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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.

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 ttest_ind function of SciPy returns only the T-value and the p-value. By contrast, the 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

Chat

If you have questions, please ask them in GitHub Discussions.

Installation

Dependencies

The main dependencies of Pingouin are :

• NumPy
• SciPy
• Pandas
• Pandas-flavor
• Statsmodels
• Matplotlib
• Seaborn

In addition, some functions require :

• Scikit-learn
• Mpmath

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

pip install pingouin

or conda

conda install -c conda-forge pingouin

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

pip install --upgrade pingouin

Development

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

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.

10 minutes to Pingouin

1. T-test

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)

Output

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

pg.corr(x, y)

Output

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

---

3. Robust correlation

# Introduce an outlier
x[5] = 18
# Use the robust biweight midcorrelation
pg.corr(x, y, method="bicor")

Output

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.

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

Output

W	pval	normal
0.615	0.000	False

(False, 0.00018)

---

5. One-way ANOVA using a pandas DataFrame

# 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)

Output

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

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

Output

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

# 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')

Output

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

# 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)

Output

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

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')

Output

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

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

Pairwise T-tests, with T-values on the lower triangle and p-values on the upper triangle

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

---

11. Multiple linear regression

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

Linear regression summary

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

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

Mediation summary

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

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

Chi-squared tests summary

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:

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
• pingouin.ancova
• pingouin.rm_anova
• pingouin.mixed_anova
• pingouin.welch_anova
• pingouin.pairwise_tests
• pingouin.pairwise_tukey
• pingouin.pairwise_corr
• pingouin.partial_corr
• pingouin.pcorr
• pingouin.rcorr
• pingouin.ptests
• pingouin.mediation_analysis

Development

Pingouin was created and is maintained by Raphael Vallat, 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.

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
• Arthur Paulino
• Eelke Spaak
• Johannes Elfner
• Stefan Appelhoff

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

Acknowledgement

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

• effsize package (R)
• ezANOVA package (R)
• pwr package (R)
• circular statistics (Matlab)
• robust correlations (Matlab)
• repeated-measure correlation (R)
• real-statistics.com