A symmetric analysis of paired rankings with application to temporal patterns of hormonal concentration

Mallows (1957, Biometrika 44, 114-130) introduced a simple model to describe the distribution of subjects' rankings of the items from some fixed set. Both Feigin (1992, in Probability Models and Statistical Analyses for Ranking Data, 75-91. New York: Springer-Verlag) and Critchlow and Verducci (1992, Journal of the Royal Statistical Society, Series C 41, 17-29) have considered an asymmetric extension of this model, designed to analyze the distribution of subjects' post-treatment rankings, conditional on their pretreatment rankings. Here a symmetric extension is introduced and is used to analyze the joint distribution of paired rankings associated with the patterns of prolactin hormonal response of wife-husband pairs during the course of a marital conflict. Locally most powerful tests are developed to check for independence of the wife and husband responses, and for differences in their divergence from a theoretical pattern of response. Additionally, conditional on the rankings of one group (e.g., the wives), the locally most powerful test of an affinity for the theoretical pattern in the other group (e.g., the husbands) turns out to be closely related to the test given by Critchlow and Verducci.