Chapter 7: Analysing the Data Part IV : Analysis of Variance

# Scenario and Data Set #5 SPSS Output 7.2 General Linear Model - General Factorial

## Profile Plots

### Between Subjects Factors

Here the variables being analysed are identified and the basic design (i.e., a 2 X 2 factorial design).

### Descriptive Statistics

Here are all the means, sds, and Ns that we want.

### Levene's Test of Equality of Error Variance

Here is the homogeneity test on the four groups of data (notice df = 3). The thing to focus on is the "Sig." value. Here .970 is clearly not significant, so we have no reason to doubt the assumption of homogeneity of variance.

### Tests of Between Subjects Effects

Here is the main summary table for the analysis. There is more in this table than we really want. In particular, ignore "Intercept". This is like the constant in normal regression. First look at the "Sig." column and notice that the two main effects are not significant but that the interaction is highly significant. The plot of the means clearly displays this result as well.

Notice the Sums of Squares column. The "model" is the overall, total sums of squares (855.0) in the numcorr variable that is explained by the two main effects and interaction considered together. The SS for Lecture room and Testing room are both = 5.0, whereas the SS for the interaction is 845.0. Obviously these data have been set up to show a highly significant interaction while having two main effects that are not significant Ð just to illustrate their independence.

The error Sums of Squares is 146.0. Together with the explained SS, a total of 1001.0 was the total variability in the numcorr variable. Eta-square for the interaction effect is a very high .884 or 88.4%.