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I am currently evaluating a mixed research design, where a treatment and a control group are evaluated over time. I am interested in the effectiveness of the treatment and therefore evaluate the significance and size of the interaction effect.

Theoretically it would be important, if the two groups are in fact equal before the treatment. This is not tested in the Mixed-ANOVA, since the maineffect group is pooled over both timepoints.

Is an additional t-test the right way to evaluate this initial equalness of the groups? And would I have to think about some alpha-corrections due to multiple testing?

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As with any ANOVA, mixed or not, the common approach would be to test for simple effects of treatment (i.e. pair-wise differences between groups at each time point) AFTER a significant interaction (as liberal as p<0.01 is rather common). This can be done with T-tests.

These comparisons allow you to interpret the interaction with statements such as "the treatment increased parameter A compared to control (P-value) by weeks X, Y, and Z." You would also be able to confirm that groups did not differ at baseline.

It would be prudent to then correct for these multiple comparisons with a Bonferroni adjustment (OK) or Holm-Bonferroni (Better).

If you do not have a significant interaction, but you do have a significant main effect of treatment, this could very-well indicate that your groups differed at baseline, yet there was no effect of treatment.

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