Sequential versus Partial Sums of Squares In SPSS, the default mode is Type IIType III Sums of Squares, also known as partial Sums of Squares (SS). In a partial SS model, the increased predictive power with a variable added is compared to the predictive power of the model with all the other variables except the one being tested.
Crosscomparison of the type III method (e. g. with ezANOVA) to SPSS 17 gives identical output (using the" levenecentermean" option if you want to use Levene's original test, like SPSS does) to the following SPSS syntax: Mar 02, 2011 The anova and aov functions in R implement a sequential sum of squares (type I). As indicated above, for unbalanced data, this rarely tests a hypothesis of interest, since essentially the effect of one factor is calculated based on the varying levels of the other factor.
From SPSS Keywords, Volume 53, 1994 Many users of SPSS are confused when they see output from REGRESSION, ANOVA or MANOVA in which the sums of squares for two or more factors or predictors do not add up to the total sum of squares for the model. Let R() represent the residual sum of squares for a model, so for example R(A, B, AB) is the residual sum of squares fitting the whole model, R(A) is the residual sum of squares fitting just the main effect of A, and R(1) is the residual sum of squares fitting just the Type I and II sums of squares At least four types of sums of squares exist.
We will discuss two of these, the so called Type I and Type II sums of squares. The dierence between the two is explained below. Type I sums of squares These are also called sequential sums of squares. There is one sum of squares (SS) for each variable in ones linear model. The sequential sum of squares obtained by adding x 1 to the model already containing only the predictor x 2 is denoted as SSR(x 1 x 2).
The sequential sum of squares obtained by adding x 1 to the model in which x 2 and x 3 are predictors is denoted as SSR(x 1 x 2, x 3). The sequential sum of squares is the unique portion of SS Regression explained by a factor, given any previously entered factors.
For example, if you have a model with three factors or predictors, X1, X2, and X3, the sequential sum of squares for X2 shows how much of the remaining variation X2 explains, given that X1 is already in the model.
May 20, 2008 WARNING: R provides Type I sequential SS, not the default Type III marginal SS reported by SAS and SPSS. Reporting the Type III sum of squares (as SPSS does per default) for the main effect of stereotype threat means doing so while correcting for the interaction.
Even more so, TypeIII sums of squares do" NOT sum to the The adjusted sums of squares can be less than, equal to, or greater than the sequential sums of squares. Suppose you fit a model with terms A, B, C, and AB. Let SS (A, B, C, AB) be the sum of squares when A, B, C, and AB are in the model. Calculation of Sums of Squares for Intercept in SPSS UNIANOVA and GLM. Technote (troubleshooting) This calculation is first discussed below in terms of the matrix operations that SPSS uses to compute the sums of squares (SS).
the intercept would be fitted after those terms to get its sum of squares. Computing Type I, Type II, and Type III Sums of Squares directly using the general linear model. Data These are the data from Howell (2007) Table 16. 5 except