Configure the Test
Enter realistic planning assumptions, then calculate the estimated power.
Formula Used
Power is the probability of rejecting the null hypothesis when the planned alternative is true. For mean tests, the calculator starts with a standardized test signal. For proportion and chi-square tests, it uses their matching large-sample planning approximations.
| Test | Core effect calculation | Power approach |
|---|---|---|
| One mean / paired mean | δ = Δ ÷ (SD / √n) | Normal approximation around δ. |
| Two means | δ = Δ ÷ √(SD₁²/n₁ + SD₂²/n₂) | Welch standard error and normal approximation. |
| One proportion | SE₀ = √[p₀(1−p₀)/n] | Critical proportion under p₀, evaluated under p₁. |
| Two proportions | SE = √[p(1−p)(1/n₁ + 1/n₂)] | Pooled null threshold and alternative variance. |
| Chi-square | λ = n × w² | Noncentral chi-square normal approximation. |
For a two-sided test, power includes both rejection tails. The reported sample estimate searches upward until the selected target power is reached.
How to Use This Calculator
- Select the test family that matches your planned analysis.
- Set alpha and choose a two-sided or directional alternative.
- Enter sample sizes and realistic expected effects or event rates.
- Set a planning target, commonly 0.80 or 0.90.
- Calculate power, inspect the sample estimate, and review the chart.
- Export the result after recording assumptions in your protocol.
Example Data Table
| Scenario | Test | Key assumptions | Expected use |
|---|---|---|---|
| Training outcome | Two means | n₁ = 50, n₂ = 50, difference = 5, SD = 12 | Compare average assessment scores. |
| Service adoption | Two proportions | n₁ = 120, n₂ = 120, p₁ = 0.55, p₂ = 0.40 | Compare conversion rates. |
| Before and after | Paired means | Pairs = 40, difference = 3, SD difference = 7 | Evaluate participant change. |
| Category pattern | Chi-square | n = 180, w = 0.30, df = 3 | Check distribution differences. |
Planning Reliable Tests
Statistical power is the probability that a planned test detects a real effect. A useful design balances power, sample size, variability, and the chosen significance level. Low power can miss worthwhile effects. Very large samples can detect trivial differences. This calculator helps you inspect those tradeoffs before data collection begins.
Power is commonly written as 1 minus beta. Beta is the chance of a false negative. Researchers often target 80% or 90% power. The best target depends on consequences, budget, recruitment limits, and scientific importance. A higher target usually requires more observations. It also reduces the chance that a real result is overlooked.
The selected test determines the inputs. Mean tests use an expected difference and standard deviation. Proportion tests use expected event rates. Chi-square tests use Cohen's w. Two-group designs also need group sizes. Unequal groups reduce efficiency when total recruitment is fixed. Paired designs can improve power because each participant acts as a partial control.
The significance level controls the rejection threshold. A two-sided test looks for effects in either direction. A one-sided test concentrates power in a planned direction. Use one-sided testing only when the opposite direction would not change your decision. Choose this before reviewing outcomes. Do not select it simply because it gives more power.
Power estimates rely on assumptions. A standard deviation taken from a small pilot may be unstable. Event rates can change across sites. Attrition can reduce the final sample. Use conservative values, then check several realistic scenarios. The chart makes this sensitivity work easier. Record assumptions in the study protocol for transparent planning.
This tool uses normal and large-sample approximations for displayed power. They are practical for early design checks. Exact methods, simulation, or dedicated R packages may be better for sparse data, complex models, repeated measures, clustered samples, survival analysis, or nonstandard tests. Treat the output as a planning estimate, not a guarantee.
After calculating, review the standardized effect and required sample size. Ask whether the assumed effect is meaningful. Check whether recruitment can reach the suggested size. Compare alternative significance levels and allocation ratios. Export the result for your design notes. Recalculate whenever the protocol, measurement process, or expected dropout changes. Reviews support defensible studies, practical budgets, and transparent decisions. Teams gain clearer interpretations after final analyses are completed.
Frequently Asked Questions
1. What does statistical power mean?
Power is the probability of detecting a real effect under the assumptions you enter. It equals one minus the Type II error rate. It does not prove that an observed result will be correct.
2. Is 80% power always enough?
No. Eighty percent is common, but consequences matter. Higher-stakes decisions, costly false negatives, or confirmatory studies may justify 90% or greater power. Feasibility and the smallest meaningful effect should guide the final choice.
3. Why does a smaller effect need more observations?
Small effects are harder to separate from random variation. More observations reduce the standard error. That increases the signal relative to noise and improves the chance of crossing the rejection threshold.
4. Should I use a one-sided test?
Use a one-sided test only when the opposite direction would not affect the decision and this rule is set before data collection. Do not choose it after seeing results because that weakens the planned inference.
5. What is Cohen's w?
Cohen's w is a standardized effect size for chi-square tests. Values near 0.10, 0.30, and 0.50 are often described as small, medium, and large. Context remains more important than generic labels.
6. Does the calculator perform an exact t distribution calculation?
It uses a normal approximation for mean-test power and reports the relevant degrees of freedom. This is useful for planning. Dedicated R functions or simulation may be preferable for small samples or unusual distributions.
7. How should dropout affect sample size?
Increase recruitment above the required completed sample. Divide the needed completed size by one minus the expected dropout proportion. For example, 100 completed observations with 20% dropout requires recruiting about 125.
8. Why are unequal group sizes less efficient?
For a fixed total sample, balanced groups usually minimize the standard error. Unequal allocation can still be sensible when one group is scarce, expensive, or ethically limited. Use the expected ratio in the calculator.
9. Can I use this for clustered data?
Not directly. Clustering changes the effective sample size because observations within a cluster are related. Apply a design effect, use a multilevel power method, or simulate the intended clustered analysis.
10. What is the standardized effect shown in results?
For mean tests, it is a Cohen-like difference divided by a standard deviation. For proportions, it is an arcsine-based h value. For chi-square, it is the entered w value.
11. Why might R give a slightly different value?
R functions can use exact noncentral t, F, or chi-square distributions, while this page uses practical approximations for several tests. Small differences are expected, especially with small samples or extreme probabilities.