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I used to think that tests of normality were completely useless.

However, now I do consulting for other researchers. Often, obtaining samples is extremely expensive, and so they will want to do inference with n = 8, say.

In such a case, it is very difficult to find statistical significance with non-parametric tests, but t-tests with n = 8 are sensitive to deviations from normality. So what we get is that we can say "well, conditional on the assumption of normality, we find a statistically significant difference" (don't worry, these are usually pilot studies...).

Then we need some way of evaluating that assumption. I'm half-way in the camp that looking at plots is a better way to go, but truth be told there can be a lot of disagreement about that, which can be very problematic if one of the people who disagrees with you is the reviewer of your manuscript.

In many ways, I still think there are plenty of flaws in tests of normality: for example, we should be thinking about the type II error more than the type I. But there is a need for them.

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