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Which Statistical Test Should I Use?
The right statistical test depends on three things: what you want to find out (a difference, a relationship, a prediction), what type of data your outcome is (numbers or categories), and how the data was collected (how many groups, and whether they are the same subjects). Answer the questions below and the chooser recommends the test, with its null hypothesis, an example and the main assumption to check. Free, and nothing is stored.
Question 1
How to choose a statistical test
Most wrong choices come from skipping one of the three questions. Start with the goal: comparing groups calls for a different family of tests than measuring how closely two variables move together. Then look at the outcome. Numerical outcomes (scores, times, weights) are analysed with means - t-tests, ANOVA, regression - while categorical outcomes (pass/fail, choices) are analysed with counts and proportions, usually through chi-square tests.
Finally, look at the design. If the same people are measured twice, their two results are linked, and a paired test uses that link instead of treating them as strangers. And for numerical data, check the shape: tests such as the t-test assume roughly normal data, though with fairly large samples they cope well. When the data is clearly skewed, ranked or small, the rank-based (non-parametric) alternative is the safer choice.
Whatever test you use, the logic of interpreting it is the same: you assume a null hypothesis of no effect, and the p-value tells you how surprising your data would be if that were true. Our step-by-step guide to hypothesis testing walks through that logic with worked examples.
Statistical tests at a glance
| Situation | Test | Null hypothesis |
|---|---|---|
| Compare one group's mean with a known or claimed value | One-sample t-test | The population mean equals the claimed value. |
| Compare one group with a claimed value when the data isn't normal | Wilcoxon signed-rank test (one sample) | The population median equals the claimed value. |
| Compare one proportion with a claimed value | One-proportion z-test | The population proportion equals the claimed value. |
| Compare the means of 2 independent groups (numerical data) | Two-sample t-test (Welch's) | The two group means are equal. |
| Compare 2 independent groups when the data isn't normal or is ordinal | Mann-Whitney U test (Wilcoxon rank-sum) | The two groups come from the same distribution (neither tends to have larger values). |
| Compare 2 measurements on the same subjects (before/after, matched pairs) | Paired t-test | The mean of the paired differences is zero. |
| Paired data when the differences aren't normal | Wilcoxon signed-rank test | The paired differences are centred on zero. |
| Compare the means of 3 or more independent groups | One-way ANOVA | All the group means are equal. |
| Compare 3 or more independent groups when the data isn't normal | Kruskal-Wallis test | All the groups come from the same distribution. |
| Compare 3 or more measurements on the same subjects | Repeated-measures ANOVA | The mean is the same at every time point or condition. |
| 3 or more measurements on the same subjects, data not normal | Friedman test | The distributions are the same at every time point or condition. |
| Is there a relationship between two categorical variables? | Chi-square test of independence | The two variables are independent - there is no association. |
| Paired yes/no outcomes (before/after on the same subjects) | McNemar's test | The proportion answering yes is the same both times. |
| Yes/no outcomes measured 3 or more times on the same subjects | Cochran's Q test | The proportion of yes is the same under every condition. |
| Do counts in categories match an expected distribution? | Chi-square goodness-of-fit test | The data follows the claimed distribution. |
| Linear relationship between two numerical variables | Pearson correlation | There is no linear correlation (r = 0) in the population. |
| Relationship between two variables that are ordinal, skewed or curved | Spearman rank correlation | There is no monotonic association between the variables. |
| Predict a numerical outcome from one or more variables | Linear regression | Each slope is zero - the predictor has no linear effect on the outcome. |
| Predict a yes/no outcome from one or more variables | Logistic regression | Each coefficient is zero - the predictor doesn't change the odds of the outcome. |
Covers the tests taught in introductory, AP Statistics and first-year university courses. Always check your course's conventions - some teachers prefer the pooled t-test or a specific post-hoc test.
Frequently asked questions
How do I know which statistical test to use?+
Answer three questions: what you want to find out (a difference between groups, a relationship, a prediction, or a comparison with a claimed value), what type of data your outcome is (numerical or categorical), and how the data was collected (how many groups, and whether they are independent or the same subjects measured more than once). For numerical data, also check whether it is roughly normal or the sample is fairly large - that decides between a t-test or ANOVA and its non-parametric alternative.
When should I use a t-test instead of ANOVA?+
Use a t-test to compare the means of exactly two groups, and ANOVA when there are three or more. Running lots of separate t-tests between three or more groups inflates the chance of a false positive, which is the problem ANOVA solves - then a post-hoc test such as Tukey's HSD tells you which groups differ.
What is the difference between parametric and non-parametric tests?+
Parametric tests (t-tests, ANOVA, Pearson correlation) assume the data roughly follows a particular distribution, usually the normal distribution. Non-parametric tests (Mann-Whitney, Wilcoxon, Kruskal-Wallis, Spearman) work on ranks instead, so they suit skewed data, outliers, rating scales and small samples. When their assumptions hold, parametric tests are a little more powerful.
When do I use a chi-square test?+
Use a chi-square test with categorical data - counts in categories. The test of independence asks whether two categorical variables are related (for example, club choice and year group); the goodness-of-fit test asks whether one variable's counts match an expected pattern (for example, whether a die is fair). Both need expected counts of about 5 or more per cell; with smaller counts, use Fisher's exact test.
What is the difference between paired and independent samples?+
Independent samples are separate groups of different subjects, such as two different classes. Paired samples come from the same subjects measured twice (before and after) or from matched pairs. Paired data needs a paired test - the paired t-test, Wilcoxon signed-rank or McNemar's test - because each subject acts as their own control.
Is this statistical test chooser free?+
Yes - it is completely free, runs in your browser, needs no signup and stores nothing. It covers the tests taught in introductory, AP and first-year university statistics.
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