Power Analysis Calculator

Power analysis connects four quantities that shape a statistical study: effect size, significance level, statistical power, and sample size. This calculator performs an a priori analysis, meaning that it estimates the minimum number of independent observations before data collection begins. The effect size is entered as Cohen's d, a standardized difference measured in standard deviation units. A value around 0.2 is often described as small, 0.5 as medium, and 0.8 as large, but a meaningful value should come from subject knowledge, prior evidence, or the smallest effect worth detecting. The significance level, commonly called alpha, controls the tolerated probability of a false positive when the null hypothesis is true. A conventional value is 0.05. Statistical power is the probability of detecting the specified effect when that effect really exists. Researchers commonly plan for 0.80 or 0.90 power. Raising power, lowering alpha, or targeting a smaller effect all increase the required sample size because the study must distinguish a weaker signal under stricter evidence requirements. The calculation uses a two-sided normal approximation. It adds the standard-normal critical value for half of alpha to the critical value for desired power, divides that sum by the standardized effect, squares the result, and rounds upward. This model is useful for early planning of a one-sample standardized mean test and as a transparent approximation for related designs. A two-independent-group study generally needs the displayed amount in each group multiplied according to its allocation and variance assumptions, so consult a design-specific method before final recruitment. The result should be treated as a statistical minimum rather than a complete recruitment target. Increase it for expected dropout, missing records, clustering, repeated measurements, unequal group allocation, multiple primary outcomes, or uncertain effect estimates. Power calculations cannot correct biased sampling, poor measurement, or an inappropriate analysis model. Document every assumption in a protocol and consider sensitivity calculations with several plausible effect sizes so stakeholders can see how uncertainty changes the practical sample requirement.