Hypothesis test calculators
Every significance test on the site, grouped by what you are comparing: means, proportions, variances or ranks. Alongside them are the pieces a test is built from, such as test statistics, degrees of freedom, p-values and critical values, and the tools for planning a study and reporting its effect size.
Which calculator do I need?
| You have or want | Use |
|---|---|
| Two group means from a sample, population SD unknown (the usual case) | T-test |
| Three or more group means at once | ANOVA |
| Conversion rates from two versions of a page or email | A/B test |
| A 2×2 table with small counts (any expected count below 5) | Fisher's exact test |
| The same people measured yes/no before and after | McNemar's test |
| Two groups of skewed data or ratings, where a t-test is doubtful | Mann–Whitney U test |
| A test statistic already in hand and you need its p-value | P-value calculator |
| How many participants you need before collecting data | Power analysis |
Compare means
Is the difference between a sample mean and a target, or between group means, larger than chance?
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Hypothesis testing calculator
One-sample z or t test for a mean, or z test for a proportion, with the decision and a shaded rejection region.
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T-test calculator
One-sample, two-sample (pooled or Welch) and paired t-tests with df, p-value, confidence interval and Cohen's d.
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Z-test calculator
One- and two-sample z-tests for means and proportions, with p-value and decision.
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ANOVA calculator
One-way ANOVA for three or more groups: the sum-of-squares table, F, p-value and eta squared.
Compare proportions and counts
Tests for categorical outcomes: observed counts, 2×2 tables, paired yes/no data and conversion rates.
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Chi-square calculator
Chi-square goodness-of-fit test on observed and expected counts, with p-value, per-category contributions and effect size.
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Fisher's exact test calculator
Exact one- and two-sided p-values for a 2×2 table, with the odds ratio and every possible table.
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McNemar's test calculator
Paired yes/no test: χ² with and without continuity correction, exact binomial p and the odds ratio b/c.
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A/B test calculator
Conversion rates, uplift, p-value and confidence interval for an A/B test, plus the sample size per variant.
Compare variances and ranks
Equal-variance checks, and rank-based tests that do not assume normal data.
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F-test calculator
Test whether two variances are equal, from raw data or from s and n.
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Mann–Whitney U test calculator
Rank-based comparison of two groups: U₁, U₂, exact or normal p-value and effect size r.
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Wilcoxon rank-sum test calculator
The rank sum W with its expected value, standard error, z and p-value, ties handled.
Test statistics, p-values and corrections
The building blocks: compute a statistic, its degrees of freedom, the cut-off and the p-value, then adjust for multiple tests.
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T statistic calculator
One-sample, Welch, pooled and paired t from summary statistics, with df and p-value.
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F statistic calculator
F from ANOVA sums of squares, regression R² or two variances, with p-value and critical value.
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Degrees of freedom calculator
Degrees of freedom for t-tests, Welch, chi-square, ANOVA and regression, with formulas.
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P-value calculator
Turn a z, t, chi-square or F statistic into a one- or two-tailed p-value, with the interpretation.
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Critical value calculator
Critical z, t, chi-square or F at any significance level, one- or two-tailed, with the rejection region.
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Bonferroni correction calculator
The α/m threshold, and Bonferroni, Holm and Benjamini–Hochberg adjusted p-values for a list of tests.
Plan the study and report the effect
Sample size before the data, effect size after it.
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Power analysis calculator
Sample size or power for t-tests, two proportions and correlations, with a power curve.
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Effect size calculator
Cohen's d, Hedges' g and Glass's Δ from two groups, plus d ↔ r and η² from F.
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Cohen's d effect size calculator
Cohen's d from two means, SDs and sample sizes, with Hedges' g, Glass's delta and a 95% interval.
How the pieces fit together
Every test here follows the same four steps. Compute a test statistic (t, z, F or χ²) that measures how far the data sit from the null hypothesis. Find its degrees of freedom. Convert the statistic to a p-value, or compare it with a critical value. Then report an effect size, because a p-value says whether a difference is likely real, not whether it is large. The full test calculators do all four at once; the statistic and p-value pages are for when a textbook or paper gives you one step and asks for the next.
A worked comparison
Group A: n = 10, mean 52, SD 8. Group B: n = 10, mean 45, SD 6. The pooled SD is √[(9 × 64 + 9 × 36) / 18] = √50 = 7.07, so the standard error of the difference is 7.07 × √(1/10 + 1/10) = 3.16 and t = 7 / 3.16 = 2.21 on 18 degrees of freedom. The two-sided p-value is 0.040, just under 0.05. Welch's test, which does not assume equal variances, gives the same t here (the groups are the same size) but 16.7 degrees of freedom and p = 0.041. Cohen's d = 7 / 7.07 = 0.99, a large effect.
Now suppose this was one of five comparisons in the same study. The Bonferroni threshold becomes 0.05 / 5 = 0.01, and p = 0.040 no longer counts as significant. With only ten per group, a power analysis would have warned that even an effect this large is easy to miss.
Common mix-ups
- z or t? Use a z-test only when the population SD is known or you are testing a proportion with a large sample. For means with a sample SD, use the t-test.
- Several t-tests instead of ANOVA. Running every pairwise t-test inflates the false-positive rate. Run ANOVA first, then correct any follow-up comparisons.
- Paired data tested as independent. Before-and-after measurements on the same people need the paired t-test, or McNemar's test for yes/no outcomes.
- Mann–Whitney and Wilcoxon rank-sum are the same test. U and W differ by a constant and give the same p-value; pick whichever your course or journal expects.
Guides to read alongside
Common questions
What does a p-value of 0.03 actually mean?
If the null hypothesis were true, a result at least as extreme as yours would turn up about 3% of the time. It is not the probability that the null hypothesis is true, and it says nothing about how large or important the effect is.
Should I use a one-tailed or two-tailed test?
Use two-tailed unless you decided before seeing the data that only one direction matters and a result in the other direction would be treated the same as no effect. A one-tailed test halves the p-value, so choosing it after looking at the data overstates the evidence.
My data are not normal. Can I still use a t-test?
With moderate samples (about 30 or more per group) the t-test is fairly robust, because the sampling distribution of the mean is close to normal. With small, skewed samples or ordinal ratings, a rank test such as the Mann–Whitney U test is safer.