Smoothing Balanced Single-Error-Term Analysis of Variance

We present an approach to smoothing balanced, single–error term analysis of variance (ANOVA), descended from Smith, that also allows spatial, temporal, or spatiotemporal smoothing. The approach addresses unreplicated designs, masked contrasts in effects with many degrees of freedom, and subgroup analysis, demonstrated using a study of denture-lining materials. Our approach is Bayesian but can be viewed as a way to generate frequentist procedures. A simulation experiment compares four priors, unsmoothed ANOVA, and dropping nonsignificant interactions. Three priors have advantages when some interactions are absent; dropping nonsignificant interactions has serious flaws. We contrast our approach with the approaches of Nobile–Green and Gelman.