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Large-Scale Inference by Bradley Efron

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6

Theoretical, Permutation, and Empirical Null Distributions

In classical significance testing, the null distribution plays the role of devil’s advocate: a standard that the observed data must exceed in order to convince the scientific world that something interesting has occurred. We observe, say, z = 2, and note that in a hypothetical “long run” of observations from a image(0, 1) distribution less than 2.5% of the draws would exceed 2, thereby discrediting the uninteresting null distribution as an explanation.

Considerable effort has been expended trying to maintain the classical model in large-scale testing situations, as seen in Chapter 3, but ...

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