What is statistical power, and what drives it?

Question

You are testing a null H0 ("this signal has no edge") against an alternative H1 ("it does"). Define statistical power, name the factors that increase it, and explain why an underpowered test is dangerous even when it returns a significant result.

Accepted Answer

Definition. Power is the probability of correctly rejecting H0 when H1 is true: 	ext{power} = 1 - \beta = \mathbb{P}(	ext{reject } H0 \mid H1 	ext{ true}), where \beta is the type II (false-negative) rate. High power means you reliably detect a real effect; low power means you often miss it. What raises power. Four levers, three you control: 1. Sample size n. More data shrinks the standard error, so a fixed effect stands out; power rises with n. 2. Effect size. Bigger true effects are easier to detect. You do not choose this, but you can target regimes where the effect is larger. 3. Signif…

What is statistical power, and what drives it?

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