If the conditions are grossly violated, you cannot put full faith into all p-values and confidence intervals, and thus results should be taken with a grain of salt and viewed as preliminary. Further model improvements must be made for so that conditions can be met
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this is mostly what I tell them too. For more advanced students they notice that inclusion of an interaction/other specifications helps, but I mostly tell them we are identifying whether we can use these results, or if a more advanced approach is needed (which will be covered in future classes).
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I agree with all the above, but I also say you could perform a permutation test instead of a t-test. since this question often arises as a part of the final project, I don't actually recommend they get into this for the project, but I think pointing it out helps students feel a bit more comfortable with why we learned two different approaches to hypothesis testing in general. because one of them is quite useful when the assumptions behind the form of the null hypothesis distribution break down!
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