# How to Perform the Nemenyi Post-Hoc Test in Python

## Introduction

In statistical analysis, the Nemenyi Post-Hoc Test is often used for comparing multiple group means after a Friedman test, especially when dealing with non-parametric data. It is primarily used when the data does not meet the assumptions for using the traditional ANOVA test, such as normal distribution and homogeneity of variance. This article walks you through the process of performing the Nemenyi Post-Hoc Test in Python, from setting up your environment to visualizing the results.

1. Background and Use Cases
2. Understanding the Nemenyi Post-Hoc Test
3. Setting Up the Python Environment
4. Preparing the Data
5. Performing the Friedman Test
6. Performing the Nemenyi Post-Hoc Test
7. Interpreting the Results
8. Visualizing the Results
9. Conclusion

## 1. Background and Use Cases

### 1.1. Post-Hoc Tests and Nemenyi Test

Post-Hoc tests are used to conduct multiple pairwise comparisons after obtaining a significant result from an omnibus test, such as ANOVA or Friedman Test. The Nemenyi Test is a non-parametric test used for pairwise comparison of multiple groups, especially after the Friedman Test.

### 1.2. Use Cases

Nemenyi Test is useful when you need to compare three or more paired groups. It is widely used in cases where the assumptions of ANOVA are not met. For example, it can be used to compare the effects of different treatment methods on a set of patients using ranking rather than raw data.

## 2. Understanding the Nemenyi Post-Hoc Test

The Nemenyi test compares the mean ranks of each pair of groups. It is based on the assumption that the observations are from continuous distributions and are independent within and among groups.

## 3. Setting Up the Python Environment

To perform the Nemenyi Post-Hoc Test, you’ll need Python and several libraries:

• pandas
• numpy
• scipy
• scikit-posthocs

You can install these libraries using pip:

pip install pandas numpy scipy scikit-posthocs

## 4. Preparing the Data

Your data should be structured with one categorical variable representing the groups and a continuous variable representing the observations. Here’s an example dataset:

Method, Score
A, 85
A, 89
B, 87
B, 90
C, 88
C, 91
...

import pandas as pd

data = pd.read_csv('data.csv')

## 5. Performing the Friedman Test

Before you perform the Nemenyi test, it is crucial to perform the Friedman Test to determine if there are any significant differences among the groups.

from scipy.stats import friedmanchisquare

group_a = data[data['Method'] == 'A']['Score']
group_b = data[data['Method'] == 'B']['Score']
group_c = data[data['Method'] == 'C']['Score']

stat, p = friedmanchisquare(group_a, group_b, group_c)

print('Statistics=%.3f, p=%.3f' % (stat, p))

## 6. Performing the Nemenyi Post-Hoc Test

If the p-value from the Friedman Test is below 0.05, you can perform the Nemenyi Post-Hoc Test.

import scikit_posthocs as sp

# Stack the data
stacked_data = data.stack().reset_index()
stacked_data.columns = ['id', 'methods', 'scores']

# Perform the Nemenyi Test
nemenyi_results = sp.posthoc_nemenyi_friedman(stacked_data, y_col='scores', block_col='id', group_col='methods')
print(nemenyi_results)

## 7. Interpreting the Results

Nemenyi Post-Hoc Test provides a matrix of p-values for each pair of groups. A p-value below 0.05 typically indicates a statistically significant difference between the groups.

## 8. Visualizing the Results

Visualizations can help in understanding the analysis. You can create box plots to visualize the distribution of data among different groups.

import seaborn as sns
import matplotlib.pyplot as plt

sns.boxplot(x='Method', y='Score', data=data)
plt.title('Comparison of Methods')
plt.xlabel('Method')
plt.ylabel('Score')
plt.show()

## 9. Conclusion

The Nemenyi Post-Hoc Test is an important non-parametric test for comparing multiple groups, especially when the assumptions for ANOVA are not met. Python, with its extensive libraries, provides an excellent platform for conducting this analysis. However, it’s essential to understand the assumptions and limitations of the Nemenyi Test and to interpret the results with caution. Furthermore, visualizing the data can provide additional insights into the relationships among the groups. Always ensure that the Nemenyi Test is used as part of a larger statistical analysis plan, which should be thoughtfully developed based on the research questions and the nature of the data.