**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 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

## Chat

If you have questions, please ask them in the public Gitter chat

## Installation

### Dependencies

The main dependencies of Pingouin are :

- NumPy (>= 1.16.5)
- SciPy (>= 1.3.0)
- Pandas (>= 0.24)
- Pandas-flavor (>= 0.1.2)
- Matplotlib (>= 3.0.2)
- Seaborn (>= 0.9.0)
- Outdated

In addition, some functions require :

Pingouin is a Python 3 package and is currently tested for Python 3.6 and 3.7. Pingouin does not work with Python 2.7.

### 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)
```

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 | outliers | r | CI95% | r2 | adj_r2 | p-val | power |
---|---|---|---|---|---|---|---|

30 | 1 | 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. 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 | 0.023 | 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)`

Source | SS | DF | MS | F | p-unc | np2 | eps |
---|---|---|---|---|---|---|---|

Time | 7.628 | 2 | 3.814 | 3.913 | 0.023 | 0.062 | 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_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 | 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 | -0.485 |

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)
```

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')
```

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 | 0.257 | 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 |

#### 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'])`

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)`

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
```

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_ttests
- pingouin.pairwise_ttests
- pingouin.pairwise_corr
- pingouin.partial_corr
- pingouin.pcorr
- pingouin.rcorr
- pingouin.mediation_analysis

## 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
- 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: