In a mixed two-way ANOVA, why does a Groups x Intervals interaction decompose under SSwithin and not SSbetween? Say I've got three treatment groups, and I measure them at three time points. Since the interaction in question involves both the groups (which occur between subjects) and the time points (which occur within subjects), why should the Groups x Intervals interaction be decomposed under SSwithin and not SSbetween?
 A: In (repeated-measures + between-groups) ANOVA the RM factor Intervals and the Intervals*Group interaction are both tested against the usual error term. So they are customarily shown in the same table, within-subject effects. The Group factor, though, is tested against a special error term, which is the mean square of the implied random factor subject as nested within factor Group. Hence test for Group go along with Intercept in another table, between subject effects.
You may obtain the same as in (repeated-measures + between-groups) ANOVA results via split-plot ANOVA. It is univariate ANOVA with dependent characteristic Y and between-subject factors Group, Intervals and Subject. The latter is explicit factor, random, nested in Group. Model is Intercept + Group + Subject(Group) + Intervals + Intervals*Group. You will see in the ANOVA table that all effects but the first two are tested against MS(Error), while in testing the first two, Intercept and Group, the error-denominator is MS(Subject(Group)) is used.
