Creating a Chi-Square Table in Python

This code uses the scipy.stats library to calculate chi-square critical values and organizes them into a table using pandas. The values are rounded to two decimal places for clarity.

import pandas as pd
import numpy as np
from scipy.stats import chi2

# Define degrees of freedom and significance levels
degrees_of_freedom_extended = np.arange(1, 41)
alpha_values_extended = [0.5, 0.25, 0.1, 0.05, 0.025, 0.01, 0.005, 0.001]

# Build the table with the specified parameters
chi_square_table_extended = pd.DataFrame({
    f'α = {alpha}': [round(chi2.ppf(1 - alpha, df), 2) for df in degrees_of_freedom_extended]
    for alpha in alpha_values_extended
}, index=degrees_of_freedom_extended)

chi_square_table_extended.index.name = 'Degrees of Freedom'

# Display the table
chi_square_table_extended

Let’s walk through the code in detail.

First, I import the necessary libraries:

import pandas as pd
import numpy as np
from scipy.stats import chi2

The code makes use of three external modules:

• Pandas is used to create and manage the table as a DataFrame.
• NumPy is used to generate an array for the degrees of freedom.
• scipy.stats.chi2 provides the chi-square distribution for calculating the critical values.

Next, I set the parameters for the table: the degrees of freedom and the significance levels.

degrees_of_freedom_extended = np.arange(1, 41)
alpha_values_extended = [0.5, 0.25, 0.1, 0.05, 0.025, 0.01, 0.005, 0.001]

The variable degrees_of_freedom_extended creates an array ranging from 1 to 40 using the function np.arange(1, 41). These values represent the degrees of freedom for the table.

The variable alpha_values_extended stores a list of the significance levels (α) to be considered.

Now, I construct the table:

chi_square_table_extended = pd.DataFrame({
f'α = {alpha}': [round(chi2.ppf(1 - alpha, df), 2) for df in degrees_of_freedom_extended]
for alpha in alpha_values_extended
}, index=degrees_of_freedom_extended)

This part of the code creates a DataFrame using pandas.

The table structure is built using a dictionary comprehension where:

• The keys of the dictionary are the column names, formatted as `α = {alpha}` to indicate the significance level.
• The column values are generated by calculating the critical values for each degree of freedom using `chi2.ppf(1 - alpha, df)`.
• `chi2.ppf(1 - alpha, df)` calculates the chi-square critical value for a specific significance level and degree of freedom.
• `round(..., 2)` rounds each value to two decimal places.
• `index=degrees_of_freedom_extended` sets the DataFrame index to the array of degrees of freedom.

I then assign the name “Degrees of Freedom” to the DataFrame index to clearly indicate that the rows represent the degrees of freedom.

chi_square_table_extended.index.name = 'Degrees of Freedom'

Finally, I display the table that has been created:

chi_square_table_extended

This line displays the DataFrame. In an interactive environment (such as a Jupyter notebook), this command shows the chi-square table in a tabular format.

The code generates a chi-square critical values table for various degrees of freedom (from 1 to 40) and specific significance levels (α), rounding values to two decimal places for better readability.

And so on.