In two comprehensive papers, Box (1954a, 1954b) examined the effect of inequality of variance on the standard F-tests for one-way and two-way analysis of variance classifications. (We shall use the shorthand 'ANOVA’ to represent 'analysis of variance.') These papers provided a number of theorems on the exact and approximate distributions of various quadratic forms and ratios of quadratic forms, and applied them to the ANOVA situations mentioned above. (Some ap¬plication was also made to ANOVA situations where the errors were correlated.) In the present paper, we shall examine certain results found by Box for the one-way classification, and show how a Bayesian analysis can throw light on the consequences of Box's work in a given experimental situation.
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