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.
ANOVAs: N-ways, repeated measures, mixed, ancova
Pairwise post-hocs tests (parametric and non-parametric) and pairwise correlations
Robust, partial, distance and repeated measures correlations
Linear/logistic regression and mediation analysis
Bayes Factors
Multivariate tests
Reliability and consistency
Effect sizes and power analysis
Parametric/bootstrapped confidence intervals around an effect size or a correlation coefficient
Circular statistics
Chi-squared tests
Plotting: Bland-Altman plot, Q-Q plot, paired plot, robust correlation…
Pingouin is designed for users who want simple yet exhaustive stats 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.
Installation
Pingouin is a Python 3 package and is currently tested for Python 3.5, 3.6 and 3.7. It will not work with Python 2.7.
The main dependencies of Pingouin are :
NumPy (>= 1.15)
SciPy (>= 1.3.0)
Pandas (>= 0.24)
Matplotlib (>= 3.0.2)
Seaborn (>= 0.9.0)
In addition, some functions require :
Statsmodels
Scikit-learn
Mpmath
Pingouin can be easily installed using pip
pip install pingouin
or conda
conda install -c conda-forge pingouin
Pingouin is under heavy development and it is likely that bugs/mistakes will be discovered in future releases. Please always make sure that you are using the latest version of Pingouin (new releases are frequent, i.e. about one per month).
To be notified whenever a new release of Pingouin is available, you can click on “Watch releases” on the GitHub of Pingouin (see below).
Whenever a new release is out there, you can upgrade your version by typing the following line in a terminal window:
pip install --upgrade pingouin
Quick start
If you have questions, please ask them in the public Gitter chat.
If you want to report a bug, please open an issue on the GitHub repository.
If you want to see Pingouin in action, please click on the link below and navigate to the notebooks/ folder to open a collection of interactive Jupyter notebooks.
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)
T |
dof |
tail |
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)
n |
r |
CI95% |
r2 |
adj_r2 |
p-val |
BF10 |
power |
|---|---|---|---|---|---|---|---|
30 |
0.595 |
[0.3 0.79] |
0.354 |
0.306 |
0.001 |
69.723 |
0.95 |
3. Robust correlation
# Introduce an outlier
x[5] = 18
# Use the robust Shepherd's pi correlation
pg.corr(x, y, method="shepherd")
n |
r |
CI95% |
r2 |
adj_r2 |
p-val |
power |
|---|---|---|---|---|---|---|
30 |
0.561 |
[0.25 0.77] |
0.315 |
0.264 |
0.002 |
0.917 |
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
W |
pval |
normal |
|---|---|---|
0.615 |
0.000 |
False |
(False, 0.00018)
5. Q-Q plot
import numpy as np
import pingouin as pg
np.random.seed(123)
x = np.random.normal(size=50)
ax = pg.qqplot(x, dist='norm')
6. 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)
Source |
SS |
DF |
MS |
F |
p-unc |
np2 |
|---|---|---|---|---|---|---|
Group |
5.460 |
1 |
5.460 |
5.244 |
0.02320 |
0.029 |
Within |
185.343 |
178 |
1.041 |
7. Repeated measures ANOVA
pg.rm_anova(data=df, dv='Scores', within='Time', subject='Subject', detailed=True)
Source |
SS |
DF |
MS |
F |
p-unc |
np2 |
eps |
|---|---|---|---|---|---|---|---|
Time |
7.628 |
2 |
3.814 |
3.913 |
0.022629 |
0.062 |
0.999 |
Error |
115.027 |
118 |
0.975 |
8. Post-hoc tests corrected for multiple-comparisons
# FDR-corrected post hocs with Hedges'g effect size
posthoc = pg.pairwise_ttests(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')
Contrast |
A |
B |
Paired |
Parametric |
T |
dof |
tail |
p-unc |
p-corr |
p-adjust |
BF10 |
CLES |
hedges |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Time |
August |
January |
True |
True |
-1.740 |
59.000 |
two-sided |
0.087 |
0.131 |
fdr_bh |
0.582 |
0.585 |
-0.328 |
Time |
August |
June |
True |
True |
-2.743 |
59.000 |
two-sided |
0.008 |
0.024 |
fdr_bh |
4.232 |
0.644 |
-0.485 |
Time |
January |
June |
True |
True |
-1.024 |
59.000 |
two-sided |
