SciPy Stats: scipy.stats Functions for Research, With Examples

scipy.stats is the statistics module of the SciPy library for Python. It holds probability distributions, summary statistics, hypothesis tests, correlation measures and resampling methods, and it returns result objects you can read field by field. This guide maps research questions to the right function, then walks one complete workflow (a normality check followed by an independent-samples t-test) using the signatures in the SciPy 1.18.0 reference.

What scipy.stats is used for in research

The SciPy reference groups the module into probability distributions, summary statistics, frequency statistics, hypothesis tests, resampling and multiple-testing tools. It states plainly that statistics is a very large area and that some topics are out of scope for SciPy, so it is a toolkit of building blocks, not a full modelling environment. For regression models with formula interfaces and ANOVA tables, see ANOVA in Python with statsmodels.

Which function for which question

The function groupings in the official reference translate directly into a task map:

Research question	Functions in scipy.stats
One sample against a value, or paired measurements	ttest_1samp, ttest_rel, wilcoxon, binomtest, chisquare
Two independent groups	ttest_ind, mannwhitneyu, ks_2samp
Three or more groups	f_oneway, kruskal
Is the data normal?	shapiro, probplot
Association between two variables	pearsonr, spearmanr, kendalltau, linregress
Categorical tables	chi2_contingency, fisher_exact
Resampling instead of formulas	permutation_test, bootstrap, monte_carlo_test
Many tests at once	combine_pvalues, false_discovery_control
Transforming skewed data	boxcox, yeojohnson

Distributions such as norm, gamma, beta, binom and poisson are also in the module, and the reference notes that the fit method of the univariate continuous distributions uses maximum likelihood estimation.

Install or access (official source only)

The scipy.org install page gives two routes. With pip, create and activate a virtual environment, then run:

python -m pip install scipy

With conda, run conda install scipy (or mamba install scipy); the page recommends Miniforge and the conda-forge channel. To pin the same versions across a team, see sharing a reproducible conda environment.

Step-by-step: normality check, then independent-samples t-test

This example compares a measurement in two independent groups. The numbers are made up for illustration; the outputs shown were produced by running exactly this code with SciPy 1.18.0.

1. Import the module and enter the data:

   from scipy import stats
   a = [5.1, 4.9, 6.2, 5.8, 5.5, 6.0, 5.3, 5.7]
   b = [6.1, 6.8, 5.9, 7.2, 6.5, 6.9, 6.3, 7.0]

2. Check each group for normality with shapiro, whose null hypothesis is that the data were drawn from a normal distribution:

   stats.shapiro(a)  # statistic=0.9788, pvalue=0.9569
   stats.shapiro(b)  # statistic=0.9564, pvalue=0.7754

   Neither p-value gives evidence against normality here. With samples this small the test has little power, so also look at a plot (probplot). More on the idea in normality of distribution.

3. Run the t-test. Student’s version is the default (equal_var=True). Passing equal_var=False runs Welch’s t-test, which does not assume equal population variances:

   res = stats.ttest_ind(a, b, equal_var=False)
   res

4. Read the confidence interval for the difference in means:

   res.confidence_interval(confidence_level=0.95)

5. If normality is doubtful, run the rank-based alternative:

   stats.mannwhitneyu(a, b)

Output and how to read it

ttest_ind returns a TtestResult with statistic, pvalue and df (the df field was added in SciPy 1.11.0), plus a confidence_interval() method. For the example above:

Field	Value from the run	How to read it
statistic	-4.514	(mean of a – mean of b) / standard error. Negative because group a has the smaller mean; the docs state the statistic is positive when the mean of a is larger.
pvalue	0.000487	Two-sided by default (alternative='two-sided'). See p-value.
df	13.99	Fractional because Welch’s test was used. The documented Student example shows df=998.0 against 997.46 for Welch.
confidence_interval()	-1.512 to -0.538	Interval for the difference in means (a minus b) at the 95% level by default.

The Mann-Whitney run returned a statistic of 3.0 and a p-value of about 0.0011. For the underlying logic, see the t-test guide; for distribution-free comparisons, see the Kolmogorov-Smirnov test and permutation tests.

Troubleshooting

My result is nan

The default is nan_policy='propagate', which returns NaN if the input contains NaN. Use nan_policy='omit' to drop missing values, or 'raise' to stop with an error. Decide this on purpose: omitting values changes the sample you are testing.

Shapiro-Wilk with more than 5000 observations

The documentation says that for N > 5000 the W statistic is accurate but the p-value may not be. For large samples, rely on a Q-Q plot (probplot) rather than the p-value.

Student or Welch?

The default assumes equal population variances. If you cannot justify that, set equal_var=False.

Resampling p-values

ttest_ind accepts method=PermutationMethod or MonteCarloMethod (added in SciPy 1.15.0). The documentation cautions that permutation tests can be slow and are not necessarily more accurate than the analytical test.

ImportError or a missing module

Install SciPy into the same environment that runs your script: activate the virtual environment first, then use python -m pip install scipy so pip and the interpreter match.

Free alternatives

Tool	Relationship to scipy.stats
statsmodels (Python)	Python package for model-based analyses such as ANOVA tables; see ANOVA in Python with statsmodels.

For a worked regression across tools, see linear regression with Excel, R and Python.

FAQ

What is scipy.stats?

It is the statistics module of SciPy: probability distributions, summary statistics, hypothesis tests, correlation and resampling functions for Python.

How do I run a t-test in scipy.stats?

Use scipy.stats.ttest_ind(a, b) for two independent groups, ttest_rel for paired data and ttest_1samp for one sample against a value. Add equal_var=False for Welch’s test.

How do I get a confidence interval from ttest_ind?

Call confidence_interval(confidence_level=0.95) on the returned result; it gives low and high bounds for the difference in means.

Does scipy.stats replace statsmodels?

No. SciPy states that there are statistical topics out of scope for SciPy, so for model-based analyses such as ANOVA tables you can pair it with statsmodels.

Sources (official docs)

• SciPy 1.18.0 reference, Statistical functions (scipy.stats): docs.scipy.org/doc/scipy/reference/stats.html, checked 2026-10-29
• scipy.stats.ttest_ind: docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html, checked 2026-10-29
• scipy.stats.shapiro: docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html, checked 2026-10-29
• Installing SciPy: scipy.org/install, checked 2026-10-29