Power analysis

Works out the relationship between significance level, statistical power, effect size, and sample size for a chosen test — fixing three of them to solve for the fourth. No data set is needed.

When to use it

  • Before a study, to plan the sample size needed to detect an effect.

  • After (or while planning), to check the power of a given design, or the effect size it can detect.

Inputs (all numbers you type)

  • Test type — Two-sample t-test, Paired / one-sample t-test, One-way ANOVA, or Correlation.

  • Solve for — Sample size, Power, or Effect size.

  • Alpha (e.g. 0.05), Power (e.g. 0.80), Effect size, Sample size — provide the three you know.

  • Number of groups — for ANOVA.

  • Tails — two-sided or one-sided.

Output

  • The solved quantity with the inputs that produced it.

  • A power-vs-sample-size curve for the chosen test.

Notes

  • Effect sizes follow Cohen’s conventions: d for t-tests, f for ANOVA, r for correlation.

  • t-tests and ANOVA use the standard non-central distributions; correlation uses the Fisher-z approximation.