Seeking evidence of absence: Reconsidering tests of model assumptions
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Statistical tests can only reject the null hypothesis, never prove it. However, when researchers test modeling assumptions, they often interpret the failure to reject a null of "no violation" as evidence that the assumption holds. We discuss the statistical and conceptual problems with this approach. We show that equivalence/non-inferiority tests, while giving correct Type I error, have low power to rule out many violations that are practically significant. We suggest sensitivity analyses that may be more appropriate than hypothesis testing.
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