Power Analysis Calculator
Power and sample size online for t-tests, ANOVA, correlation, chi square and proportions.
When to use it
Use before collecting data to compute the sample size needed to detect an effect of interest at a chosen alpha and power. Use after data collection to report achieved power as part of methods. Standard requirement of grant proposals, IRB / ethics submissions, and pre-registered studies.
When NOT to use it
Do not use post-hoc to defend a non-significant result; the achieved-power calculation is mathematically tied to the observed p and is not a meaningful diagnostic (Hoenig and Heisey 2001). Do not use a single number for the effect size if it is genuinely uncertain; report a range.
What you get
For each test type (two-sample t, paired t, one-way ANOVA, correlation, chi-square, two-proportion z): pick which of n, power, alpha, or effect size to solve for; the calculator returns the missing value with the formula. Includes Cohen-style effect size benchmarks (small / medium / large) for each test family.
How to interpret the output
By convention, power of 0.80 is the minimum acceptable for confirmatory studies. Cohen's small/medium/large effect sizes (0.2/0.5/0.8 for d, 0.1/0.25/0.4 for f, 0.1/0.3/0.5 for r, 0.1/0.3/0.5 for w) are useful starting points but are domain-specific. Sample size scales roughly with 1 / effect-size-squared, so halving the detectable effect quadruples the required n.
Common pitfalls
- Reporting post-hoc 'observed power' to argue a non-significant result is informative.
- Using a Cohen 'medium' effect size when a domain-specific minimum important difference is known.
- Forgetting to inflate sample size for expected dropout or missingness.
- Mixing one-sided and two-sided alpha (most reports use two-sided).
Try it in StatVeda
The Power & Sample Size engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open Power & Sample SizeReferences
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey.
- Hoenig, J. M. and Heisey, D. M. (2001). The abuse of power: the pervasive fallacy of power calculations for data analysis. The American Statistician, 55(1), 19 to 24.
- Faul, F., Erdfelder, E., Lang, A.-G. and Buchner, A. (2007). G*Power 3: a flexible statistical power analysis program. Behavior Research Methods, 39(2), 175 to 191.