A bayesian approach to prediction in analysis of variance settings

This paper takes the results of Lindley and smith ( 1972 ) one step further, by finding the predictive distribution of an observation y^* whose distribution is normal, and centred at A^* ₁θ₁ We then apply this distribution to the case of prediction based on data obtained in one and two wau ANOVA situations. For Example, it turns out that for two way ANOVA with interaction, the predictive mean, (which we would use as the predictor) is a weighted combination of sample main effects and interaction effects