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SSTYPE(1) Type I sum-of-squares method. The Type I sum-of-squares method is also known as the hierarchical decomposition of the sum-of-squares method. Each term is adjusted only for the terms that precede it on the DESIGN subcommand. Under a balanced design, it is an orthogonal decomposition, and the sums of squares in the model add up to the total sum of squares.

SSTYPE(2) Type II sum-of-squares method. This method calculates the sum of squares of an effect in the model adjusted for all other “appropriate” effects. Anappropriate effect is one that corresponds to all effects that do not contain the effect being examined. For any two effects F1 and F2 in the model, F1 is said to be contained in F2 under the following three conditions: · Both effects F1 and F2 have the same covariate, if any. · F2 consists of more factors than F1. · All factors in F1 also appear in F2. The intercept effect is treated as contained in all the pure factor effects. However, it is not contained in any effect involving a covariate. No effect is contained in the intercept effect. Thus, for any one effect F of interest, all other effects in the model can be classified as in one of the following two groups: the effects that do not contain F or the effects that contain F. If the model is a main-effects design (that is, only main effects are in the model), the Type II sum-of-squares method is equivalent to the regression approach sums of squares. This means that each main effect is adjusted for every other term in the model.

SSTYPE(3) Type III sum-of-squares method. This is the default. This method calculates the sum of squares of an effect F in the design as the sum 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 —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 used 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, and it also coincides with the overparameterized -restricted model.

SSTYPE(4) Type IV sum-of-squares method. 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, then Type IV distributes the contrasts being made among the parameters in F to all higher-level effects equitably.

[Last updated on 27 November, 2003]

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