The Effect of Categorization on Balanced Incomplete Blocks and Latin Squares

Abstract

Robustness in the various analysis of variance models should be assessed with regard to all the assumptions. Here we assess the effect of the continuity assumption. The models considered were chosen because they are in a sense fragile, and the effects might be anticipated to be more dramatic here. We identify at least one of the balanced incomplete block models for which severe categorization leads to tests with unacceptable sizes and aberrant power curves. Otherwise most of the models examined are generally satisfactory – that is, robust with respect to the continuity assumption.