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---

.. image:: https://pingouin-stats.org/build/html/_images/logo_pingouin.png :align: center

Pingouin is an open-source statistical package written in Python 3 and based mostly on Pandas and NumPy. Some of its main features are listed below. For a full list of available functions, please refer to the API documentation <https://pingouin-stats.org/build/html/api.html#>_.

1. ANOVAs: N-ways, repeated measures, mixed, ancova

2. Pairwise post-hocs tests (parametric and non-parametric) and pairwise correlations

3. Robust, partial, distance and repeated measures correlations

4. Linear/logistic regression and mediation analysis

5. Bayes Factors

6. Multivariate tests

7. Reliability and consistency

8. Effect sizes and power analysis

9. Parametric/bootstrapped confidence intervals around an effect size or a correlation coefficient

10. Circular statistics

11. Chi-squared tests

12. Plotting: Bland-Altman plot, Q-Q plot, paired plot, robust correlation...

Pingouin is designed for users who want simple yet exhaustive statistical functions.

For example, the :code:ttest_ind function of SciPy returns only the T-value and the p-value. By contrast, the :code:ttest function of Pingouin returns the T-value, the p-value, the degrees of freedom, the effect size (Cohen's d), the 95% confidence intervals of the difference in means, the statistical power and the Bayes Factor (BF10) of the test.

Documentation

• Link to documentation <https://pingouin-stats.org/index.html>_

Chat

If you have questions, please ask them in GitHub Discussions <https://github.com/raphaelvallat/pingouin/discussions>_.

Installation

Dependencies

The main dependencies of Pingouin are :

• NumPy <https://numpy.org/>_
• SciPy <https://www.scipy.org/>_
• Pandas <https://pandas.pydata.org/>_
• Pandas-flavor <https://github.com/Zsailer/pandas_flavor>_
• Statsmodels <https://www.statsmodels.org/>_
• Matplotlib <https://matplotlib.org/>_
• Seaborn <https://seaborn.pydata.org/>_

In addition, some functions require :

• Scikit-learn <https://scikit-learn.org/>_
• Mpmath <http://mpmath.org/>_

Pingouin is a Python 3 package and is currently tested for Python 3.8-3.11.

User installation

Pingouin can be easily installed using pip

.. code-block:: shell

pip install pingouin

or conda

.. code-block:: shell

conda install -c conda-forge pingouin

New releases are frequent so always make sure that you have the latest version:

.. code-block:: shell

pip install --upgrade pingouin

Development

To build and install from source, clone this repository or download the source archive and decompress the files

.. code-block:: shell

cd pingouin python -m build # optional, build a wheel and sdist pip install . # install the package pip install --editable . # or editable install pytest # test the package

Quick start

Click on the link below and navigate to the notebooks/ folder to run a collection of interactive Jupyter notebooks showing the main functionalities of Pingouin. No need to install Pingouin beforehand, the notebooks run in a Binder environment.

.. image:: https://mybinder.org/badge.svg :target: https://mybinder.org/v2/gh/raphaelvallat/pingouin/develop

10 minutes to Pingouin

1. T-test #########

.. code-block:: python

import numpy as np import pingouin as pg

np.random.seed(123) mean, cov, n = [4, 5], [(1, .6), (.6, 1)], 30 x, y = np.random.multivariate_normal(mean, cov, n).T

T-test

pg.ttest(x, y)

.. table:: Output :widths: auto

====== ===== ============= ======= ============= ========= ====== ======= T dof alternative p-val CI95% cohen-d BF10 power ====== ===== ============= ======= ============= ========= ====== ======= -3.401 58 two-sided 0.001 [-1.68 -0.43] 0.878 26.155 0.917 ====== ===== ============= ======= ============= ========= ====== =======

---

2. Pearson's correlation ########################

.. code-block:: python

pg.corr(x, y)

.. table:: Output :widths: auto

=== ===== =========== ======= ====== ======= n r CI95% p-val BF10 power === ===== =========== ======= ====== ======= 30 0.595 [0.3 0.79] 0.001 69.723 0.950 === ===== =========== ======= ====== =======

---

3. Robust correlation #####################

.. code-block:: python

Introduce an outlier

x[5] = 18

Use the robust biweight midcorrelation

pg.corr(x, y, method="bicor")

.. table:: Output :widths: auto

=== ===== =========== ======= ======= n r CI95% p-val power === ===== =========== ======= ======= 30 0.576 [0.27 0.78] 0.001 0.933 === ===== =========== ======= =======

---

4. Test the normality of the data #################################

The pingouin.normality function works with lists, arrays, or pandas DataFrame in wide or long-format.

