# Which statistical test should I use?

> Answer 3–6 questions (groups, paired, data type, normality, sample size) to get the right test: t-test, Mann–Whitney, ANOVA, chi-square, log-rank and more.

URL: https://www.labcanvas.com/tools/statistical-test-chooser

Answer a few questions about your experiment: what you want to do (compare groups, relate two variables, predict an outcome or compare survival), what kind of data you measured, how many groups, whether they are independent or paired, whether the data look normal and how large the sample is. The guide recommends the test, explains why, lists its assumptions and gives the non-parametric (or parametric) alternative. It covers t-tests, Mann–Whitney, Wilcoxon signed-rank, one-way and repeated-measures ANOVA, Kruskal–Wallis, Friedman, chi-square, Fisher’s exact, McNemar, Pearson and Spearman correlation, linear and logistic regression and the log-rank test, with a full table below.

## Quick answer

- **What it does:** Recommends a statistical test from your answers about the goal, outcome type, number of groups, pairing, normality and sample size, with the reason, assumptions and alternative.
- **Formula:** 2 groups: Welch t (normal) or Mann–Whitney (not); paired: paired t or Wilcoxon; 3+ groups: ANOVA or Kruskal–Wallis (paired: repeated-measures ANOVA or Friedman); counts: χ² (expected ≥ 5) or Fisher’s exact; paired yes/no: McNemar.
- **Example:** Comparing tumour volume between 2 independent groups of 8 mice, not normally distributed → Mann–Whitney U test (e.g. U = 63 of 64, exact p = 0.00031 for the box plot maker’s example).

Free, in the browser, no account needed. Updated 2026-10-19.

## Features

- Step-by-step questions that adapt to your answers (only the relevant ones are asked)
- Recommended test with the reasons, its assumptions and an example experiment
- The non-parametric alternative for every parametric test, and the parametric one for every rank test
- 17 tests: t-tests, Mann–Whitney, Wilcoxon, ANOVA, repeated-measures ANOVA, Kruskal–Wallis, Friedman, chi-square, Fisher’s exact, McNemar, Cochran’s Q, Pearson, Spearman, linear and logistic regression, log-rank
- Links to run the test on your data in the box plot maker or the LabCanvas Graphs app
- A full reference table of all tests below the guide

## How to use it

1. **Say what you want to do**: Compare groups, relate two variables, predict an outcome or compare survival curves.
2. **Describe the data**: Pick the outcome type, the number of groups, independent or paired, and whether the data look normal and how many values you have.
3. **Read the recommendation**: Read the test, why it fits, its assumptions and the alternative, then run it on your data in the box plot maker or the Graphs app.

## At a glance

| | |
| --- | --- |
| Questions | Goal, outcome type, number of groups, independent or paired, normality, sample size |
| Tests covered | 17: t-tests, Mann–Whitney, Wilcoxon, ANOVA, repeated-measures ANOVA, Kruskal–Wallis, Friedman, \(\chi^2\), Fisher, McNemar, Cochran’s Q, Pearson, Spearman, linear and logistic regression, log-rank |
| Gives | The test, why, its assumptions, the alternative and an example |
| Run the test | Box plot maker (2–k group tests) or the LabCanvas Graphs app (all except Cochran’s Q) |

## How it works

The guide applies the standard decision rules taught in biostatistics courses. Four things decide the test:

- **The type of outcome.** A continuous measurement (volume, concentration) can use tests of means; scores and ranks (ordinal) need rank-based tests; categories and yes/no outcomes are counts and need tests on contingency tables.
- **How many groups.** Two groups use a t-test or its rank equivalent; three or more need one overall test (ANOVA, Kruskal–Wallis) followed by post hoc comparisons, because running every pairwise t-test inflates the false-positive rate.
- **Independent or paired.** Measurements on the same subjects (before/after, time points, matched pairs) are correlated, and paired tests use the within-subject differences, which is usually more powerful.
- **Normality and sample size.** Tests of means assume roughly normal data in each group. With about 30 or more per group they are robust to moderate skew (central limit theorem); with small, skewed samples or outliers, rank-based tests are safer. Check with a histogram or Q–Q plot; a Shapiro–Wilk test (Shapiro and Wilk 1965) has little power in small samples and flags trivial departures in large ones, so it should not decide alone.

