Power Analysis
Also known as: sample size calculation, power calculation, sensitivity analysis, a priori power analysis
Power analysis is a planning and evaluation technique that quantifies the probability of detecting a real effect of a given magnitude at a chosen significance level. It links four quantities — sample size, effect size, significance level (alpha), and statistical power (1 minus beta) — so that researchers can determine the sample size needed before data collection or evaluate the sensitivity of a completed study.
Key highlights
- Prevents both underpowered studies (which waste resources and yield unreliable results) and overpowered studies (which flag trivially small effects as significant).
- Forces explicit specification of the smallest effect considered practically meaningful, improving research clarity.
- Applicable to virtually any statistical test with a known power function.
- Accepted universally by ethics boards and funding agencies as evidence of rigorous design.
- Sensitivity variants can identify the effect size a completed study could reliably detect.
Intuition
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How it works
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When to use it
Use power analysis before any confirmatory study to justify the sample size and demonstrate that the design is sensitive enough to detect a meaningful effect. It is required or strongly recommended by most ethics committees, grant agencies, and high-quality journals. Also use a sensitivity analysis (computing the smallest detectable effect for a fixed n) when sample size is externally constrained. Do not confuse post hoc power — calculated after collecting data using the observed effect size — with a priori power; post hoc power adds little beyond what the p-value already conveys and is discouraged in modern reporting guidelines.
Strengths & limitations
- Prevents both underpowered studies (which waste resources and yield unreliable results) and overpowered studies (which flag trivially small effects as significant).
- Forces explicit specification of the smallest effect considered practically meaningful, improving research clarity.
- Applicable to virtually any statistical test with a known power function.
- Accepted universally by ethics boards and funding agencies as evidence of rigorous design.
- Sensitivity variants can identify the effect size a completed study could reliably detect.
- Accuracy depends entirely on the assumed effect size, which is often uncertain before data collection.
- Post hoc power is nearly redundant with the p-value and should not be used to interpret a non-significant result.
- Complex designs (multilevel models, mixed designs) require specialized software and more parameters.
- Does not account for assumption violations (non-normality, heteroscedasticity) that reduce actual power.
Common pitfalls
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Applications
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Frequently asked
What power level should I target?
Cohen (1988) suggested 0.80 as a conventional minimum, accepting a 20% chance of a Type II error. Many clinical, safety, and replication studies target 0.90 or 0.95. The appropriate threshold depends on the relative costs of missing a real effect versus running a larger study.
How do I choose the effect size for planning?
Prefer the smallest effect considered practically or clinically meaningful rather than the effect from a prior study. If prior literature exists, use a conservative (downward-adjusted) estimate. Meta-analytic summaries provide more stable starting points than individual pilot studies.
Is post hoc power useful after a non-significant result?
Rarely. Post hoc power computed from the observed effect size is mathematically redundant with the p-value — low p always means high observed power and vice versa. Instead, report the confidence interval around the effect size to show what values are compatible with the data.
What software can I use?
G*Power (free, Windows/macOS) covers a wide range of tests. R packages include pwr (Cohen-style), WebPower, and simr (for multilevel designs). Python's statsmodels provides power functions for common tests. Many online calculators handle t-tests, ANOVA, chi-square, and correlations.
Does power analysis apply to Bayesian studies?
Yes. Bayesian power analysis — sometimes called design analysis — asks how likely a study is to yield a Bayes factor or credible interval that supports a conclusion. It requires specifying a prior predictive effect distribution and is implemented in packages such as BayesFactor (R) and BFDA.
Sources
- 1.Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.ISBN 978-0805802832
- 2.Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175–191.
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Cite this page
ScholarGate. (2026, June 3). Power analysis. ScholarGate. https://scholargate.app/statistics/power-analysis