In this paper we discuss the sample size problem for balanced one-way ANOVA under a posterior Bayesian formulation of the problem. Using the distribution theory of appropriate quadratic forms we derive explicit sample sizes for prespecified posterior precisions. Comparisons with classical sample sizes are made. Instead of extensive tables, a Mathematica program for sample size calculation is given. The formulations given in this article form a foundational step towards Bayesian calculation of sample size, in general.
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