different technical conditions in t-test vs ANOVA

[hardin47]

Hi Jo,

We're getting towards the end of the term, which means that I just finished teaching ANOVA. I am once again confused about a technical detail, based both on your textbook and Whitlock and Schluter. I'm wondering if you can help.

When we think about the assumptions of a t-test, we always emphasize that the sampling distribution of the mean needs to be approximately normal. However, when we talk about ANOVA your book (and Whitlock and Schluter's) talks about the data being approximately normal. Of course data being normal is only one way to get an approximately normal sampling distribution, and so this difference in language has always left me puzzled.

Is it really the case that ANOVA requires the data to be sampled from a normal population, or is it that the sampling distribution of the mean needs to be normal, just like a t-test?

Thanks, Dan Daniel Stoebel (he/him)

Jo's response: Your intuition is right. The thing that matters is that the distribution of the mean is normal. And if the data are normal, then you get there. Of if you have large random samples you get there (CLT).

I think in our book we do say “normal data or large samples” for t-tests. But your point is well taken that we could say “normal data or large samples” for ANOVA too.