.. code-block:: python

print(pg.normality(x)) # Univariate normality print(pg.multivariate_normality(np.column_stack((x, y)))) # Multivariate normality

.. table:: Output :widths: auto

===== ====== ======== W pval normal ===== ====== ======== 0.615 0.000 False ===== ====== ========

.. parsed-literal::

(False, 0.00018)

---

5. One-way ANOVA using a pandas DataFrame #########################################

.. code-block:: python

Read an example dataset

df = pg.read_dataset('mixed_anova')

Run the ANOVA

aov = pg.anova(data=df, dv='Scores', between='Group', detailed=True) print(aov)

.. table:: Output :widths: auto

======== ======= ==== ===== ======= ======= ======= Source SS DF MS F p-unc np2 ======== ======= ==== ===== ======= ======= ======= Group 5.460 1 5.460 5.244 0.023 0.029 Within 185.343 178 1.041 nan nan nan ======== ======= ==== ===== ======= ======= =======

---

6. Repeated measures ANOVA ##########################

.. code-block:: python

pg.rm_anova(data=df, dv='Scores', within='Time', subject='Subject', detailed=True)

.. table:: Output :widths: auto

======== ======= ==== ===== ======= ======= ======= ======= Source SS DF MS F p-unc ng2 eps ======== ======= ==== ===== ======= ======= ======= ======= Time 7.628 2 3.814 3.913 0.023 0.04 0.999 Error 115.027 118 0.975 nan nan nan nan ======== ======= ==== ===== ======= ======= ======= =======

---

7. Post-hoc tests corrected for multiple-comparisons ####################################################

.. code-block:: python

FDR-corrected post hocs with Hedges'g effect size

posthoc = pg.pairwise_tests(data=df, dv='Scores', within='Time', subject='Subject', parametric=True, padjust='fdr_bh', effsize='hedges')

Pretty printing of table

pg.print_table(posthoc, floatfmt='.3f')

.. table:: Output :widths: auto

========== ======= ======= ======== ============ ====== ====== ============= ======= ======== ========== ====== ======== Contrast A B Paired Parametric T dof alternative p-unc p-corr p-adjust BF10 hedges ========== ======= ======= ======== ============ ====== ====== ============= ======= ======== ========== ====== ======== Time August January True True -1.740 59.000 two-sided 0.087 0.131 fdr_bh 0.582 -0.328 Time August June True True -2.743 59.000 two-sided 0.008 0.024 fdr_bh 4.232 -0.483 Time January June True True -1.024 59.000 two-sided 0.310 0.310 fdr_bh 0.232 -0.170 ========== ======= ======= ======== ============ ====== ====== ============= ======= ======== ========== ====== ========

---

8. Two-way mixed ANOVA ######################

.. code-block:: python

Compute the two-way mixed ANOVA

aov = pg.mixed_anova(data=df, dv='Scores', between='Group', within='Time', subject='Subject', correction=False, effsize="np2") pg.print_table(aov)

.. table:: Output :widths: auto

=========== ===== ===== ===== ===== ===== ======= ===== ======= Source SS DF1 DF2 MS F p-unc np2 eps =========== ===== ===== ===== ===== ===== ======= ===== ======= Group 5.460 1 58 5.460 5.052 0.028 0.080 nan Time 7.628 2 116 3.814 4.027 0.020 0.065 0.999 Interaction 5.167 2 116 2.584 2.728 0.070 0.045 nan =========== ===== ===== ===== ===== ===== ======= ===== =======

