ANCOVA (GLM 2) (II)

ANCOVA in SPSS:

• ANOVA without including covariates

For the purpose of comparison, the ANOVA table that does not not consider the covariates is generated first. Nothing needs explanation.

• The main analysis

The Levene’s test is used to test the assumption of variance homogeneity. The format of the ANOVA table is largely the same as without the covariate, except that there is an additional row of information about the covariate.

The parameter estimates is selected in the option dialog box. In this table the reference group is set as the last group by default; the reference group is compared with all the other groups.

Groups’ B values represent the differences between the means of these groups (by comparing all other groups to the reference group). The significance of the t-tests tells whether the group means differ significantly. The degree of freedom for these t-test can be calculated as in normal regression as N – p – 1; N is the total sample size, and p is the number of predictors (see Page 406).

The value of B for the covariate tells us that other things being equal, if the covariate increases by on unit, how the outcome would change. The sign of this coefficient tells us the direction of the relationship between the covariate and the outcome.

• Contrast

Remember in “Analyze >> GLM >> Univariate >> Contrast” we set the reference group to be compared with all the other groups. Here are the relevant tables.

In the ANOVA table without including covariates, we generate the group means. However, these means could not be used for comparison because they have not been adjusted for the effect of the covariate.

The group means in the above “Estimate” table are generated after selecting “Display means for option”; they are adjusted means, and could be used for comparison.

• Post hoc test

This table shows the results of the corrected post hoc comparison.