And to follow up on what @PaigeMiller was saying about an interval, it doesn't depend on the unrealistic assumption that the underlying population values are identical, which is what the hypothesis test p value assumes. You know a priori that they are not identical, and so whatever p value comes out, it isn't "correct", and you don't know how far away from correct the p value is (or else you could apply some non-central correction). For some things (say a binomial underlying variable), it isn't even a smooth curve as you move away from identical.
(Thanks and a tip of the hat to my Math Stat prof Dr. Norm Matloff)
SteveDenham
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