It’s a balmy day today on Ship StatInfasST: An invigorating wind has a salutary effect on our journey. So, for the first time I’m excerpting all of Excursion 5 Tour I (proofs) of Statistical Inference as Severe Testing How to Get Beyond the Statistics Wars (2018, CUP)
A salutary effect of power analysis is that it draws one forcibly to consider the magnitude of effects. In psychology, and especially in soft psychology, under the sway of the Fisherian scheme, there has been little consciousness of how big things are. (Cohen 1990, p. 1309)
So how would you use power to consider the magnitude of effects were you drawn forcibly to do so? In with your breakfast is an exercise to get us started on today’ s shore excursion.
Suppose you are reading about a statistically signifi cant result x (just at level α ) from a one-sided test T+ of the mean of a Normal distribution with n IID samples, and known σ: H0 : μ ≤ 0 against H1 : μ > 0. Underline the correct word, from the perspective of the (error statistical) philosophy, within which power is defined.
- If the test’ s power to detect μ′ is very low (i.e., POW(μ′ ) is low), then the statistically significant x is poor/good evidence that μ > μ′ .
- Were POW(μ′ ) reasonably high, the inference to μ > μ′ is reasonably/poorly warranted.