Allmut Hörmann

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We describe two rank tests of association for paired exchangeable data motivated by the study of lifespans in twins. The pooled sample is ranked. The nonparametric test of association is based on R+, the sum of the smaller within-pair ranks. A second measure L+ is the sum of within-pair rank products. Under the null hypothesis of within-pair independence, the two test statistics are approximately normally distributed. Expressions for the exact means and variances of R+ and L÷ are given. We describe the power of these two statistics under a close alternative hypothesis to that of independence. Both the R+ and L+ tests indicate nonparametric statistical evidence of positive association of longevity in identical twins and a negligible relationship between the lifespans of fraternal twins listed in the Danish twin registry. The statistics are also applied to the analysis of a clinical trial studying the time to failure of ventilation tubes in children with bilateral otitis media.