For two independent groups the guide recommends Welch’s t-test rather than Student’s, because it does not assume equal variances and loses little when they are equal (Welch 1947; Delacre et al. 2017). For counts it recommends Fisher’s exact test when any expected count is below 5 and the \(\chi^2\) test otherwise. The rank tests are those of Wilcoxon (1945), Mann and Whitney (1947), Kruskal and Wallis (1952) and Friedman (1937); paired proportions use McNemar’s test (1947); survival curves use the log-rank test (Mantel 1966).

Sources: Welch BL. *Biometrika* 1947;34:28–35, [doi:10.1093/biomet/34.1-2.28](https://doi.org/10.1093/biomet/34.1-2.28). Delacre M, Lakens D, Leys C. Why psychologists should by default use Welch’s t-test instead of Student’s t-test. *Int Rev Soc Psychol* 2017;30:92–101, [doi:10.5334/irsp.82](https://doi.org/10.5334/irsp.82). Wilcoxon F. Individual comparisons by ranking methods. *Biometrics Bull* 1945;1:80–83, [doi:10.2307/3001968](https://doi.org/10.2307/3001968). Mann HB, Whitney DR. *Ann Math Stat* 1947;18:50–60, [doi:10.1214/aoms/1177730491](https://doi.org/10.1214/aoms/1177730491). Kruskal WH, Wallis WA. *J Am Stat Assoc* 1952;47:583–621, [doi:10.1080/01621459.1952.10483441](https://doi.org/10.1080/01621459.1952.10483441). Friedman M. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. *J Am Stat Assoc* 1937;32:675–701. McNemar Q. Note on the sampling error of the difference between correlated proportions or percentages. *Psychometrika* 1947;12:153–157, [doi:10.1007/BF02295996](https://doi.org/10.1007/BF02295996). Mantel N. Evaluation of survival data and two new rank order statistics arising in its consideration. *Cancer Chemother Rep* 1966;50:163–170, PMID [5910392](https://pubmed.ncbi.nlm.nih.gov/5910392/). Shapiro SS, Wilk MB. An analysis of variance test for normality (complete samples). *Biometrika* 1965;52:591–611, [doi:10.1093/biomet/52.3-4.591](https://doi.org/10.1093/biomet/52.3-4.591).

## Examples and the full table of tests

Five common lab questions and the test the guide recommends:

- **Tumour volume in 2 independent groups of 8 mice, skewed with one large tumour.** Compare groups → continuous → 2 groups → independent → not normal → small: **Mann–Whitney U test**. In the [box plot maker](https://www.labcanvas.com/tools/box-plot-maker)’s example (vehicle vs Drug A), \(U = 63\) of a possible 64, exact \(p = 0.00031\); Welch’s t-test on the same data gives \(p = 0.0014\).
- **Cell viability under 3 doses and a vehicle, triplicate wells, roughly normal.** 3 or more groups, independent, normal: **one-way ANOVA**, followed by Dunnett’s test against the vehicle or Tukey’s test for all pairs.
- **Blood glucose of the same 8 rats at 0, 30, 60 and 120 min.** 3 or more conditions, paired: **repeated-measures ANOVA** if the values are roughly normal, otherwise the **Friedman test**.
- **Tumours in 2 of 9 treated and 7 of 10 control mice.** Categorical outcome, independent, small counts: **Fisher’s exact test**, since several expected counts are below 5.
- **Survival of mice on drug vs vehicle over 60 days, some still alive at the end.** Survival: **log-rank test** on Kaplan–Meier curves.

