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If there are only 2 groups for each manipulation (2x2 factorial design), how can you do planned contrast or post-hoc analysis comparing between two specific groups? Do you just do t-test?

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There are 4 possible treatment combinations in this case. You can do a priori contrasts between specific treatment combinations or a pairwise post hoc to compare all of them.

No, you do not just do t-tests because you will inflate your Type I error. Pairwise procedures adjust type I error rates, eg Tukey.

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