Plan your research. Analyse your data.
Sample size, power analysis and hypothesis-testing calculators for researchers and graduate students. Exact methods, worked formulas and a paragraph you can adapt for your methods section.
Two-sample t-test with 40 per group has 59.8% power to detect d = 0.50. For 80% power you need 64 per group.
Plan a study
- Sample sizeHow many participants for a survey or estimate, with finite population correction.
- Power analysisA priori and post-hoc power for t-tests, correlation, ANOVA, chi-square and proportions.
- Cochran's formulaThe classic survey sample size formula, worked step by step.
- Slovin's formulan = N / (1 + Ne²), and why reviewers question it.
- Margin of errorHow precise is an estimate from n responses?
- Significance (two proportions)Compare two conversion or response rates; plan the sample for an A/B test.
Analyse your data
- Hypothesis testThe five steps of a test, from H₀ to decision, with your numbers.
- t-testOne-sample, independent (Welch or Student) and paired.
- Chi-squareTest of independence for any r × c table, or goodness of fit.
- One-way ANOVACompare three or more group means, with η² and a full table.
- Mann–Whitney UNonparametric test for two independent groups, exact p for small samples.
- Wilcoxon signed-rankNonparametric paired test for before/after data.
- Kruskal–Wallis testNonparametric ANOVA for 3+ groups with Dunn post-hoc.
- McNemar testPaired yes/no data: exact p, chi-square and odds ratio.
- Fisher's exact testExact 2 × 2 test when counts are too small for chi-square.
- Linear regressionEquation, R², slope p-value, prediction intervals and residual plot.
- CorrelationPearson's r and Spearman's ρ with p-value, CI and scatter plot.
- p-valueFrom a z, t, χ², F or r statistic.
- z-scoreStandardise a score and read its percentile.
- Confidence intervalFor a mean (t-based) or a proportion (Wilson).
- Effect sizeCohen's d, Hedges' g, r, η² and conversions between them.
- Standard deviationSample and population SD, variance, quartiles from pasted data.
Not sure which test or sample size you need?
Describe your study in plain words: what you compare or relate, how you measure it, and roughly how many people you can reach. The assistant suggests the analysis, the effect size to plan with and which calculator to open next.
Uses an AI model via Vercel AI Gateway. It only sees what you send here; check anything you publish.
What the slider above is showing
Every hypothesis test is a bet between two pictures of the world. The solid curve is what your test statistic looks like if there is no effect (H₀). The dashed curve is what it looks like if the effect you care about is real (H₁). The critical value is where you draw the line: anything beyond it counts as “significant”.
The coral slice is α, the chance of a false positive, which you fix in advance (usually 5%). The teal area is power, the chance of detecting a real effect. The grey area is β, the chance of missing it. Increasing the sample size narrows the sampling distributions, which in standardised units pushes H₁ further away from H₀, so power rises. That is the whole logic of a power analysis: pick the smallest effect worth detecting, pick α, and find the n that gets power to 80% or 90%.
Which calculator do I need?
| Your question | Data | Use |
|---|---|---|
| How many people should I survey? | Proportion or mean, known population | Sample size, Cochran |
| How many participants for my experiment? | Planned test + expected effect | Power analysis |
| Do two groups differ on a score? | Continuous, 2 groups | t-test |
| Do three or more groups differ? | Continuous, 3+ groups | One-way ANOVA |
| Are two categorical variables related? | Counts in a table | Chi-square |
| Do two measures move together? | Two continuous variables | Correlation |
| Is version B converting better than A? | Two proportions | Significance calculator |
How the numbers are computed
Power for t-tests uses the exact noncentral t distribution; ANOVA and chi-square power use the noncentral F and χ² distributions, the same approach as G*Power (Faul et al., 2007). Correlation power uses Fisher's z transformation. Sample sizes for surveys follow Cochran (1977) with the finite population correction. Everything runs in your browser, so results appear as you type.