k-ratio t tests for multiple comparisons involving several treatments and a control

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 tG, the standardized average of the observed TvC differences, and through FT, the observed between-treatments F ratio. From these adaptive dependences on tG and FT, 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.