Critical values for testing partially ordered alternatives in the analysis of variance

In the analysis of variance of a one-way classification, the null hypothesis customarily states that the samples have been drawn from populations having the same mean. Useful alternative hypotheses order the means in simply or partially ordered sequences. The tables presented in this paper provide critical values for testing against simply or partially ordered alternatives about the means of k normal distributions with unknown common variance when k = 4 and k = 5. They cover some of the cases most likely to be encountered in practice and comprise tables of the critical values of when the amalgamation with equal weight is performed.