Sample Size and Power Calculators
Power Analysis Statistical Calculator
Statistical Power Calculator estimate power or solve for sample size for one-sample and two-sample mean tests, correlation, and one-way ANOVA. Use the tabbed test workspace below for data, variables, analysis, visualizations, results, interpretation and reporting.
Quick method summary
The Power Analysis Statistical Calculator calculates the named method using calculator-specific formulas and reports auditable results, warnings, and interpretation. It uses the calculator-specific formula and reports the intermediate values, final result, warnings, and interpretation.
Sample Size and Power Calculators
Statistical Power Calculator
Estimate power or solve for sample size for one-sample and two-sample mean tests, correlation, and one-way ANOVA.
Calculated result
Calculation method
Estimate power or solve for sample size for one-sample and two-sample mean tests, correlation, and one-way ANOVA.
Formula
Power uses the plugin’s exact noncentral t engine for supported equal-allocation two-sample t designs and its exact noncentral F engine for balanced one-way ANOVA designs. One-sample mean and correlation modes use transparent normal or Fisher-z approximations; sample-size mode searches upward to the requested target power.
Assumptions and limits
The selected design, data type, independence or pairing, missing-data handling, sample-size conditions, and model assumptions must match the research question.
Formula review
Formula, input validation, output contract, and independent control cases reviewed 2026-08-02; study-design assumptions remain visible to the user.
Statistical Power Calculator method, assumptions and reporting guideComplete selected-test explanation, assumptions, formula and reporting details
Data Import and Variable Requirements
For the Power Analysis Statistical Calculator, enter the method-specific values requested by the calculator: Analysis design, Solve for, Effect size (d, r, or f), Sample size / total sample size, Target power, Alpha. Review the selected mode, units, tails, and limits before calculating. For Statistical Power Calculator, map Analysis design, Solve for, Effect size (d, r, or f), Sample size / total sample size, Target power, Alpha from the cleaned browser-local table; every mapped variable remains editable before calculation, and the active dataset remains available while you work with this selected test and when you return to the Test Finder.
Uploaded files are processed locally in the browser. The cleaning report appears before variable selection, and the selected cleaned columns are mapped to this exact calculator rather than a generic fallback.
Statistical Power Calculator Workspace Features
- Dedicated Statistical Power Calculator variable mapping, calculation contract, result explanation, and diagnostics
- Calculator-specific inputs and validation instead of a generic fallback form
- Visible formula, substituted values, intermediate quantities, and final result
- Method-specific assumptions, warnings, decision guidance, and interpretation
- Responsive chart or visual that changes with entered values where the method benefits
- Copy, result CSV, chart PNG, and result-only print controls
- Protected canonical URL, focused FAQs, and a dedicated selected-test workspace
About the Statistical Power Calculator
Estimate power or solve for sample size for one-sample and two-sample mean tests, correlation, and one-way ANOVA. Planning calculators connect effect size, precision, alpha, power, group count, and sample size for the specific design shown.
When to Use the Statistical Power Calculator
Use the Power Analysis Statistical Calculator when your research question, variable types, and sampling or experimental design require statistical power. Do not select it only because the data produce a convenient p-value or familiar output.
How the Statistical Power Calculator Works
Power uses exact noncentral t or F engines for equal-allocation two-sample t and balanced one-way ANOVA designs, and transparent normal/Fisher-z approximations for the remaining umbrella modes; sample-size mode searches upward to the requested target power.
The calculation runs in the browser. Submitted values are validated for required numeric ranges, data shape, units and method-specific restrictions before results are shown.
Assumptions and Checks
- The selected design, tail, alpha level, allocation ratio, effect-size definition, and variance assumptions must match the planned study.
- The effect size should be scientifically meaningful and supported by defensible pilot data or prior evidence.
- Inflate the calculated requirement for attrition, nonresponse, clustering, multiple testing, or design effects when applicable.
