# Sum of Squares

For the model, you can choose a type of sums of squares. Type III is the most commonly used and is the default.

**Type I.** This method is also known as the hierarchical decomposition of the
sum-of-squares method. Each term is adjusted only for the term that
precedes it in the model. Type I sums of squares are commonly used
for:

- A balanced ANOVA model in which any main effects are specified before any first-order interaction effects, any first-order interaction effects are specified before any second-order interaction effects, and so on.
- A polynomial regression model in which any lower-order terms are specified before any higher-order terms.
- A purely nested model in which the first-specified effect is nested within the second-specified effect, the second-specified effect is nested within the third, and so on. (This form of nesting can be specified only by using syntax.)

**Type III.** The default. This method calculates the sums of squares of an effect
in the design as the sums of squares adjusted for any other effects
that do not contain it and orthogonal to any effects (if any) that
contain it. The Type III sums of squares have one major advantage
in that they are invariant with respect to the cell frequencies as
long as the general form of estimability remains constant. Hence,
this type of sums of squares is often considered useful for an unbalanced
model with no missing cells. In a factorial design with no missing
cells, this method is equivalent to the Yates' weighted-squares-of-means
technique. The Type III sum-of-squares method is commonly used for:

- Any models listed in Type I.
- Any balanced or unbalanced models with no empty cells.