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UMP(U)‐Tests for a Binomial Parameter: A Paradox
Author(s) -
Finner Helmut,
Strassburger Klaus
Publication year - 2001
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 - 10.1002/1521-4036(200110)43:6<667::aid-bimj667>3.0.co;2-o
Subject(s) - mathematics , binomial (polynomial) , equivalence (formal languages) , sample size determination , power function , statistics , binomial distribution , parameter space , discrete mathematics , mathematical analysis
We consider uniformly most powerful (UMP) as well as uniformly most powerful unbiased (UMPU) tests and their non‐randomized versions for certain hypotheses concerning a binomial parameter. It will be shown that the power function of a UMP(U)‐test based on sample size n can coincide on the entire parameter space with the power function of the corresponding test based on sample size n + 1. A complete characterization of this paradox will be derived. Apart some exceptional cases for two‐sided tests and equivalence tests the paradox appears if and only if a test based on sample size n is non‐randomized.