### Nonorthogonal Factorial Designs via SPSS point and click

The following data represent the relative effectiveness of three forms of psychotherapy for alleviating depression. Fifteen individuals were randomly assigned to one of three groups. After the fact, these individuals where placed into one of three categories based on the severity of their depression. Thus, this data set represents a 3 by 3 nonorthogonal factorial design with post hoc blocking.

#### 1. The analysis of the data given in Table 7.23 precedes in the typical way for factorial ANOVAs, that is, by making use of the SPSS univariate GLM procedure (recall the univariate procedure is available by clicking Analyze, then General Linear Model, and then Univariate). Because there are unequal sample sizes in the cells, the sums of squares can be decomposed in different ways (as formally explained in Tables 7.19 through 7.22). For purposes of replicating the Type I sums of squares results, we will do the analysis twice, once with therapy entered into the Fixed Factor(s) box first and once with severity entered into the Fixed Factor(s) box first.

#### 2. At this point clicking Continue on the Univariate: Model box and then OK on the Univariate box will yield the results. Because *severity* was entered first, this analysis gives the results to the “Type I—B entered first” summary in Table 7.25.

#### 3. It can be seen below that therapy was entered into the Fixed Factor(s) box first. Thus, they results of this analysis correspond to those from the “Type I—A entered first” summary in Table 7.25.

#### 4. At this point clicking Continue on the Univariate: Model box and then OK on the Univariate box will yield the results.

*Note: We could also perform Type II and Type III sums of squares to replicate the rest of the results given in Table 7.25. This is, however, Unnecessary, as all that is required is to change the desired sum of squares in the Sum of squaresbox (lower left-hand side of the Univariate: Model box). It does not make a difference which effect is entered into the Fixed Factor(s) box for Type II and Type III sums of squares.*