Type I, II, III (IV, V) Sums of Squares

When there are missing cells in a factorial ANOVA design, 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 STATISTICA General Linear Model (GLM) module implements the methods commonly labeled Type I, II, III, and IV sums of squares; in addition, STATISTICA offers methods for testing effects in incomplete designs, that are widely used in other areas (and traditions) of research.

Type V sums of squares. We propose the term Type V sums of squares to denote the approach that is widely used in industrial experimentation, to analyze fractional factorial designs; these types of designs are discussed in detail in the 2(k-p) Fractional Factorial Designs of the Introductory Overview to the Experimental Design module. In effect, for those effects for which tests are performed all population marginal means (least squares means) are estimable.

Type VI sums of squares. We propose the term Type VI sums of squares to denote the approach that is often used in programs that only implement the sigma restricted model (GLM offers the user a choice between the sigma restricted and overparameterized model). This approach is identical to what is described as the effective hypothesis method in Hocking (1996).

For additional details, see Six Types of Sums of Squares and GLM Index.