Category
Hypothesis Test Calculators
Every test here answers the same question in a different setting: could this pattern have come from chance alone? Start with the decision guide if you are not sure which one you need.
Which test should I use?
Almost every choice comes down to four questions, and the answers narrow it to one test.
1. What kind of thing are you comparing? Means (a measurement — height, revenue, time on page) point toward the t-test family. Proportions (a yes/no outcome — converted, survived, clicked) point toward chi-square and the z-test for proportions. A relationship between two measurements points toward correlation or regression.
2. How many groups? Two groups of measurements is a t-test. Three or more is ANOVA — not several t-tests, because running three t-tests at α = 0.05 gives you roughly a 14% chance of a false positive instead of 5%. When ANOVA says something differs, Tukey's HSD says which.
3. Are the observations paired? The same people measured twice, matched pairs, before and after — that is a paired design, and using it is free statistical power. Paired measurements go to the paired t-test, the Wilcoxon signed-rank test, or McNemar's test for yes/no outcomes.
4. Do the assumptions hold? The t-test and ANOVA assume roughly normal data with comparable spread. When the data are heavily skewed, have outliers, or are ordinal rather than numeric, switch to the rank-based version: Mann-Whitney instead of the two-sample t-test, Wilcoxon instead of the paired t-test, Kruskal-Wallis instead of ANOVA. Check normality with Shapiro-Wilk and equal spread with Levene's test — but treat both as evidence, not as a gate: with a large sample they reject on departures too small to matter, and with a small one they miss departures that do.
The one thing every test on this page shares
They all compute how surprising your data would be if nothing were going on, and express that as a p-value. A small p-value means the data sit awkwardly with the null hypothesis. It does not mean the effect is large, or important, or that the alternative is 95% likely to be true. For size, look at the effect size and the confidence interval; for whether the study could have found the effect at all, look at statistical power.
Counts rather than measurements
When the data are counts in categories, the chi-square family takes over. Chi-square handles a contingency table of any size and asks whether the rows and columns are independent. When the counts are small — any expected count below 5 — Fisher's exact test computes the answer exactly instead of approximating it. For a single proportion against a target, or two proportions against each other, use the z-test for proportions.
The 14 calculators in this category
- Chi-Square Test CalculatorChi-square calculator for contingency tables of any size and for goodness of fit.
- ANOVA CalculatorOne-way ANOVA calculator with the full ANOVA table, F statistic, exact p-value, η² and Welch's correction for unequal variances.
- T-Test CalculatorFree t-test calculator for one-sample, paired and independent two-sample tests.
- P-Value CalculatorConvert a test statistic into a p-value: z, t, chi-square or F, one- or two-tailed, with the critical value, a comparison against common thresholds and the distribution drawn.
- Fisher's Exact Test CalculatorFisher's exact test for a 2×2 table: exact one- and two-sided p-values, the conditional maximum-likelihood odds ratio and its exact confidence interval.
- Wilcoxon Signed-Rank Test CalculatorWilcoxon signed-rank test for paired data: exact p-values for small samples, tie and continuity corrections, the signed-rank table and the rank-biserial effect size.
- Tukey's HSD CalculatorTukey's honestly significant difference test: every pairwise comparison after ANOVA, with adjusted p-values, simultaneous confidence intervals and the critical studentized range value.
- Z-Test for Proportions CalculatorTest one proportion against a target, or compare two proportions.
- Mann-Whitney U Test CalculatorMann-Whitney U test (Wilcoxon rank-sum) with exact p-values for small samples, tie correction for large ones, rank sums, the rank-biserial effect size and a dot plot.
- McNemar's Test CalculatorMcNemar's test for paired binary outcomes: before-and-after, two raters, matched pairs.
- Kruskal-Wallis Test CalculatorKruskal-Wallis H test for three or more independent groups, with the tie correction, rank sums, mean ranks, epsilon-squared effect size and a dot plot of the groups.
- Shapiro-Wilk Normality Test CalculatorShapiro-Wilk test for normality using Royston's AS R94 algorithm, with W, the exact p-value, skewness, kurtosis and a normal Q-Q plot that shows how the data depart.
- Levene's Test CalculatorLevene's test for equal variances across groups, with the Brown-Forsythe median-centred version as the default.
- ANCOVA CalculatorFree one-way ANCOVA calculator.
Questions people ask
What is the difference between a one-tailed and a two-tailed test?
A two-tailed test asks whether the groups differ in either direction; a one-tailed test asks whether one is specifically larger. The one-tailed p-value is half the two-tailed one, which makes it tempting — and it is only legitimate if you fixed the direction before seeing the data. Choosing the tail after looking doubles your real false-positive rate.
Can I run several t-tests instead of an ANOVA?
Not without adjusting. Each test at α = 0.05 carries a 5% false-positive risk, and three tests carry about 14%. ANOVA tests all groups at once at the level you chose, and Tukey's HSD follows up on every pair while holding that level.
My data are not normal. Does that invalidate the t-test?
Usually less than people fear. The t-test relies on the sample mean being roughly normal, which the central limit theorem delivers even from skewed data once the sample is moderately large. It matters most with small samples, strong skew, or outliers — and in those cases Mann-Whitney makes no normality assumption at all.