---

9. Pairwise correlations between columns of a dataframe #######################################################

.. code-block:: python

import pandas as pd np.random.seed(123) z = np.random.normal(5, 1, 30) data = pd.DataFrame({'X': x, 'Y': y, 'Z': z}) pg.pairwise_corr(data, columns=['X', 'Y', 'Z'], method='pearson')

.. table:: Output :widths: auto

=== === ======== ============= === ===== ============= ======= ====== ======= X Y method alternative n r CI95% p-unc BF10 power === === ======== ============= === ===== ============= ======= ====== ======= X Y pearson two-sided 30 0.366 [0.01 0.64] 0.047 1.500 0.525 X Z pearson two-sided 30 0.251 [-0.12 0.56] 0.181 0.534 0.272 Y Z pearson two-sided 30 0.020 [-0.34 0.38] 0.916 0.228 0.051 === === ======== ============= === ===== ============= ======= ====== =======

---

10. Pairwise T-test between columns of a dataframe ###################################################

.. code-block:: python

data.ptests(paired=True, stars=False)

.. table:: Pairwise T-tests, with T-values on the lower triangle and p-values on the upper triangle :widths: auto

==== ====== ====== ===== .. X Y Z ==== ====== ====== ===== X - 0.226 0.165 Y -1.238 - 0.658 Z -1.424 -0.447 - ==== ====== ====== =====

---

11. Multiple linear regression ##############################

.. code-block:: python

pg.linear_regression(data[['X', 'Z']], data['Y'])

.. table:: Linear regression summary :widths: auto

========= ====== ===== ====== ====== ===== ======== ========== =========== names coef se T pval r2 adj_r2 CI[2.5%] CI[97.5%] ========= ====== ===== ====== ====== ===== ======== ========== =========== Intercept 4.650 0.841 5.530 0.000 0.139 0.076 2.925 6.376 X 0.143 0.068 2.089 0.046 0.139 0.076 0.003 0.283 Z -0.069 0.167 -0.416 0.681 0.139 0.076 -0.412 0.273 ========= ====== ===== ====== ====== ===== ======== ========== ===========

---

12. Mediation analysis ######################

.. code-block:: python

pg.mediation_analysis(data=data, x='X', m='Z', y='Y', seed=42, n_boot=1000)

.. table:: Mediation summary :widths: auto

======== ====== ===== ====== ========== =========== ===== path coef se pval CI[2.5%] CI[97.5%] sig ======== ====== ===== ====== ========== =========== ===== Z ~ X 0.103 0.075 0.181 -0.051 0.256 No Y ~ Z 0.018 0.171 0.916 -0.332 0.369 No Total 0.136 0.065 0.047 0.002 0.269 Yes Direct 0.143 0.068 0.046 0.003 0.283 Yes Indirect -0.007 0.025 0.898 -0.069 0.029 No ======== ====== ===== ====== ========== =========== =====

---

13. Contingency analysis ########################

.. code-block:: python

data = pg.read_dataset('chi2_independence')
expected, observed, stats = pg.chi2_independence(data, x='sex', y='target')
stats

.. table:: Chi-squared tests summary :widths: auto

================== ======== ====== ===== ===== ======== ======= test lambda chi2 dof p cramer power ================== ======== ====== ===== ===== ======== ======= pearson 1.000 22.717 1.000 0.000 0.274 0.997 cressie-read 0.667 22.931 1.000 0.000 0.275 0.998 log-likelihood 0.000 23.557 1.000 0.000 0.279 0.998 freeman-tukey -0.500 24.220 1.000 0.000 0.283 0.998 mod-log-likelihood -1.000 25.071 1.000 0.000 0.288 0.999 neyman -2.000 27.458 1.000 0.000 0.301 0.999 ================== ======== ====== ===== ===== ======== =======

Integration with Pandas

Several functions of Pingouin can be used directly as pandas DataFrame methods. Try for yourself with the code below:

.. code-block:: python

import pingouin as pg

Example 1 | ANOVA

df = pg.read_dataset('mixed_anova') df.anova(dv='Scores', between='Group', detailed=True)

