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This is a modified reblog of an earlier post, since I keep seeing papers that confuse this.
Suppose you are reading about a result x that is just statistically significant at level α (i.e., P-value = α) in a one-sided test T+ of the mean of a Normal distribution with n iid samples, and (for simplicity) known σ: H0: µ ≤ 0 against H1: µ > 0.
I have heard some people say:
A. If the test’s power to detect alternative µ’ is very low, then the just statistically significant x is poor evidence of a discrepancy (from the null) corresponding to µ’. (i.e., there’s poor evidence that µ > µ’ ).*See point on language in notes.
They will generally also hold that if POW(µ’) is reasonably high (at least .5), then the inference to µ > µ’ is warranted, or at least not problematic.
I have heard other people say:
B. If the test’s power to detect alternative µ’ is very low, then the just statistically significant x is good evidence of a discrepancy (from the null) corresponding to µ’ (i.e., there’s good evidence that µ > µ’).
They will generally also hold that if POW(µ’) is reasonably high (at least .5), then the inference to µ > µ’ is unwarranted.
Which is correct, from the perspective of the (error statistical) philosophy, within which power and associated tests are defined? Continue reading →
Excursion 3 Tour III:
