The Matched Pairs Problem with Exponential Variates

Abstract

AbstractTwo classes of tests for the hypothesis of bivariate symmetry are studied. For paired exponential survival times (t1j, t2j), the classes of tests are those based on t1j‐t2j and those based on log t1j–log t2j. For each class the sign, signed ranks, t and likelihood ratio tests are compared via Pitman's criterion of asymptotic relative efficiency (ARE). For tests based on t1j — t2j, it is found that: (1) the efficacy of the paired t depends on the coefficient of variation (CV) of the pair means, (2) the signed rank test has the same ARE to the sign test as for the usual location problem.For tests based on log t1j — log t2j, the ARE comparisons reduce to the well‐known results for the one‐sample location problem for samples from a logistic density. Hence, the signed rank test is asymptotically efficient. Furthermore, analyses based on log t1j — log t2j are not complicated by the underlying pairing mechanism.