Chi-squared test in SciPy - Mini Project: Build & Apply

Chi-squared Test for Independence

📖 Scenario: You work in a small shop and want to check if the type of product customers buy depends on their age group. You collected data on how many customers in each age group bought each product type.

🎯 Goal: You will create a table of observed counts, set up the test, run the chi-squared test for independence, and print the test results to see if product choice depends on age group.

📋 What You'll Learn

Create a 2D list called observed with exact counts for each age group and product type

Create a variable called alpha and set it to 0.05 for the significance level

Use scipy.stats.chi2_contingency on observed to get the test results

Print the chi-squared statistic, p-value, degrees of freedom, and expected frequencies

💡 Why This Matters

🌍 Real World

Chi-squared tests help businesses understand if two categories, like age group and product choice, are related or independent.

💼 Career

Data analysts and scientists use chi-squared tests to analyze survey data, customer behavior, and other categorical data to make informed decisions.

1

Create the observed data table

Create a 2D list called observed with these exact counts: [[30, 10, 20], [20, 20, 20], [10, 30, 10]]. Each inner list represents an age group and each number is the count of customers buying a product type.

SciPy

# Create the observed counts table
# Your code here

Hint

Use a list of lists to represent the table of counts.

2

Set the significance level

Create a variable called alpha and set it to 0.05 to represent the significance level for the test.

SciPy

observed = [[30, 10, 20], [20, 20, 20], [10, 30, 10]]
# Set the significance level alpha
# Your code here

Hint

The significance level is usually 0.05 for many tests.

3

Run the chi-squared test

Import chi2_contingency from scipy.stats. Use chi2_contingency on the observed table and save the results in variables chi2, p, dof, and expected.

SciPy

observed = [[30, 10, 20], [20, 20, 20], [10, 30, 10]]
alpha = 0.05
# Import chi2_contingency and run the test
# Your code here

Hint

Use from scipy.stats import chi2_contingency and then call it with observed.

4

Print the test results

Print the variables chi2, p, dof, and expected to see the chi-squared statistic, p-value, degrees of freedom, and expected frequencies.

SciPy

from scipy.stats import chi2_contingency

observed = [[30, 10, 20], [20, 20, 20], [10, 30, 10]]
alpha = 0.05

chi2, p, dof, expected = chi2_contingency(observed)
# Print the test results
# Your code here

Hint

Use four print statements, one for each variable.

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