Statistics
Statistical power
Also called: power analysis
Statistical power is the probability that a study will detect an effect of a given size when that effect truly exists. It depends on sample size, effect size, variability, and the significance threshold. Underpowered studies miss real effects and, paradoxically, exaggerate the ones they do find.
Power is usually the flip side of a Type II error: a study with 80 percent power has a 20 percent chance of failing to detect a real effect of the assumed size. Convention aims for 80 to 90 percent, and reaching it requires an a priori power analysis that specifies the smallest effect worth detecting before data collection begins.
Underpowered research does more than waste effort. When a small, noisy study does cross the significance threshold, the estimated effect is almost always inflated, a phenomenon known as the winner's curse or Type M (magnitude) error. This is a major engine of the replication crisis, because splashy findings from tiny samples rarely hold up.
Reviewers should check whether a power calculation exists, whether its assumed effect size is plausible or conveniently large, and whether post hoc power (calculated from the observed effect) is being misused to excuse a null result. A credible sample-size justification tied to a meaningful minimum effect is a hallmark of careful design.
Example
A trial powered to detect a 20 percent relative risk reduction was too small to say anything reliable about the 8 percent reduction it observed.
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