# pingouin Release 0.5.2

Pingouin: statistical package for Python

Keywords
anova, bayesian-statistics, circular-statistics, cohens-d, correlations, effect-size, multiple-comparisons, pandas, statistical-methods, statistical-tests, statistics, ttest
GPL-3.0
Install
``` pip install pingouin==0.5.2 ```

### Documentation       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.

## Chat

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

## Installation

### Dependencies

The main dependencies of Pingouin are :

In addition, some functions require :

Pingouin is a Python 3 package and is currently tested for Python 3.7-3.9. It does not support Python 2.

### 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`

## 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 = 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

# 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',

# 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. 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
```

#### 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.anova(dv='Scores', between='Group', detailed=True)

# Example 2 | Pairwise correlations
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, 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

## How to cite Pingouin?

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

## Acknowledgement

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