Choose a statistical test based on how observations are related and what you want to compare—not simply on whether the data look normal. In SciPy, an independent-samples t-test compares means, Mann–Whitney U compares distributions using ranks, Wilcoxon signed-rank handles paired observations, and Kruskal–Wallis provides a rank-based omnibus test for multiple independent groups. Their hypotheses differ, so they are not interchangeable substitutes.
Start with the study design and the question
Before choosing a test, answer two questions: Are the observations independent or paired, and what quantity should the analysis compare? A test can be computationally correct yet answer the wrong question if it ignores the study design or targets a different quantity than intended.
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- Independent groups: Each observation belongs to one group, and observations are not paired across groups.
- Paired observations: Each value in one sample is meaningfully linked to a value in the other—for example, measurements from the same participants at two times.
- Target: Decide whether the question concerns average values, or whether the groups’ distributions differ.
SciPy’s statistical test reference organizes functions by common uses and sample structures, while noting that no broad index can cover every use case.
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| Design and target | SciPy method | What to keep in mind |
|---|---|---|
| Two independent groups; compare means | scipy.stats.ttest_ind |
Tests equality of average values. Its default, equal_var=True, assumes identical population variances. |
| Two independent groups; compare distributions using ranks | scipy.stats.mannwhitneyu |
The null is that the underlying distributions are the same. It is not universally a test of medians. |
| Two related or paired samples | scipy.stats.wilcoxon |
Tests paired differences; the documented null describes differences as symmetric about zero. |
| Several independent groups; rank-based omnibus comparison | scipy.stats.kruskal |
Small group sizes can make the chi-square approximation inappropriate. A significant omnibus result does not identify which groups differ. |
| Several groups; mean-based comparison | One-way ANOVA | SciPy lists this option; select it according to the model, design, target, and assumptions. |
For current signatures and details, consult the official SciPy references for ttest_ind, mannwhitneyu, wilcoxon, and kruskal.
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Independent samples: t-test or Mann–Whitney U?
Use an independent t-test when the target is a difference in means
scipy.stats.ttest_ind compares the average values of two independent samples. Its default assumes equal population variances. If that assumption is not appropriate for your analysis, make the variance choice explicit with equal_var=False; do not let the default silently determine the model you intended. The SciPy documentation also describes a permutation method, whose availability and calling convention should be checked against the version you use.
from scipy import stats
result = stats.ttest_ind(group_a, group_b, equal_var=False)
print(result.statistic, result.pvalue)This example makes the unequal-variance choice explicit. The returned result includes a test statistic and p-value; neither alone communicates the estimated effect or its practical importance.
Use Mann–Whitney U when a rank-based distribution comparison fits
scipy.stats.mannwhitneyu is for two independent samples. Its null hypothesis concerns equality of the underlying distributions. It is often used to assess a location difference, but calling it a universal median test overstates what it establishes: a median-focused interpretation requires additional conditions on the distributions’ shapes.
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print(result.statistic, result.pvalue)A rank-based test is not simply a t-test with a normality switch flipped. The methods have different hypotheses and target different features of the data. Choose the one aligned with the scientific question rather than selecting whichever returns the preferred p-value.
Paired measurements: use the paired structure
For two related samples, SciPy documents scipy.stats.wilcoxon, the paired rank-based option. The analysis concerns within-pair differences, and the documented null describes those differences as symmetric about zero.
result = stats.wilcoxon(before, after)
print(result.statistic, result.pvalue)Keep the observations in corresponding order so each pair remains intact. Running an independent-samples test on these values discards the pairing and analyzes a different design.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.More than two independent groups
Kruskal–Wallis is an omnibus rank-based test
scipy.stats.kruskal compares several independent groups using ranks. SciPy cautions that group sizes must not be too small for its chi-square approximation to be appropriate.
result = stats.kruskal(group_a, group_b, group_c)
print(result.statistic, result.pvalue)A significant omnibus result indicates evidence against the overall null, but it does not say which particular groups differ. Plan a suitable follow-up analysis separately, accounting for the fact that multiple comparisons may be involved.
For a mean-based question, consider one-way ANOVA
SciPy’s statistical-functions index also lists one-way ANOVA for comparisons involving multiple groups. The index is a starting point, not a complete decision rule: choose the model and procedure in light of the design, target, and assumptions.
A practical selection sequence
- Identify the design. Determine whether groups are independent or measurements are paired.
- State the target. Decide whether you are comparing means or asking about distributions with a rank-based method.
- Match the number of groups. For two independent groups, consider
ttest_indormannwhitneyu; for paired samples, considerwilcoxon; for several independent groups, consider Kruskal–Wallis for a rank-based omnibus comparison or ANOVA for a mean-based question. - Check assumptions and implementation choices. In particular, decide whether the equal-variance default in
ttest_indis appropriate, and verify method details in the documentation for your installed SciPy version. - Plan interpretation and follow-up. Report what the test evaluates, and remember that an omnibus result does not locate group differences.
These common choices do not cover every design, such as every repeated-measures or more complex model. When the observations or question do not fit the cases above, consult SciPy’s statistical functions index and select a method designed for that structure.
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