|  | Independent, normal | Independent, not normal / ordinal | Paired, normal | Paired, not normal / ordinal |
| --- | --- | --- | --- | --- |
| 2 groups | Unpaired (Welch’s) t-test | Mann–Whitney U | Paired t-test | Wilcoxon signed-rank |
| 3 or more groups | One-way ANOVA | Kruskal–Wallis | Repeated-measures ANOVA | Friedman |

|  | Independent groups | Paired |
| --- | --- | --- |
| Expected counts \(\ge 5\) | Chi-square test | McNemar (2 conditions), Cochran’s Q (3 or more) |
| Small counts | Fisher’s exact test | Exact McNemar (binomial) |

| Test | Use it to | Assumptions | Alternative | Example | Run it in |
| --- | --- | --- | --- | --- | --- |
| Unpaired t-test (Welch's) | Compare the means of 2 independent groups of a continuous, roughly normal measurement. | Independent observations; each group roughly normal (or n ≳ 30 per group). Welch’s version does not assume equal variances. | Mann–Whitney U test | Body weight of 10 knockout vs 10 wild-type mice. | Box plot maker, Graphs app |
| Paired t-test | Compare 2 measurements on the same subjects (before/after, left/right, matched pairs). | The paired differences are roughly normal; pairs are independent of each other. | Wilcoxon signed-rank test | Blood pressure of 12 patients before and after treatment. | Graphs app |
| Mann–Whitney U test (Wilcoxon rank-sum) | Compare 2 independent groups when the data are ordinal, skewed or have outliers. | Independent observations; the outcome can be ranked. Tests whether values in one group tend to be larger; it compares medians only if the two distributions have the same shape. | Unpaired t-test | Tumour volume in 8 treated vs 8 control mice, skewed. | Box plot maker, Graphs app |
| Wilcoxon signed-rank test | Compare 2 paired measurements when the differences are not normal, or the data are ordinal. | Paired data; differences can be ranked and are roughly symmetric around their median. | Paired t-test | Pain score (0–10) of 15 patients before and after a drug. | Graphs app |
| One-way ANOVA | Compare the means of 3 or more independent groups of a continuous, roughly normal measurement. | Independent observations; each group roughly normal; similar variances (otherwise Welch’s ANOVA). Follow with Tukey’s or Dunnett’s post hoc test. | Kruskal–Wallis test | Cell viability with 3 drug doses and a vehicle control. | Box plot maker, Graphs app |
| Repeated-measures ANOVA | Compare 3 or more measurements on the same subjects (time points or conditions). | Differences roughly normal; sphericity (equal variances of all pairwise differences; else Greenhouse–Geisser correction). A mixed model handles missing values. | Friedman test | Glucose in 8 rats at 0, 30, 60 and 120 min. | Graphs app |
| Kruskal–Wallis test | Compare 3 or more independent groups when the data are ordinal, skewed or have outliers. | Independent observations; the outcome can be ranked; groups of similar shape to compare medians. Follow with Dunn’s test. | One-way ANOVA | Histology score (0–4) in 4 treatment groups. | Box plot maker, Graphs app |
| Friedman test | Compare 3 or more paired or repeated measurements when they are not normal or are ordinal. | Each subject measured under every condition; values can be ranked within each subject. | Repeated-measures ANOVA | Ratings of 4 formulations by the same 10 tasters. | Graphs app |
| Chi-square test (χ²) of independence | Compare proportions or categories between independent groups (a contingency table of counts). | Independent observations; counts, not percentages; expected count ≥ 5 in at least 80% of cells and none below 1. | Fisher’s exact test (small counts) | Responders vs non-responders in 60 treated and 60 control patients. | Graphs app |
| Fisher’s exact test | Compare proportions between independent groups when counts are small (2 × 2 table, any expected count < 5). | Independent observations; counts. Exact, so valid at any sample size. | Chi-square test (large counts) | Tumours in 2 of 9 treated vs 7 of 10 control mice. | Graphs app |
| McNemar’s test | Compare a yes/no outcome measured twice on the same subjects (paired proportions). | Paired binary data; uses only the discordant pairs (exact binomial version when they are few). | Cochran’s Q for 3 or more time points | Positive/negative by two diagnostic tests on the same 50 samples. | Graphs app |
| Cochran’s Q test | Compare a yes/no outcome across 3 or more paired conditions. | Binary outcome; every subject measured in every condition. | McNemar’s test for 2 conditions | Whether each of 20 patients responds to 3 different drugs. | — |
| Pearson correlation (r) | Measure the strength of a linear relation between two continuous variables. | Linear relation; both variables roughly normal (for the p-value); no strong outliers. | Spearman rank correlation | Protein concentration vs absorbance. | Graphs app |
| Spearman rank correlation (ρ) | Measure a monotonic relation when data are ordinal, skewed or have outliers. | Monotonic (always rising or always falling) relation; values can be ranked. | Pearson correlation | Tumour grade vs expression of a marker. | Graphs app |
| Linear regression | Predict or explain a continuous outcome from one or more predictors. | Linear relation; independent, normally distributed residuals with constant variance. | Rank-based or robust regression; transform the outcome | Enzyme activity against temperature and pH. | Graphs app |
| Logistic regression | Predict or explain a yes/no outcome from one or more predictors (gives odds ratios). | Independent observations; a linear relation between predictors and the log-odds; about 10 events per predictor. | Fisher’s exact or chi-square test for a single categorical predictor | Disease (yes/no) against age, sex and a biomarker. | Graphs app |
| Log-rank test (Kaplan–Meier) | Compare survival (time-to-event) curves between 2 or more groups, with censored data. | Censoring unrelated to outcome; proportional hazards for best power. For covariates use Cox regression. | Gehan–Breslow–Wilcoxon test (weights early events) | Survival of mice on drug vs vehicle over 60 days. | Graphs app |