0.310 |
0.310 |
fdr_bh |
0.232 |
0.571 |
-0.170 |
9. Two-way mixed ANOVA
# Compute the two-way mixed ANOVA and export to a .csv file
aov = pg.mixed_anova(data=df, dv='Scores', between='Group', within='Time',
subject='Subject', correction=False,
export_filename='mixed_anova.csv')
pg.print_table(aov)
Source |
SS |
DF1 |
DF2 |
MS |
F |
p-unc |
np2 |
eps |
|---|---|---|---|---|---|---|---|---|
Group |
5.460 |
1 |
58 |
5.460 |
5.052 |
0.028 |
0.080 |
|
Time |
7.628 |
2 |
116 |
3.814 |
4.027 |
0.020 |
0.065 |
0.999 |
Interaction |
5.168 |
2 |
116 |
2.584 |
2.728 |
0.070 |
0.045 |
10. 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'])
X |
Y |
method |
tail |
n |
r |
CI95% |
r2 |
adj_r2 |
z |
p-unc |
BF10 |
power |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
X |
Y |
pearson |
two-sided |
30 |
0.366 |
[0.01 0.64] |
0.134 |
0.070 |
0.384 |
0.047 |
1.500 |
0.525 |
X |
Z |
pearson |
two-sided |
30 |
0.251 |
[-0.12 0.56] |
0.063 |
-0.006 |
0.256 |
0.181 |
0.534 |
0.272 |
Y |
Z |
pearson |
two-sided |
30 |
0.020 |
[-0.34 0.38] |
0.000 |
-0.074 |
0.020 |
0.916 |
0.228 |
0.051 |
11. Convert between effect sizes
# Convert from Cohen's d to Hedges' g
pg.convert_effsize(0.4, 'cohen', 'hedges', nx=10, ny=12)
0.384
12. Multiple linear regression
pg.linear_regression(data[['X', 'Z']], data['Y'])
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 |
13. Mediation analysis
pg.mediation_analysis(data=data, x='X', m='Z', y='Y', seed=42, n_boot=1000)
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 |
-0.070 |
0.029 |
No |
14. Contingency analysis
data = pg.read_dataset('chi2_independence')
expected, observed, stats = pg.chi2_independence(data, x='sex', y='target')
stats
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 |
15. Bland-Altman plot
import numpy as np
import pingouin as pg
np.random.seed(123)
mean, cov = [10, 11], [[1, 0.8], [0.8, 1]]
x, y = np.random.multivariate_normal(mean, cov, 30).T
ax = pg.plot_blandaltman(x, y)
16. Plot achieved power of a paired T-test
Plot the curve of achieved power given the effect size (Cohen d) and the sample size of a paired T-test.
import matplotlib.pyplot as plt
import seaborn as sns
import pingouin as pg
import numpy as np
sns.set(style='ticks', context='notebook', font_scale=1.2)
d = 0.5 # Fixed effect size
n = np.arange(5, 80, 5) # Incrementing sample size
# Compute the achieved power
pwr = pg.power_ttest(d=d, n=n, contrast='paired', tail='two-sided')
# Start the plot
plt.plot(n, pwr, 'ko-.')
plt.axhline(0.8, color='r', ls=':')
plt.xlabel('Sample size')
plt.ylabel('Power (1 - type II error)')
plt.title('Achieved power of a paired T-test')
sns.despine()
17. Paired plot
import pingouin as pg
import numpy as np
df = pg.read_dataset('mixed_anova').query("Group == 'Meditation' and Time != 'January'")
ax = pg.plot_paired(data=df, dv='Scores', within='Time', subject='Subject', dpi=150)
ax.set_title("Effect of meditation on school performance")
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:
Development
Pingouin was created and is maintained by Raphael Vallat, 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.
Note that this program is provided with NO WARRANTY OF ANY KIND. If you can, always double check the results with another statistical software.
Contributors
Nicolas Legrand
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
@ARTICLE{Vallat2018,
title = "Pingouin: statistics in Python",
author = "Vallat, Raphael",
journal = "The Journal of Open Source Software",
volume = 3,
number = 31,
pages = "1026",
month = nov,
year = 2018
}
Acknowledgement
Several functions of Pingouin were inspired from R or Matlab toolboxes, including:
circular statistics (Matlab) (Berens 2009)
robust correlations (Matlab) (Pernet, Wilcox & Rousselet, 2012)
repeated-measure correlation (R) (Bakdash & Marusich, 2017)
I am also grateful to Charles Zaiontz and his website www.real-statistics.com which has been useful to understand the practical implementation of several functions.