Effective Hypothesis Decomposition

When in a factorial ANOVA design there are missing cells, then there is ambiguity regarding the specific comparisons between the (population, or least-squares ) cell means that constitute the main effects and interactions of interest. The General Linear Model chapter discusses the methods commonly labeled Type I, II, III, and IV sums of squares , and a unique Type V sums of squares option.
In addition, for sigma restricted models (e.g., in General Stepwise Regression ; some software offers the user a choice between the sigma restricted and overparameterized models), we propose a Type VI sums of squares option; this approach is identical to what is described as the effective hypothesis method in Hocking (1996). For details regarding these methods, refer to the Six types of sums of squares topic of the General Linear Model chapter.