PowerAnalyse

Poweranalyse, or power analysis, is a set of statistical methods used to determine the sample size needed to detect an effect of a specified size with a given level of significance and statistical power. It can be conducted before data collection (a priori power analysis) to plan a study, or after data collection (post hoc power analysis) to interpret results, though the latter is often considered of limited value.

Key concepts include the effect size (the magnitude of the expected difference or association), the alpha level (type I error rate, commonly 0.05), and the power (1 minus the type II error rate, commonly 0.80 or 0.90). The required sample size depends on these inputs as well as the study design, such as the type of statistical test (t-test, ANOVA, regression, chi-squared), one- or two-tailed tests, and whether groups are equal in size. Effect sizes are often expressed as Cohen’s d or f, odds ratios, or correlation coefficients, and variance estimates or pilot data are typically used to inform the calculation.

Practical use includes planning sample size for clinical trials, psychology and social science experiments, and other fields. Software tools such as GPower, R (pwr package), SAS, and STATA are commonly employed. Design considerations can include anticipated dropout, cluster sampling, or repeated measures, which may require adjusted or simulation-based power analyses.

Limitations include sensitivity to inaccurate assumptions about effect size and variance. If estimates are optimistic, studies may be underpowered; if conservative, resources may be wasted. Post hoc power analyses are generally discouraged in favor of reporting observed effects and confidence intervals.