Chi-squared test in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of the Chi-squared test?

The Chi-squared test checks if there is a significant difference between expected and observed data in categories. It helps us see if two things are related or independent.

beginner

What are the two main types of Chi-squared tests?

1. Chi-squared test for independence: checks if two categorical variables are related.
2. Chi-squared goodness-of-fit test: checks if observed data fits an expected distribution.

intermediate

In Python's scipy library, which function is used to perform a Chi-squared test for independence?

The function is scipy.stats.chi2_contingency(). It takes a contingency table (observed counts) and returns the test statistic, p-value, degrees of freedom, and expected frequencies.

beginner

What does a low p-value (e.g., less than 0.05) mean in a Chi-squared test?

A low p-value means the observed data is unlikely if the variables were independent. So, we reject the idea that they are independent and say there is a relationship.

beginner

What is a contingency table in the context of the Chi-squared test?

A contingency table is a grid that shows counts of observations for combinations of two categorical variables. It helps organize data to perform the Chi-squared test.

Which scipy function is used for the Chi-squared test of independence?

A scipy.stats.ttest_ind

B scipy.stats.chi2_contingency

C scipy.stats.f_oneway

D scipy.stats.pearsonr

The correct function for Chi-squared test of independence is scipy.stats.chi2_contingency.

What does the Chi-squared test compare?

A Observed and expected frequencies

B Means of two groups

C Correlation between two variables

D Variance of a dataset

The Chi-squared test compares observed counts with expected counts under a hypothesis.

If the p-value from a Chi-squared test is 0.03, what should you do at a 0.05 significance level?

A Reject the null hypothesis

B Fail to reject the null hypothesis

C Increase the sample size

D Ignore the result

A p-value less than 0.05 means reject the null hypothesis of independence.

Which data structure is needed to perform a Chi-squared test of independence?

A List of means

B Time series

C Scatter plot

D Contingency table

A contingency table with counts of categories is required for the test.

The Chi-squared test is best suited for which type of data?

A Time series data

B Continuous data

C Categorical data

D Text data

Chi-squared test analyzes categorical data frequencies.

Explain how to perform a Chi-squared test of independence using scipy with a simple example.

Think about a table showing counts of two categories and how to check if they relate.

Describe what a p-value tells you in the context of a Chi-squared test.

Focus on what the p-value means about the relationship between variables.

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