Statistical Power Analysis
Updated 2026-08-13
INTRODUCTION
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CORE DEFINITION
Statistical power is the probability of correctly rejecting the null hypothesis when a real effect exists, equal to one minus the probability of a false negative. Power depends on the sample size, the size of the effect, and the significance level chosen, and it is computed in advance so that the study is designed to detect the effect it is looking for. The core proposition is that an underpowered study is uninformative even when executed perfectly, because a non-significant result cannot distinguish a small effect from no effect. The key qualification is that the calculation requires an estimate of the effect size, which must come from prior evidence rather than hope.
SCAFFOLDING EFFECT
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- Pre-registration step: compute the required sample size before collecting any data. - Effect estimate: base the calculation on prior evidence about how large the effect is likely to be. - Interpretation guard: treat a non-significant result from an underpowered study as inconclusive rather than negative.
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A smaller sample produces noisier estimates, so a real effect is easily hidden by sampling variation. Raising the sample size narrows that variation until the effect stands out reliably. Because the required size depends on the effect being sought, power analysis forces the researcher to state what magnitude of effect would matter before the study runs.
MINIMUM ACTION
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Power_(statisticsverified
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