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The Matched Pairs Problem with Exponential Variates
Author(s) -
Lachenbruch P. A.,
Woolson R. F.
Publication year - 1984
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710260407
Subject(s) - mathematics , combinatorics , statistics , sign test , bivariate analysis , sign (mathematics) , rank (graph theory) , exponential family , exponential function , mathematical analysis , wilcoxon signed rank test , mann–whitney u test
Two classes of tests for the hypothesis of bivariate symmetry are studied. For paired exponential survival times ( t 1j , t 2j ), the classes of tests are those based on t 1j ‐ t 2j and those based on log t 1j –log t 2j . 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 t 1j — t 2j , 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 t 1j — log t 2j , 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 t 1j — log t 2j are not complicated by the underlying pairing mechanism.