Generalized bayes and multiple contrasts tests for simple loop-ordered normal means

Abstract

For testing the simple loop-ordered k normal means, Abelson-Tukey(1963)'s maximin single contrast test is obtained and N shown to be generalized Bayes for uniform diffuse prior on equally spaced means. Generalized Bayes test for a uniform diffuse prior on a pair of the nearest corner vectors to the center is derived and also that on pahs of the most distant corner vectors from the center is derived. When k=4, it is shown numerically that for given noncentrality parameter, the former test improves neither the maximum nor the minimum power of Abelson-Tukeys maximin single contrast test and thai the latter does improve the minimum power. It also improves the maximum power of the likelihood ratio test. We can say that the minimum power of the likelihood ratio test is believed to occur at the most distant corner vectors from the center as is observed by Singh and Schell (1992), contrary to Robertson,Wright and Dykstra(1988). Multiple contrast tests which may be regarded as an approximation of the generalized Bayes tests are obtained and their power comparisons are shown for the cases of k=A, 5 and 6. They are computationally easy and have better minimum power than that of Abel-son-Tukey s maximin single contrast test.