GLM Hypothesis Testing - Type II Sums of Squares

Type II sums of squares are sometimes called partially sequential sums of squares. Like Type I sums of squares, Type II sums of squares for an effect controls for the influence of other effects. Which other effects to control for, however, is determined by a different criterion. In Type II sums of squares, the sums of squares for an effect is computed by controlling for the influence of all other effects of equal or lower degree. Thus, sums of squares for main effects control for all other main effects, sums of squares for two-way interactions control for all main effects and all other two-way interactions, and so on.

Unlike Type I sums of squares, Type II sums of squares are invariant to the order in which effects are entered into the model. This makes Type II sums of squares useful for testing hypotheses for multiple regression designs, for main effect ANOVA designs, for full-factorial ANOVA designs with equal cell ns, and for hierarchically nested designs.

There is a drawback to the use of Type II sums of squares for factorial designs with unequal cell ns. In these situations, Type II sums of squares test hypotheses that are complex functions of the cell n's that ordinarily are not meaningful. Thus, a different method for testing hypotheses is usually preferred.

Whole Model Tests

Partitioning of Sums of Squares

Six Types of Sums of Squares

Contained Effects

Error Terms for Tests

Lack-of-Fit Tests Using Pure Error

Testing Specific Hypotheses

Estimability of Hypotheses

Testing Hypotheses for Repeated Measures and Dependent Variables

See also GLM - Index.