Overpowered and underpowered chi-squared tests – or are they?

This is a very quick thought for teaching, in passing. People often talk about chi-squared tests being overpowered when n is large. It occurs to me that a good way to broach this concept in an intuitive way is to point out that they are no different to t-tests and the like, but do not provide a meaningful point estimate. When you see the mean difference in blood pressure from drug X is 0.3mmHg, with p<0.001, you know it is clinically meaningless. When you see X2=3.89, nobody knows what to think. So perhaps the best thing to do is to mention this alongside non-parametric rank-based procedures, when you explain that they don’t give you an estimate or confidence interval.

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