For testing the equality of k normal means against simple tree order, it is shown that Abelson-Tukey's minimax single contrast test is generalized Bayes and the orthogonal contrasts test by Mukerjee, Robertson and Wright (1987) may be regarded as an approximate generalized Bayes test for uniform diffuse priors. For testing simple order, a single contrast Bayes test and approximate multiple contrast Bayes test are derived for uniform diffuse priors. A prior distribution is shown for which Abelson-Tukey's test is generalized Bayes. Their power surfaces including likelihood ratio tests are drawn to give a global look when k=3. Power comparison is made for k=3,4 by numerical integration and k=10 by simulation.