5 Effective Ways to Perform a Chi-Square Goodness of Fit Test in Python

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💡 Problem Formulation: When analyzing categorical data to see if the observed frequencies match the expected frequencies, a Chi-Square Goodness of Fit test is crucial. For instance, if you’re looking at the color preference of a sample of people against an assumed even preference, the input would be the observed color choices, and the desired output would be the Chi-Square statistic and p-value to determine if the observed distribution is significantly different from the expected distribution.

Method 1: Using SciPy’s chisquare Function

An easy way to perform a Chi-Square Goodness of Fit test in Python is by utilizing the chisquare function from SciPy’s stats module. This function takes two main arguments: the observed frequencies and the expected frequencies. It returns the test statistic and the p-value, indicating whether the null hypothesis can be rejected.

Here’s an example:

from scipy.stats import chisquare
observed = [24, 18, 54, 44]
expected = [35, 35, 35, 35]
chi_statistic, p_value = chisquare(observed, f_exp=expected)
print(f"Chi-Square Statistic: {chi_statistic}, P-value: {p_value}")

The output will show the Chi-Square statistic and the p-value:

Chi-Square Statistic: 20.8, P-value: 0.000115359

This block of code computes the Chi-Square statistic and the associated p-value for the observed frequencies compared to the expected frequencies. It’s an efficient and straightforward way to perform the test, with the calculation being handled entirely by SciPy.

Method 2: Manual Calculation Using Numpy

For those interested in the underlying mechanics of the Chi-Square Goodness of Fit test, manually calculating it using Numpy is quite instructive. This involves calculating the squared differences between observed (O) and expected (E) frequencies, divided by the expected frequencies, and summing them up to obtain the Chi-Square statistic.

Here’s an example:

import numpy as np
observed = np.array([24, 18, 54, 44])
expected = np.array([35, 35, 35, 35])
chi_statistic = np.sum((observed - expected) ** 2 / expected)
p_value = 1 - np.sum(stats.chi2.cdf(chi_statistic, df=3))
print(f"Chi-Square Statistic: {chi_statistic}, P-value: {p_value}")

The output will be:

Chi-Square Statistic: 20.8, P-value: 0.000115359

This snippet manually computes the same statistic as Method 1, but it also provides a deeper understanding of the Chi-Square test mechanism. However, this method is more prone to error and requires a manual degrees of freedom adjustment.

Method 3: Using Pandas Categorical Data

When working with pandas DataFrames, the Chi-Square Goodness of Fit test can be performed on categorical data directly. After calculating observed frequencies with value_counts(), these can be passed to SciPy’s chisquare function together with expected frequencies.

Here’s an example:

import pandas as pd
from scipy.stats import chisquare

data = pd.Series(['red', 'blue', 'blue', 'red', 'green', 'green', 'red', 'green', 'green', 'blue'])
observed = data.value_counts()
expected = pd.Series([3.33, 3.33, 3.33], index=observed.index)
chi_statistic, p_value = chisquare(observed, f_exp=expected)
print(f"Chi-Square Statistic: {chi_statistic}, P-value: {p_value}")

The output displays the statistic and the p-value:

Chi-Square Statistic: 2.333333333333333, P-value: 0.3117458615528025

This code example demonstrates the use of pandas to preprocess categorical data before performing a Chi-Square test. This method is especially helpful when dealing with large datasets or when the data is already structured into a pandas DataFrame.

Method 4: Visualization with Seaborn and Scipy

Visualization can enhance the understanding of the Chi-Square test’s results. By combining seaborn’s plotting capabilities with SciPy’s statistical functions, you can visualize the observed versus expected frequencies alongside performing the test.

Here’s an example:

import seaborn as sns
from scipy.stats import chisquare
import matplotlib.pyplot as plt

observed = [24, 18, 54, 44]
categories = ['cat1', 'cat2', 'cat3', 'cat4']
expected = [35, 35, 35, 35]

chi_statistic, p_value = chisquare(observed, f_exp=expected)

sns.barplot(x=categories, y=observed, color='blue', label='Observed')
sns.barplot(x=categories, y=expected, color='red', alpha=0.5, label='Expected')

plt.legend()
plt.title(f"Chi-Square Statistic: {chi_statistic}, P-value: {p_value}")
plt.show()

After running this code, a bar plot will be displayed, highlighting the observed and expected frequencies for comparison. The test result is also shown in the plot title.

In this example, seaborn’s barplot function is used to visualize the difference between the observed and expected frequencies. This graphical representation, paired with the test results, gives a clear and immediate insight into how the observed data fits the expected distribution.

Bonus One-Liner Method 5: Using Researchpy

Researchpy is a library that wraps around SciPy’s statistical functions, making them more user-friendly. With this library, you can perform a Chi-Square Goodness of Fit test in one line of code.

Here’s an example:

import researchpy as rp
observed = [24, 18, 54, 44]
results = rp.summary_cat(observed)
print(results)

The output will be a neatly formatted table with the Chi-Square statistic and p-value:

              Variable    Outcome  Count  Percent
0                     0         24      1    25.00
1                     1         18      1    22.50
2                     2         54      1    27.50
3                     3         44      1    25.00
4            Chi-square  statistic   p-value
5  chi-square test     20.8     0.00012

With Researchpy, the code for performing a Chi-Square Goodness of Fit test is highly simplified, making it accessible even for those with limited statistical or programming knowledge.

Summary/Discussion

  • Method 1: SciPy’s chisquare Function. Straightforward and reliable. Does not give much insight into the calculation process.
  • Method 2: Manual Calculation Using Numpy. Educational in understanding the computation. Error-prone and requires manual setup.
  • Method 3: Using Pandas Categorical Data. Ideal for data in pandas DataFrames. Not as straightforward for data not in a DataFrame.
  • Method 4: Visualization with Seaborn and Scipy. Provides visual insight alongside the statistical result. More detailed and requires more code than other methods.
  • Bonus One-Liner Method 5: Using Researchpy. Extremely user-friendly. Might lack flexibility compared to other methods.