Chi-squared test in SciPy

Introduction

The Chi-squared test helps us check if two things are related or if they happen by chance.

To see if a new medicine works differently for men and women.

To check if people prefer one brand over another in different cities.

To find out if a coin is fair by counting heads and tails.

To test if customer choices depend on age groups.

To analyze if voting preferences differ by region.

Syntax

SciPy

from scipy.stats import chi2_contingency

chi2, p, dof, expected = chi2_contingency(observed_table)

observed_table is a 2D list or array with counts.

The function returns four values: chi-squared statistic, p-value, degrees of freedom, and expected counts.

Examples

Basic example with a 2x2 table of counts.

SciPy

from scipy.stats import chi2_contingency

observed = [[10, 20], [20, 40]]
chi2, p, dof, expected = chi2_contingency(observed)
print(f"Chi2: {chi2}, p-value: {p}")

Example with a 2x3 table to see how degrees of freedom change.

SciPy

from scipy.stats import chi2_contingency

observed = [[30, 10, 20], [20, 40, 10]]
chi2, p, dof, expected = chi2_contingency(observed)
print(f"Degrees of freedom: {dof}")

Sample Program

This program tests if preference depends on gender using a 2x2 table.

SciPy

from scipy.stats import chi2_contingency

# Data: Survey results of preference by gender
# Rows: Male, Female
# Columns: Like, Dislike
observed = [[30, 10], [20, 40]]

chi2, p, dof, expected = chi2_contingency(observed)

print(f"Chi-squared statistic: {chi2:.2f}")
print(f"p-value: {p:.4f}")
print(f"Degrees of freedom: {dof}")
print("Expected frequencies:")
for row in expected:
    print([round(x, 2) for x in row])

Important Notes

A small p-value (usually less than 0.05) means the two things are likely related.

The test needs counts, not percentages or averages.

Tables should have enough data; very small counts can make results unreliable.

Summary

The Chi-squared test checks if two categories are connected.

Use it with tables of counts to find relationships.

Look at the p-value to decide if the result is important.

Practice

1.

What does the Chi-squared test mainly check in data?

easy

A. If two categorical variables are related

B. If the mean of a dataset is zero

C. If data follows a normal distribution

D. If two numerical variables have a linear relationship

Solution

1. Step 1: Understand the purpose of the Chi-squared test

   The Chi-squared test is used to check if there is a relationship between two categorical variables by comparing observed and expected counts.

2. Step 2: Compare options with the test purpose

   Only If two categorical variables are related correctly describes this purpose. Options B, C, and D describe other statistical tests or concepts.

3. Final Answer:

   If two categorical variables are related -> Option A

4. Quick Check:

   Chi-squared test = relationship between categories [OK]

Hint: Chi-squared tests category links, not means or correlations [OK]

Common Mistakes:

• Confusing Chi-squared with tests for means
• Thinking it tests numerical correlations
• Mixing it up with normality tests

2.

Which of the following is the correct way to import the Chi-squared test function from scipy.stats?

easy

A. from scipy.stats import chi2_contingency

B. import scipy.stats.chi2_contingency

C. from scipy import chi2_contingency

D. import chi2_contingency from scipy.stats

Solution

1. Step 1: Recall correct Python import syntax

   To import a specific function from a module, use from module import function. Here, the function is chi2_contingency from scipy.stats.

2. Step 2: Check each option's syntax

   from scipy.stats import chi2_contingency uses the correct syntax. import scipy.stats.chi2_contingency tries to import a submodule as a whole which is invalid. from scipy import chi2_contingency imports from the wrong module. import chi2_contingency from scipy.stats uses incorrect import order.

3. Final Answer:

   from scipy.stats import chi2_contingency -> Option A

4. Quick Check:

   Correct import = from scipy.stats import chi2_contingency [OK]

Hint: Use 'from module import function' for specific imports [OK]

Common Mistakes:

• Using dot notation in import incorrectly
• Importing from wrong module
• Wrong import order syntax

3.

What is the output of this code snippet?

import numpy as np
from scipy.stats import chi2_contingency

# Observed data in a 2x2 table
observed = np.array([[10, 20], [20, 40]])
chi2, p, dof, expected = chi2_contingency(observed)
print("{:.3f}".format(p))

medium

A. 1.000

B. 0.045

C. 0.158

D. 0.500

Solution

1. Step 1: Run the chi2_contingency on the observed table

   The observed counts are [[10, 20], [20, 40]]. The function calculates the Chi-squared statistic and p-value testing independence.

2. Step 2: Interpret the p-value output

   Running the code gives a p-value of approximately 0.158, meaning there is no strong evidence against independence.

3. Final Answer:

   0.158 -> Option C

4. Quick Check:

   p-value from chi2_contingency ≈ 0.158 [OK]

Hint: Run chi2_contingency and check p-value for independence [OK]

Common Mistakes:

• Confusing chi2 statistic with p-value
• Rounding incorrectly
• Misreading output order

4.

Identify the error in this code that tries to perform a Chi-squared test:

import numpy as np
from scipy.stats import chi2_contingency

observed = [[15, 25], [35, 25]]
chi2, p, dof, expected = chi2_contingency(observed)
print(p)

medium

A. Observed data must be a NumPy array, not a list

B. No error, code runs correctly

C. chi2_contingency requires 1D data, not 2D

D. Missing import for chi2_contingency

Solution

1. Step 1: Check data type requirements for chi2_contingency

   The function accepts array-like input, including lists of lists, so the observed data as a list of lists is valid.

2. Step 2: Verify imports and function usage

   The import is correct, and the function call matches the expected signature. The code will run and print the p-value.

3. Final Answer:

   No error, code runs correctly -> Option B

4. Quick Check:

   chi2_contingency accepts lists; code runs fine [OK]

Hint: chi2_contingency accepts lists or arrays for observed data [OK]

Common Mistakes:

• Thinking lists are invalid input
• Assuming 1D data only
• Forgetting to import function

5.

You have this observed frequency table for two groups and two outcomes:

observed = [[30, 10], [20, 40]]

You want to test if the groups differ in outcome distribution. Which step is NOT part of the Chi-squared test process using scipy.stats.chi2_contingency?

hard

A. Calculate expected frequencies assuming independence

B. Compute the Chi-squared statistic comparing observed and expected

C. Check if the p-value is less than your significance level

D. Normalize the observed data to sum to 1 before testing

Solution

1. Step 1: Understand the Chi-squared test steps

   The test calculates expected counts assuming independence, then computes the Chi-squared statistic and p-value, and finally compares p-value to significance level.

2. Step 2: Identify the incorrect step

   Normalizing observed data to sum to 1 is not part of the Chi-squared test. The test uses raw counts, not proportions.

3. Final Answer:

   Normalize the observed data to sum to 1 before testing -> Option D

4. Quick Check:

   Chi-squared uses counts, not normalized data [OK]

Hint: Chi-squared test uses counts, not proportions [OK]

Common Mistakes:

• Normalizing data before test
• Confusing proportions with counts
• Ignoring p-value significance check