In relation to another question, Ben Bolker writes that
- if you have all-categorical predictors, you can test for heteroscedasticity (and other issues such as non-Normality) by dividing the data into unique combinations of categories (i.e., in the t-test, compare the variability in each group).
- if you have continuous predictors, then the only way to test the conditional distribution is to fit the model first, then evaluate the distribution of the residuals. Furthermore, even after you have the residuals, there generally aren't discrete groups in the data to which you could apply Levene's test.
In ANCOVA we do have a continuous predictor (the covariate). However, some statistical programs still report Levene's test in relation to ANCOVA. Here's an example a textbook provides from SPSS, in which Dose is a categorical predictor and Partner_Libido is a continuous covariate.
According to the author, this table
shows the results of Levene's test when partner's libido is included in the model as a covariate. Levene's test is significant, indicating that the group variances are not equal (and hence the assumption of homogeneity of variance has likely been violated).
Is ANCOVA a case in contradiction to Ben's general point that "even after you have the residuals, there generally aren't discrete groups in the data to which you could apply Levene's test"? Why/why not?
I realise that there's a school of thought that Levene's test is not really ever worth doing, even in relation to ANOVA/t-tests. But my question is whether Levene's test makes less sense in relation to ANCOVA than ANOVA/t-tests.