Power Analysis for Proportion Tests
Sample Size and Power Analysis for Proportion Tests · Also known as: proportion power analysis, two-proportion z-test power, z-test for proportions power, Oran Testi Güç Analizi
Power analysis for proportion tests is a prospective sample-size planning method used to determine how many participants are needed to detect a meaningful difference between two (or one) proportions with a specified probability. Formalised by Jacob Cohen in his 1988 landmark text, it applies the arcsine transformation to convert proportions into the effect-size index h, enabling direct calculation of the required sample size.
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When to use it
Use this analysis when planning a study that will compare binary or categorical proportions — such as success rates, prevalence estimates, response rates, or event rates — between one or two groups with independent observations. The method assumes the outcome is binary (or reducible to a proportion), the expected proportion difference or single target proportion is specified in advance, and an a priori alpha level (typically 0.05) and desired power (typically 0.80 or 0.90) are set before data collection. It is not suitable for paired proportions (use McNemar power) or for count outcomes modelled with Poisson distributions.
Strengths & limitations
- Provides a principled, transparent justification for the chosen sample size, as required by ethical review boards and grant agencies.
- The arcsine effect-size index h is variance-stabilising, making it valid across a wide range of baseline proportions.
- Can be used in reverse (given n, compute achievable power) for feasibility assessments of existing resources.
- Directly tied to Cohen's well-established small/medium/large benchmarks, facilitating cross-study comparisons.
- Requires a credible advance estimate of the expected proportions, which is often uncertain; optimistic assumptions lead to underpowered studies.
- The closed-form formula assumes the normal approximation to the binomial, which can be imprecise when proportions are near 0 or 1 or sample sizes are very small.
- Does not account for complex sampling designs, clustering, or stratification without further adjustment.
- With n < 10, the power calculation is unreliable and simulation-based methods should be used instead.
Frequently asked
What is Cohen's h and why is the arcsine transformation used?
Cohen's h = 2 arcsin(√p₁) − 2 arcsin(√p₂) is an effect-size index that maps proportions onto a scale where the variance is approximately constant, regardless of the baseline proportion. This stabilisation is necessary because the variance of a proportion (p(1−p)/n) changes with p, making a raw difference between proportions a poor measure of effect magnitude.
What proportions should I plug in if I have no prior data?
The best source is published literature on the same population and outcome. If no data exist, you can specify the minimum difference you would consider clinically or practically meaningful, paired with a plausible baseline proportion. Cohen's benchmarks (h = 0.20, 0.50, 0.80) can serve as a last resort but tend to produce sample sizes that are too small or too large for a specific context.
Is 80% power always sufficient?
80% power is a widely adopted default, meaning you accept a 20% chance of missing a real effect. In high-stakes settings — such as confirmatory phase III clinical trials or studies with serious safety implications — 90% or 95% power is commonly required, which substantially increases the required sample size.
Can I use this for a single proportion instead of two?
Yes. For a one-sample test, you specify the null-hypothesis proportion and the target proportion, and the formula reduces to a single-group version. The StatWise tool supports both the one-sample and two-sample proportion power calculations.
Sources
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates. DOI: 10.4324/9780203771587 ↗
How to cite this page
ScholarGate. (2026, June 1). Sample Size and Power Analysis for Proportion Tests. ScholarGate. https://scholargate.app/en/statistics/power-analysis-proportion
Which method?
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