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In this chapter, it is assumed that the reader has some familiarity with the basic concepts of Bayesian inference and of conventional analysis of variance. This allows attention to be focused on what happens when the two are brought together. For this purpose, extensive use is made of results presented by Box and Tiao ( 1973). This source provides, by far, the most extensive treatment of analysis of variance from a Bayesian point of view, and the interested reader will find in it proofs and generalizations of most of the material appearing here. This having been said, the author feels relieved of the obligation to make further reference to Box and Tiao. Although occasional reference to other relevant Bayesian (and non-Bayesian) work will be made, there has been no attempt to be systematic or exhaustive in this respect. Instead, the emphasis is on laying out, as clearly as possible, a Bayesian approach to analysis of variance. Readers wishing to see a similar approach for multivariate analysis of variance and covariance are referred to Woodworth ( 1979).
Logically, the place for Bayesian inference to begin is with the specification of prior beliefs. This very important issue is almost completely sidestepped here. It is assumed that, in many cases at least, appropriate scientific reporting of experimental results should not include a description of the experimenter's personal posterior beliefs. Rather, the beliefs described should be those of someone whose prior knowledge was minimal compared with the information provided by the