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My question is a follow-up to this question, Statistical test for paired data at multiple time points?, where the OP asked about comparing paired data (left and right measurements) taken at three different time points. The answer that's provided is exactly what I would do: a mixed effects model with trt*time and a random effect for subject. Say my interest is not necessarily in the time trend, but whether there's a treatment effect at each time point. I have two follow-up questions: 1) if I did post-hoc comparisons of left and right at time1, time2, and time3, do I need to correct for multiple comparisons? I'm making only one comparison, but I'm making it three times. Is this the difference between familywise and experimentwise correction (let's say I had 3 trt levels instead of 2. Then I would correct for pairwise comparisons of the 3 levels, but would I correct for 3 comparisons or 9)?; 2) Is it inappropriate to simply conduct a t-test at each time point? And either correct for multiple comparisons or not. The answer to the original question advises against doing that, and I generally agree, but I see colleagues do that and I don't have a solid reason as to why it feels "wrong," except for the multiple comparison issue.

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