G*Power: Calculate Statistical Power and Sample Size

G*Power is a free statistical software program for calculating statistical power, required sample size, and related quantities for many common tests. Enter details such as the test, effect size, significance level, and desired power; the program estimates the sample size or power implied by those assumptions. This page explains how its calculations work and how to interpret them.

What G*Power Calculates

Statistical power is the probability that a statistical test will reject its null hypothesis when a specified alternative is true. G*Power calculates power or sample size for a range of statistical procedures, including t tests, analysis of variance (ANOVA), correlation and regression tests, and tests of proportions. The exact choices depend on the test family and statistical design selected.

The program can answer several different planning questions:

• A priori: How many observations are needed to reach a chosen power, given an effect size and significance level?
• Post hoc: What power follows from a sample size, effect size, and significance level?
• Sensitivity: What is the smallest effect detectable at a chosen sample size and power?
• Compromise: What combination of Type I and Type II error rates results when both are considered?

These are calculations under a statistical model, not guarantees about what a study will find. The result is only as credible as the assumptions supplied.

How Power and Sample Size Work

Power is commonly written as 1 − β, where β is the probability of a Type II error: failing to reject the null hypothesis when the specified alternative is true. The significance level, α, is the planned probability of a Type I error: rejecting the null hypothesis when it is true. A conventional α of 0.05 and desired power of 0.80 are common planning choices, not universal requirements.

For a fixed statistical test and effect size, increasing the sample size generally increases power. A larger effect is also easier to detect than a smaller one. More stringent significance thresholds, such as lowering α from 0.05 to 0.01, generally require a larger sample to maintain the same power.

G*Power uses the probability distribution associated with the chosen test to calculate the result. It may use a central or noncentral distribution depending on the procedure. Consequently, there is no single formula that applies to every screen or analysis: a two-sample t test, a repeated-measures design, and a multiple regression require different inputs and assumptions.

How to Set Up a G*Power Calculation

Start by identifying the test that matches the planned analysis, not the one that produces the most convenient sample size. In the program, the main selections are the test family, statistical test, and type of power analysis. Then supply the test-specific parameters.

1. Choose the test family and test. For example, select a t-test procedure for a planned comparison of means, or an F-test procedure for an appropriate ANOVA or regression test.
2. Select the analysis type. For planning a study before data collection, an a priori calculation is usually the relevant option.
3. Set α and desired power. These should reflect the study plan and scientific context. If several primary tests are planned, consider whether multiplicity changes the significance threshold.
4. Enter the effect size and design parameters. These may include group allocation, numbers of groups, repeated measurements, correlation assumptions, or predictor counts, depending on the test.
5. Calculate and check the output. Review the implied sample size, degrees of freedom, and any group-specific totals. Confirm that the settings match the intended design.

A useful cross-check is to run a sensitivity calculation using the planned sample size. This shows what effect size the design can detect under the same assumptions. It does not establish that smaller effects are unimportant.

Choosing and Justifying an Effect Size

Effect size describes the magnitude of the difference or relationship the calculation is designed to detect. It is not the same as statistical significance. For a standardized difference in means, for example, Cohen’s d expresses a mean difference in standard-deviation units. Other tests use measures such as correlation, odds ratios, proportions, or Cohen’s f.

Base the assumed effect on relevant prior research, a substantive threshold, or a clearly explained range of plausible values. Avoid choosing a value solely because it is labeled “small,” “medium,” or “large”: those labels are rough conventions and can be misleading in a specific field. A sensitivity analysis across several plausible effect sizes can show how strongly the required sample depends on this choice.

Published studies can help, but their observed effects may be imprecise, especially in small samples. A calculation based on an unusually large estimate can produce an underpowered study. Where possible, justify the target effect in practical terms as well as citing evidence.

Reading Results and Common Problems

In an a priori analysis, G*Power generally reports the required total sample size and related quantities for the chosen test. If participants are divided into unequal groups, pay attention to the allocation setting: the total may not split evenly. If the result is not a whole number, plan for at least the next whole participant, then account separately for expected exclusions or missing data. Do not simply treat an attrition allowance as part of the statistical formula.

• Wrong test or tail: A one-tailed test has different assumptions and power from a two-tailed test. Use a one-tailed test only when the directional hypothesis and interpretation are justified in advance.
• Effect-size mismatch: Each test has its own effect-size definition. Entering a correlation where the field expects a standardized mean difference makes the calculation invalid.
• Ignoring dependence: Paired, repeated-measures, clustered, and independent observations are not interchangeable. The design and assumed correlations can materially affect the result.
• Confusing total and per-group sample size: Check the selected test and output labels before translating a total into recruitment targets.
• Treating post hoc power as new evidence: Power calculated after a study from its observed effect often adds little beyond the result and its uncertainty. Confidence intervals and the study design are generally more informative for interpretation.

What a Power Calculation Cannot Tell You

Power does not say that a result is likely to be true, nor does 80% power mean an 80% chance that a particular study will be statistically significant in every real-world circumstance. It means that, under the specified model and effect, repeated studies would reject the null about 80% of the time in the long run.

The calculation may not account for every feature of a real study. Missing observations, noncompliance, measurement error, non-normal data, clustering, multiple comparisons, interim analyses, and model misspecification can change actual performance. For complex designs, a simulation or specialist statistical review may be more suitable than a standard G*Power calculation. G*Power also does not decide whether an effect matters scientifically or whether the study is feasible.

Frequently Asked Questions

Is G*Power free?
G*Power is distributed as free statistical software. Check the project’s official distribution source for current download and use information.

What power should I use in G*Power?
There is no required value for every study. Researchers commonly plan around 0.80 or 0.90, but the appropriate target depends on the consequences of missed effects, study constraints, and the analysis plan.

Can G*Power calculate sample size?
Yes. Choose an a priori power analysis, then specify the test, effect size, α, desired power, and relevant design settings. The output is conditional on those inputs.

What does effect size mean in G*Power?
It is the magnitude of the effect assumed for the calculation, expressed using the measure required by the selected test. Consult the test’s definition before entering a value.

Does a significant result prove the study had enough power?
No. A significant result does not verify the assumptions or guarantee adequate power for other effects. Power planning is prospective; interpret results with estimates, uncertainty, design limitations, and the analysis plan.

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