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k ‐ratio t tests for multiple comparisons involving several treatments and a control
Author(s) -
Brant Larry J.,
Duncan David B.,
Dixon Dennis O.
Publication year - 1992
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780110704
Subject(s) - seriousness , type i and type ii errors , mathematics , bayesian probability , statistics , a priori and a posteriori , statistical hypothesis testing , type (biology) , ecology , philosophy , epistemology , political science , law , biology
We consider the problem of simultaneously comparing several treatment means with a control mean and also with one another. Following an elementary decision‐theoretic Bayesian approach requiring the choice of a type‐I to type‐II error‐seriousness ratio k, a posteriori t tests are derived for testing both treatment versus control (TvC) and treatment versus treatment (TvT) differences. These k ‐ratio t tests are strictly comparisonwise in nature. That is, the test applied to any TvC or TvT difference d , depends in no way at all on whether the other differences are being tested. The test for d , however, does depend on the sizes of the other differences through t G , the standardized average of the observed TvC differences, and through F T , the observed between‐treatments F ratio. From these adaptive dependences on t G and F T , the critical t values can be large or small, thus avoiding the intuitive objections of under‐ or over‐conservatism in classical comparisonwise or experimentwise level testing rules.