis is available.