A SYMMETRICAL ANALYSIS OF PAIRED RANKINGS WITH APPLICATION TO TEMPORAL PATTERNS OF HORMONAL CONCENTRATION

Mallows (1957, Biometrika 44, 114-130) introduced a simple model to de scribe the distribution of subjects' rankings of the items from some f ixed set. Both Feigin (1992, in Probability Models and Statistical Ana lyses for Ranking Data, 75-91. New York: Springer-Verlag) and Critchlo w and Verducci (1992, Journal of the Royal Statistical Society, Series C 41, 17-29) have considered an asymmetric extension of this model, d esigned to analyze the distribution of subjects' post-treatment rankin gs, conditional on their pretreatment rankings. Here a symmetric exten sion is introduced and is used to analyze the joint distribution of pa ired rankings associated with the patterns of prolactin hormonal respo nse of wife-husband pairs during the course of a marital conflict. Loc ally most powerful tests are developed to check for independence of th e wife and husband responses, and for differences in their divergence from a theoretical pattern of response. Additionally, conditional on t he 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.