Fixed Effects Analysis of Variance with Unequal Cell Sizes

Abstract

The so-called nonorthogonal or unequal n’s analysis of variance continues to be an area in which settled opinion apparently is absent. The lack of agreement is more apparent than real and probably results from a failure systematically to address and distinguish among certain logical, statistical, and computational problems that tend to disappear in the case of equal n’s but not otherwise. In particular, confusion has been fostered by naming results rather than stating in an unambiguous form the hypotheses being tested. Some elementary mathematical concepts and an unambiguous notation are suggested as tools to reconcile disagreements.