Required Inputs
- Analysis design (required) Options: One-sample mean, Two independent means, Correlation, One-way ANOVA
- Solve for (required) Options: Power, Sample size
- Effect size (d, r, or f) (required)
- Sample size / total sample size (required)
- Target power (required)
- Alpha (required)
- Alternative (required) Options: Two-tailed, One-tailed
- Group 2 / Group 1 ratio (required)
- Number of ANOVA groups (required)
Results Reported
The result workspace shows the final answer and intermediate quantities needed to audit the calculation. Depending on the method, reported values include:
- Mode
mode - Solve For
solve_for - Effect Size
effect_size - Sample Size
sample_size - Power
power - Alpha
alpha - Noncentrality
noncentrality - Approximation Note
approximation_note
Statistical Power Calculator Worked Example
Use the example data button, calculate, then review the result table, formula, and worked solution before using the answer.
| Input | Example value |
|---|---|
| Analysis design | two_sample_t |
| Solve for | power |
| Effect size (d, r, or f) | 0.50 |
| Sample size / total sample size | 128 |
| Target power | 0.80 |
| Alpha | 0.05 |
| Alternative | two |
| Group 2 / Group 1 ratio | 1 |
| Number of ANOVA groups | 3 |
Verified Worked Result
The packaged automated fixture produces the following checked values from the example inputs. Display rounding can differ from the full-precision browser result.
| Result | Verified value |
|---|---|
| Sample Size | 128 |
| Power | 0.80145959332967 |
| Noncentrality | 2.8284271247462 |
Statistical Power and Sample Size Explained
Statistical power is the probability that a prespecified test rejects the null hypothesis under a specified non-null effect and model. Power depends on effect size, sample size, variance assumptions, alpha and the form of the test.
What does 80% power mean?
At 80% power, if the assumed true effect and other model conditions are correct, approximately 80 of 100 comparable studies would reject the null hypothesis using the chosen rule. It does not mean there is an 80% probability that the alternative hypothesis is true.
How to use the calculator
Choose the supported test design, enter a scientifically meaningful effect size, and specify the significance level and target power. If solving for sample size, round according to the tool's output and adjust for dropout, clusters, unequal group sizes and uncertain effect estimates. Prefer realistic or conservative inputs supported by pilot data or previous research over selecting an unrealistically large effect to minimize the required sample.
How to Use This Workspace
- Confirm that the method matches the quantity, hypothesis, model or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date or option format.
- Use Example Data to inspect a valid input layout, or enter your own values and run the calculation.
- Review the result table, formula, substitutions, warnings and interpretation rather than relying only on the headline number.
- Copy, download or print the result when you need a reusable analysis record.
Understanding and Reporting the Result
Review Mode, Solve For, Effect Size, Sample Size, Power, Alpha, Noncentrality, and Approximation Note. Use the displayed assumptions, warnings, and interpretation before reporting the result. In the Statistical Power Calculator result workspace, interpret mode, solve_for, effect_size, sample_size, power, alpha together with the method assumptions, warning messages, confidence information, effect magnitude, and diagnostic plots shown for the selected variables.
Planning assumptions should be justified before data collection; attrition, clustering, unequal allocation, and multiplicity may require a larger design.
Keep the entered values, units, selected options and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size and decision. For an estimate or conversion, report the formula convention and final unit.
How to Report the Result
When reporting results from the Power Analysis Statistical Calculator, identify the design and software, state the valid sample size and exclusions, then report Mode, Solve For, Effect Size, Sample Size, Power, Alpha, Noncentrality, Approximation Note. Include the selected alpha level, tail, coding, and assumption decisions when they apply. A reproducible Statistical Power Calculator report should identify the mapped variables, valid observations, exclusions or missing-data handling, selected options, principal outputs, uncertainty, diagnostics, and the practical conclusion supported by the analysis.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Statistical Power Calculator calculate?
Estimate power or solve for sample size for one-sample and two-sample mean tests, correlation, and one-way ANOVA.
Which formula does the Statistical Power Calculator use?
Power uses exact noncentral t or F engines for equal-allocation two-sample t and balanced one-way ANOVA designs, and transparent normal/Fisher-z approximations for the remaining umbrella modes; sample-size mode searches upward to the requested target power.
When should I use the Power Analysis Statistical Calculator?
Use the Power Analysis Statistical Calculator when your research question, variable types, and sampling or experimental design require statistical power. Do not select it only because the data produce a convenient p-value or familiar output.
What inputs does the Power Analysis Statistical Calculator require?
Enter the method-specific values requested by the calculator: Analysis design, Solve for, Effect size (d, r, or f), Sample size / total sample size, Target power, Alpha. Review the selected mode, units, tails, and limits before calculating.
What does the Power Analysis Statistical Calculator report?
Review Mode, Solve For, Effect Size, Sample Size, Power, Alpha, Noncentrality, and Approximation Note. Use the displayed assumptions, warnings, and interpretation before reporting the result.
Can the Power Analysis Statistical Calculator analyze Excel or CSV data?
This page uses direct method-specific inputs because a spreadsheet is not required for the calculation. Results still include the formula, steps, visual, warnings, and export controls.