Logic Takes a Bit of a Hit!: (NN 4) Continuing: Shpower ("observed" power) vs Power:

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Logic takes a bit of a hit---student driver behind me.  Anyway, managed to get to JFK, and meant to explain a bit more clearly the first "shpower" post.
I'm not saying shpower is illegitimate in its own right, or that it could not have uses, only that finding that the logic for power analytic reasoning does not hold for shpower  is no skin off the nose of power analytic reasoning.  
Consider our one-sided test T+, with μ₀= 0 and α=.025.  Suppose σ = 1, n = 25, so x̄ is statistically significant only if it exceeds .392. Suppose x̄ just misses significance, say
x̄ = .39.

Power-analytic reasoning says (in relation to our test T+):

If x̄ is statistically insignificant and the POW(T+, μ= μ₁) is high, then x̄ indicates, or warrants inferring (or whatever phrase you like) that  μ < μ₁.