## Questions

### Which statistical test should I use to compare two groups?

For a continuous measurement in two independent groups, use Welch’s unpaired t-test if the data are roughly normal (or each group has about 30 or more values), and the Mann–Whitney U test if they are skewed, ordinal or have outliers. For the same subjects measured twice, use the paired t-test or the Wilcoxon signed-rank test.

### Which test do I use for more than two groups?

One-way ANOVA for roughly normal data in independent groups, Kruskal–Wallis otherwise; for repeated measurements on the same subjects, repeated-measures ANOVA or the Friedman test. Follow a significant result with post hoc tests (Tukey, Dunnett or Dunn) rather than separate t-tests.

### How do I know if my data are normally distributed?

Look at a histogram, box plot or Q–Q plot of each group. Concentrations, volumes, counts and times are often right-skewed and become normal after a log transform. Normality tests such as Shapiro–Wilk are weak with small samples and over-sensitive with large ones, so use them only as a guide.

### When should I use a non-parametric test?

When the outcome is ordinal (scores, grades), or when the data are clearly skewed or have outliers and the groups are small (under about 30). Non-parametric tests compare ranks, so they are robust but somewhat less powerful when the data really are normal.

### What is the difference between paired and unpaired tests?

Unpaired tests compare different subjects in each group. Paired tests are for the same subjects measured under each condition (before/after, left/right) or matched pairs; they analyse the differences within each subject, which removes between-subject variation.

### Chi-square or Fisher’s exact test?

Both test whether proportions differ between groups. Use chi-square when every expected count is at least 5 (at least 80% of cells \(\ge 5\) and none below 1 for larger tables), and Fisher’s exact test when counts are smaller; Fisher’s is valid at any size.

### Can I use a t-test with a small sample, like n = 3?

Yes, if the data are plausibly normal, as replicate measurements often are; the t-test was designed for small samples. With \(n = 3\) you cannot check normality, and a Mann–Whitney test cannot reach \(p \lt 0.05\) with 3 per group (the smallest exact two-sided p is 0.1), so rank tests are not a fix for tiny samples.

### Which test for correlation: Pearson or Spearman?

Pearson’s r for a linear relation between two roughly normal continuous variables; Spearman’s ρ for ordinal data, skewed data, outliers or a monotonic but curved relation. Plot the data first.