Statistical Test Selector
Not sure whether you need a t test, ANOVA, chi-square or a correlation? Answer a few questions about what you want to find out, what kind of data you have and how it was collected, and get the recommended test with the reasoning for each step — plus alternatives, assumption checks and a link to the matching calculator. Free, no sign-up.
Answer the questions in order. Each answer narrows the choice.
Recommended test
T-test (one-sample, independent or paired)
Why this test
- You want to know whether groups or conditions differ, so you need a test of a difference.
- A measured outcome allows a test of means, provided its assumptions hold.
- Two groups or conditions call for a two-sample test.
- Different people in each group make the groups independent, so no pairing is used.
- Normality, or a large enough sample, supports the parametric test, which has more power.
Check the assumptions first
Alternatives
After the test
How to Use the Statistical Test Selector
- 1. Start with your goal. Do you want to compare groups, relate two variables, or predict an outcome? Each goal opens its own questions.
- 2. Describe your data. The kind of outcome (numbers, ranks or categories), how many groups, and whether the same people were measured more than once.
- 3. Judge the assumptions. For tests of means and correlations the selector asks whether scores are roughly normal or the sample is large enough. If you are unsure, check with a normality test and a plot.
- 4. Read the recommendation. The test, the reason for each answer, assumption checks, alternatives, and what to do afterwards. The test name opens its calculator.
The Questions Behind Every Choice
Choosing a test is a matter of four questions. What is the outcome? Measured numbers allow tests of means; ranks or ordinal ratings call for rank-based tests; categories call for tests of counts and proportions. How many groups or conditions? One group against a known value, two groups, or three or more — three or more need one overall test rather than a string of pairwise tests, which inflates the chance of a false positive. Are the measurements independent or paired? Different people in each group are independent; the same people measured repeatedly, or matched pairs, are related and need a test that uses the pairing. Do the assumptions hold? Tests of means assume roughly normal scores (or a large enough sample); when that fails, the rank-based equivalent is safer.
| Design | Assumptions hold | Assumptions do not hold |
|---|---|---|
| One group vs a known value | One-sample t test (z test if σ is known) | Sign test |
| Two independent groups | Independent t test (Welch) | Mann–Whitney U |
| Two paired measurements | Paired t test | Wilcoxon signed-rank |
| Three or more independent groups | One-way ANOVA (two-way for two factors), then Tukey HSD | Kruskal–Wallis |
| Three or more repeated measures | Repeated-measures ANOVA | Friedman |
| Question | Test |
|---|---|
| One categorical outcome vs hypothesised proportions | Binomial test (two categories) or chi-square goodness of fit |
| Two independent groups, categorical outcome | Chi-square (Fisher's exact when expected counts are small) |
| Paired yes/no data | McNemar (two conditions) or Cochran's Q (three or more) |
| Two numeric variables | Pearson correlation; Spearman or Kendall when not linear or ordinal |
| Two categorical variables | Chi-square test of independence, or Fisher's exact test |
| Predict a number | Linear regression; multiple regression for several predictors |
| Predict a yes/no outcome | Logistic regression |
Worked Example: Two Classes, One Exam
You want to know whether two classes — different students in each — differ in exam score. The goal is a comparison; the outcome is a score on a scale; there are two groups; the groups are independent. If the scores are roughly normal, or each class has about 30 or more students, the selector recommends the independent t test (Welch's version, which does not assume equal spreads). It also suggests a Shapiro–Wilk check first, and the Mann–Whitney U test as the alternative.
Change one answer — say the scores are strongly skewed with a few extreme values — and the recommendation becomes the Mann–Whitney U test, which compares ranks rather than means. Change another — the same students sat both exams — and it becomes the paired t test, or the Wilcoxon signed-rank test if the differences are skewed. Each answer changes the test for a reason the selector spells out.
A guide, not a verdict
The selector covers the tests this site has calculators for and the textbook paths between them. Real analyses add judgement: a Likert scale summed over many items is often treated as numeric, a large sample forgives mild non-normality, and some designs (clustered data, repeated measures with missing values, counts) need models beyond these. Decide the test before looking at the results, and report it with the APA Statistics Formatter.
Frequently Asked Questions
- How do I choose between a t test and ANOVA?
- Use a t test for one or two groups (or two conditions) and ANOVA for three or more. Running several t tests on three or more groups inflates the chance of a false positive, so ANOVA tests them all at once; if it is significant, a post hoc test such as Tukey HSD shows which groups differ.
- Do I need normally distributed data for a t test?
- The t test assumes the scores (or, for a paired test, the differences) are roughly normal, but it is fairly forgiving when groups are about 30 or more, thanks to the central limit theorem. With small samples and clear skew or outliers, use the rank-based alternative (Mann–Whitney U or Wilcoxon signed-rank).
- What is the difference between a paired and an independent test?
- In an independent test the groups contain different people, so one person's score says nothing about another's. In a paired test the same people are measured twice (before and after) or are matched in pairs, so each pair's difference is analysed. Using an independent test on paired data throws away power.
- When should I use Fisher's exact test instead of chi-square?
- When expected counts are small. A common rule asks for expected counts of at least 5 in the cells of the table; below that, the chi-square approximation is unreliable and Fisher's exact test (for a 2 × 2 table) gives an exact p value.
- Pearson or Spearman correlation?
- Pearson's r measures a straight-line relationship between two numeric variables and is sensitive to outliers. Spearman's rho works on ranks, so it suits ordinal data, curved but steadily increasing relationships and data with outliers. When the two disagree, plot the data.
- Should I choose the test after looking at the p values?
- No. Decide the test from the question and the design before you analyse, and write it down. Trying several tests and reporting the one that gives p < .05 inflates false positives; the selector is built so the choice depends on your design, not your results.