Chi-squared test in Data Analysis Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Chi-squared test used for?

The Chi-squared test checks if there is a relationship between two categorical variables by comparing observed data with expected data if there was no relationship.

beginner

What are the main inputs needed to perform a Chi-squared test?

You need a contingency table showing counts of observations for combinations of categories from two variables.

intermediate

What does a low p-value in a Chi-squared test indicate?

A low p-value means the observed data is unlikely if the variables were independent, so we may conclude there is an association between the variables.

beginner

What is the null hypothesis in a Chi-squared test?

The null hypothesis says there is no association between the two categorical variables; they are independent.

intermediate

How do you calculate the expected counts in a Chi-squared test?

Expected count for each cell = (row total × column total) ÷ grand total.

What type of data is required for a Chi-squared test?

A Categorical data

B Continuous data

C Time series data

D Text data

The Chi-squared test is designed for categorical data to test relationships between categories.

If the p-value from a Chi-squared test is 0.03, what does this mean at a 0.05 significance level?

A Reject the null hypothesis; variables are likely related

B Fail to reject the null hypothesis; variables are independent

C The test is invalid

D The variables are continuous

A p-value less than 0.05 means we reject the null hypothesis and conclude there is an association.

Which Python library is commonly used to perform a Chi-squared test?

A numpy

B matplotlib

C pandas

D scipy.stats

The scipy.stats library provides the chi2_contingency function for Chi-squared tests.

What does the Chi-squared statistic measure?

A Mean of the data

B Difference between observed and expected counts

C Correlation coefficient

D Variance of the data

The Chi-squared statistic sums the squared differences between observed and expected counts, scaled by expected counts.

What is a contingency table?

A A table of text strings

B A table of continuous values

C A table showing counts of observations for combinations of categories

D A table of dates and times

A contingency table organizes counts of observations by categories of two variables.

Explain the steps to perform a Chi-squared test using Python on a dataset with two categorical variables.

Think about how to prepare data and what the test output means.

Describe what it means if the Chi-squared test shows no significant association between two variables.

Focus on the meaning of independence in this context.

Practice

1. What does the Chi-squared test primarily check in data analysis?

easy

A. If two numerical variables have a linear relationship

B. If two categorical variables are related or independent

C. If a dataset follows a normal distribution

D. If the mean of a dataset is greater than zero

Solution

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

   The Chi-squared test is used to check relationships between categorical variables, not numerical data.

2. Step 2: Identify the correct relationship tested

   It tests if two categories are independent or related based on observed counts.

3. Final Answer:

   If two categorical variables are related or independent -> Option B

4. Quick Check:

   Chi-squared tests category relationships [OK]

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

Common Mistakes:

• Confusing Chi-squared with correlation tests
• Thinking it tests numerical data relationships
• Assuming it checks data distribution shape

2. Which Python library and function is commonly used to perform a Chi-squared test on a contingency table?

easy

A. scipy.stats.chi2_contingency

B. numpy.chisquare_test

C. pandas.chi_squared

D. matplotlib.chi2_test

Solution

1. Step 1: Recall common Python libraries for statistics

   Scipy is the standard library for statistical tests in Python.

2. Step 2: Identify the correct function for Chi-squared test

   The function to perform Chi-squared test on contingency tables is chi2_contingency in scipy.stats.

3. Final Answer:

   scipy.stats.chi2_contingency -> Option A

4. Quick Check:

   Use scipy.stats.chi2_contingency for Chi-squared [OK]

Hint: Remember: scipy.stats has chi2_contingency for Chi-squared [OK]

Common Mistakes:

• Using numpy or pandas which don't have this function
• Confusing function names or libraries
• Trying to use plotting libraries for tests

3. What will be the output of this Python code snippet?

import numpy as np
from scipy.stats import chi2_contingency

observed = np.array([[10, 20], [20, 40]])
chi2, p, dof, expected = chi2_contingency(observed, correction=False)
print('{:.3f}'.format(p))

medium

A. 1.000

B. 0.000

C. 0.500

D. 0.250

Solution

1. Step 1: Understand the observed data and test

   The observed table has proportional counts (10:20 and 20:40), suggesting independence.

2. Step 2: Interpret the p-value from chi2_contingency

   The p-value is approximately 0.5, indicating no significant relationship; the test finds data consistent with independence.

3. Final Answer:

   0.500 -> Option C

4. Quick Check:

   Proportional counts give moderate p-value around 0.5 [OK]

Hint: Proportional tables yield moderate p-values near 0.5 [OK]

Common Mistakes:

• Assuming low p-value means independence
• Confusing chi2 statistic with p-value
• Rounding errors changing p-value interpretation

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

import scipy.stats as stats
observed = [[15, 25], [35, 25]]
chi2, p = stats.chi2_contingency(observed)
print(p)

medium

A. Incorrect unpacking of chi2_contingency output

B. Missing import of numpy for array input

C. Observed data must be a pandas DataFrame

D. No error; code runs correctly

Solution

1. Step 1: Check the output of chi2_contingency

   The function returns four values: chi2, p, dof, expected.

2. Step 2: Verify unpacking matches returned values

   The code unpacks only two values, causing a ValueError due to mismatch.

3. Final Answer:

   Incorrect unpacking of chi2_contingency output -> Option A

4. Quick Check:

   chi2_contingency returns 4 values, unpack all [OK]

Hint: Unpack all 4 outputs from chi2_contingency [OK]

Common Mistakes:

• Unpacking fewer than 4 values
• Assuming input must be numpy array
• Thinking pandas DataFrame is required

5. You have a 3x3 contingency table of observed counts for three categories of two variables. After running chi2_contingency, you get a p-value of 0.03. What is the best interpretation if your significance level is 0.05?

hard

A. The variables are independent

B. You need a larger sample size to decide

C. The test is inconclusive; p-value is too high

D. There is a significant relationship between the variables

Solution

1. Step 1: Compare p-value with significance level

   The p-value 0.03 is less than 0.05, indicating statistical significance.

2. Step 2: Interpret significance in context of independence

   A significant result means we reject the null hypothesis of independence; variables are related.

3. Final Answer:

   There is a significant relationship between the variables -> Option D

4. Quick Check:

   p-value < 0.05 means reject independence [OK]

Hint: p-value < alpha means variables related, not independent [OK]

Common Mistakes:

• Thinking p-value < 0.05 means independence
• Ignoring significance level in decision
• Assuming inconclusive without checking p-value