Why Chi-squared test in SciPy? - Purpose & Use Cases

The Big Idea

Discover how a simple test can reveal hidden patterns in your data without complex math!

The Scenario

Imagine you have a table of survey results showing how many people prefer different ice cream flavors across several cities. You want to know if the flavor preference is related to the city or just random chance.

The Problem

Trying to check this by hand means calculating expected counts, differences, and then summing up squared differences divided by expected counts for each cell. This is slow, confusing, and easy to make mistakes, especially with big tables.

The Solution

The Chi-squared test automates all these calculations. It quickly tells you if the differences you see are likely due to chance or if there is a real connection between categories.

Before vs After

✗ Before

expected = total_row * total_col / grand_total
chi_sq = sum((observed - expected)**2 / expected)

✓ After

from scipy.stats import chi2_contingency
chi2, p, dof, expected = chi2_contingency(observed_table)

What It Enables

It lets you confidently find relationships between categories in data without tedious math.

Real Life Example

Businesses use it to see if customer preferences differ by region, helping them tailor marketing strategies.

Key Takeaways

Manual calculations are slow and error-prone.

Chi-squared test automates and simplifies this process.

It helps find meaningful connections between categories.

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