Chi-squared test in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Chi-squared test on observed frequencies

What is the output of this code snippet performing a chi-squared test on observed frequencies?

SciPy

from scipy.stats import chi2_contingency

observed = [[10, 20, 30], [6,  9,  17]]
chi2, p, dof, expected = chi2_contingency(observed)
print(round(chi2, 2), round(p, 3), dof)

A 3.45 0.178 2

B 5.12 0.074 3

C 4.67 0.097 2

D 6.89 0.032 2

💡 Hint

Recall that degrees of freedom for a 2x3 table is (2-1)*(3-1).

The chi-squared test compares observed frequencies to expected frequencies. The degrees of freedom is (rows-1)*(columns-1) = 2. The test statistic and p-value are calculated by scipy.stats.chi2_contingency.

❓ data_output

intermediate

Expected frequencies from chi-squared test

Given the observed data, which option shows the correct expected frequencies matrix from the chi-squared test?

SciPy

from scipy.stats import chi2_contingency

observed = [[15, 25], [5,  15]]
_, _, _, expected = chi2_contingency(observed)
print(expected)

A

[[15. 25.]
 [ 5. 15.]]

B

[[14. 26.]
 [ 6. 14.]]

C

[[10. 30.]
 [10. 10.]]

D

[[12. 28.]
 [ 8. 12.]]

💡 Hint

Expected frequencies are calculated based on row and column totals.

The expected frequencies are computed by (row total * column total) / grand total for each cell. scipy.stats.chi2_contingency returns this matrix.

🧠 Conceptual

advanced

Interpreting p-value from chi-squared test

If a chi-squared test returns a p-value of 0.03, what does this mean about the null hypothesis at a 5% significance level?

A Reject the null hypothesis; there is evidence of association.

B Fail to reject the null hypothesis; no evidence of association.

C The test is inconclusive; p-value is too close to 0.05.

D Accept the null hypothesis; variables are independent.

💡 Hint

Compare p-value to significance level alpha = 0.05.

A p-value less than 0.05 means the observed data is unlikely under the null hypothesis, so we reject it and conclude there is an association.

🔧 Debug

advanced

Identify the error in chi-squared test code

What error will this code raise when run?

SciPy

from scipy.stats import chi2_contingency

observed = [10, 20, 30]
chi2, p, dof, expected = chi2_contingency(observed)

A TypeError: Expected 2D array, got 1D array instead

B ValueError: Input contains NaN

C IndexError: list index out of range

D No error, runs successfully

💡 Hint

Check the shape of the observed data passed to chi2_contingency.

chi2_contingency expects a 2D array (contingency table). Passing a 1D list causes a ValueError about input shape.

🚀 Application

expert

Choosing correct chi-squared test for data

You have a dataset with two categorical variables: 'Favorite Fruit' (Apple, Banana, Cherry) and 'Age Group' (Child, Adult). You want to test if fruit preference depends on age group. Which scipy function and input format should you use?

A Use scipy.stats.ttest_ind with raw data of ages and fruits.

B Use scipy.stats.chi2_contingency with a 2x3 contingency table of counts.

C Use scipy.stats.chisquare with a 1D array of fruit counts.

D Use scipy.stats.chi2_contingency with raw categorical data arrays.

💡 Hint

Chi-squared test for independence requires a contingency table.

The chi2_contingency function tests independence between two categorical variables using a contingency table of counts. Raw categorical arrays or 1D counts alone are not suitable inputs.

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