A formula for Type III sums of squares

Abstract

Type III methods were introduced by SAS to address difficulties in dummy-variable models for effects of multiple factors and covariates. They are widely used in practice; they are the default method in several statistical computing packages. Type III sums of squares (SSs) are defined by a set of instructions; an explicit mathematical formulation does not seem to exist.

An explicit formulation is derived in this paper. It is used to illustrate Type III SSs and to establish their properties in the two-factor ANOVA model.

Keywords:

• Type III effects
• unbalanced two-factor ANOVA
• Yates’s MWSM