# 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 for only 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 II.** This method calculates the sums of squares of
an effect in the model adjusted for all other "appropriate" effects.
An appropriate effect is one that corresponds to all effects that
do not contain the effect being examined. The Type II sum-of-squares
method is commonly used for:

- A balanced ANOVA model.
- Any model that has main factor effects only.
- Any regression model.
- A purely nested design. (This form of nesting can be specified 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 the effect, and orthogonal
to any effects (if any) that contain the effect. 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 and Type II.
- Any balanced or unbalanced model with no empty cells.

**Type IV.** This method is designed for a situation in which
there are missing cells. For any effect *F* in the design, if *F* is
not contained in any other effect, then Type IV = Type III = Type
II. When *F* is contained in other effects, Type IV distributes
the contrasts being made among the parameters in *F* to all higher-level
effects equitably. The Type IV sum-of-squares method is commonly used
for:

- Any models listed in Type I and Type II.
- Any balanced model or unbalanced model with empty cells.