Example 2 | Pairwise correlations

data = pg.read_dataset('mediation') data.pairwise_corr(columns=['X', 'M', 'Y'], covar=['Mbin'])

Example 3 | Partial correlation matrix

data.pcorr()

The functions that are currently supported as pandas method are:

• pingouin.anova <https://pingouin-stats.org/generated/pingouin.anova.html#pingouin.anova>_
• pingouin.ancova <https://pingouin-stats.org/generated/pingouin.ancova.html#pingouin.ancova>_
• pingouin.rm_anova <https://pingouin-stats.org/generated/pingouin.rm_anova.html#pingouin.rm_anova>_
• pingouin.mixed_anova <https://pingouin-stats.org/generated/pingouin.mixed_anova.html#pingouin.mixed_anova>_
• pingouin.welch_anova <https://pingouin-stats.org/generated/pingouin.welch_anova.html#pingouin.welch_anova>_
• pingouin.pairwise_tests <https://pingouin-stats.org/generated/pingouin.pairwise_tests.html#pingouin.pairwise_tests>_
• pingouin.pairwise_tukey <https://pingouin-stats.org/generated/pingouin.pairwise_tukey.html#pingouin.pairwise_tukey>_
• pingouin.pairwise_corr <https://pingouin-stats.org/generated/pingouin.pairwise_corr.html#pingouin.pairwise_corr>_
• pingouin.partial_corr <https://pingouin-stats.org/generated/pingouin.partial_corr.html#pingouin.partial_corr>_
• pingouin.pcorr <https://pingouin-stats.org/generated/pingouin.pcorr.html#pingouin.pcorr>_
• pingouin.rcorr <https://pingouin-stats.org/generated/pingouin.rcorr.html#pingouin.rcorr>_
• pingouin.ptests <https://pingouin-stats.org/generated/pingouin.ptests.html#pingouin.ptests>_
• pingouin.mediation_analysis <https://pingouin-stats.org/generated/pingouin.mediation_analysis.html#pingouin.mediation_analysis>_

Development

Pingouin was created and is maintained by Raphael Vallat <https://raphaelvallat.github.io>_, a postdoctoral researcher at UC Berkeley, mostly during his spare time. Contributions are more than welcome so feel free to contact me, open an issue or submit a pull request!

To see the code or report a bug, please visit the GitHub repository <https://github.com/raphaelvallat/pingouin>_.

This program is provided with NO WARRANTY OF ANY KIND. Pingouin is still under heavy development and there are likely hidden bugs. Always double check the results with another statistical software.

Contributors

• Nicolas Legrand
• Richard Höchenberger <http://hoechenberger.net/>_
• Arthur Paulino <https://github.com/arthurpaulino>_
• Eelke Spaak <https://eelkespaak.nl/>_
• Johannes Elfner <https://www.linkedin.com/in/johannes-elfner/>_
• Stefan Appelhoff <https://stefanappelhoff.com>_

How to cite Pingouin?

If you want to cite Pingouin, please use the publication in JOSS:

• Vallat, R. (2018). Pingouin: statistics in Python. Journal of Open Source Software, 3(31), 1026, https://doi.org/10.21105/joss.01026 <https://doi.org/10.21105/joss.01026>_

Acknowledgement

Several functions of Pingouin were inspired from R or Matlab toolboxes, including:

• effsize package (R) <https://cran.r-project.org/web/packages/effsize/effsize.pdf>_
• ezANOVA package (R) <https://cran.r-project.org/web/packages/ez/ez.pdf>_
• pwr package (R) <https://cran.r-project.org/web/packages/pwr/pwr.pdf>_
• circular statistics (Matlab) <https://www.mathworks.com/matlabcentral/fileexchange/10676-circular-statistics-toolbox-directional-statistics>_
• robust correlations (Matlab) <https://sourceforge.net/projects/robustcorrtool/>_
• repeated-measure correlation (R) <https://cran.r-project.org/web/packages/rmcorr/index.html>_
• real-statistics.com <https://www.real-statistics.com/>_