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I am measuring test performance at 10 different timepoints, before and after drug application.

So far I ran two-way repeated measures ANOVA and determined there is a significant timepoint, drug, and timepoint*drug effect.

We are particularly interested whether the test performance is different between the control and drug group at timepoints 1, 5 and 10.

I have been considering testing these three timepoints separately using paired t-test for each. I was wondering if that is an appropriate approach? Is it necessary to control for multiple comparisons? Which tests would be most suitable?

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If you have 10 time points then performing individual t-tests on each pair will get very annoying very fast. And yes, you do need to adjust for multiple comparisons. This is usually done with a GLMM (Generalized Linear Mixed Model), one model which would perform all this in one step. In case you are using R, you can use the nlme or lme4 packages.

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