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Statistics

Power Analysis

Plan how many participants a study needs before you collect data. Choose your analysis, the effect you want to be able to detect, α and the power you want, and the tool calculates the sample size, with its assumptions and a sentence you can adapt for your report.

Free, no account

Each option names the test the calculation is for.

independent-samples t test: Compares the means of two separate groups, such as a treatment and a control group.

What do you want to calculate?

Required sample size is an a priori power analysis: use it to plan a study before collecting data.

Parameters

(μ₁ − μ₂) ÷ σ: the difference between the group means, in standard deviations. For example, 0.5.

The Type I error rate you will test at, as a decimal. Common choices: 0.05, 0.01, 0.10.

The probability of detecting the effect if it exists, as a decimal. Common choices: 0.80, 0.90, 0.95.

Test direction

Decide before analysing your data. A one-sided test is in the direction of the effect you specify.

Choose an analysis, enter the values, and press Calculate.

What should I do next?

You know the sample you need. Now plan the analysis itself.

  • Statistical Test Finder

    Helps you identify statistical tests that may suit your research question and data, and explains why each may fit.

  • Effect Size Calculator

    Calculate selected standardized effects from reported summary statistics, with formulas and assumptions shown.

  • Power Analysis

    What statistical power is, how α, effect size and sample size determine it, how to plan a sample size before collecting data for t tests, proportions, correlation and one-way ANOVA, and why observed power after a study is not the same thing.

How to use it

  • Choose the analysis you plan to run. If you aren't sure, the Statistical Test Finder can help you choose.
  • Specify the smallest effect worth detecting, from previous research, a pilot study or what would matter in practice. The Effect Size Calculator can turn means and standard deviations into an effect size.
  • Choose α, the Type I error rate you will test at, and the power you want, usually 0.80 or 0.90.
  • Calculate the sample size before collecting data. That is an a priori power analysis, the use power analysis is designed for.

What it doesn't cover

  • Unequal group sizes, factorial or repeated-measures ANOVA, regression, non-parametric tests, survival analysis, mixed models, cluster designs and sequential or adaptive designs.
  • Attrition, non-response or missing data: add to the calculated sample size for the participants you expect to lose.
  • Whether the effect size you entered is realistic. The result is only as good as that assumption.
  • Power calculated from the effect observed in your own data (observed or post hoc power), which this tool doesn't offer; report confidence intervals instead.

Privacy

Calculations run entirely in your browser. The values you enter are not sent to ResearchKit or anyone else, and they aren't stored.