Chi-squared test in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Chi-squared test output interpretation

What is the output of this Python code performing a chi-squared test on a contingency table?

Data Analysis Python

import numpy as np
from scipy.stats import chi2_contingency

# Contingency table: rows = Gender (Male, Female), columns = Preference (A, B)
data = np.array([[30, 10], [20, 40]])
chi2, p, dof, expected = chi2_contingency(data)
print(round(p, 3))

A 0.001

B 0.15

C 0.05

D 0.5

💡 Hint

Look at the p-value returned by chi2_contingency and round it to three decimals.

The chi-squared test compares observed and expected counts. The p-value here is very small (0.001), indicating a significant association between gender and preference.

❓ data_output

intermediate

Expected frequencies from chi-squared test

Given this contingency table, what is the expected frequency for the cell in row 1, column 2 after running chi2_contingency?

Data Analysis Python

import numpy as np
from scipy.stats import chi2_contingency

data = np.array([[10, 20], [30, 40]])
chi2, p, dof, expected = chi2_contingency(data)
print(round(expected[0,1], 1))

A 20.0

B 18.0

C 25.0

D 30.0

💡 Hint

Expected frequency = (row total * column total) / grand total.

The expected frequency for cell (0,1) is calculated as (row 0 total * column 1 total) / grand total = (30 * 60) / 100 = 18.0.

🔧 Debug

advanced

Identify the error in chi-squared test code

What error does this code raise when trying to perform a chi-squared test?

Data Analysis Python

from scipy.stats import chi2_contingency

data = [[10, 20, 30], [5, 15]]
chi2, p, dof, expected = chi2_contingency(data)

A IndexError: list index out of range

B TypeError: unsupported operand type(s) for +: 'int' and 'list'

C ValueError: all rows in a contingency table must be of the same length

D NameError: name 'chi2_contingency' is not defined

💡 Hint

Check the shape of the input data for chi2_contingency.

The input data must be a rectangular array. Here, the second row has fewer elements, causing a ValueError.

🧠 Conceptual

advanced

Understanding degrees of freedom in chi-squared test

For a contingency table with 4 rows and 3 columns, what is the degrees of freedom used in the chi-squared test?

A 6

B 7

C 11

D 12

💡 Hint

Degrees of freedom = (number of rows - 1) * (number of columns - 1).

Degrees of freedom for chi-squared test on a contingency table is (4-1)*(3-1) = 3*2 = 6.

🚀 Application

expert

Chi-squared test on survey data

You have survey data on smoking status (Smoker, Non-Smoker) and lung disease (Yes, No). Which option shows the correct Python code to perform a chi-squared test and print the p-value?

A

import pandas as pd
from scipy.stats import chi2_contingency

survey = pd.DataFrame({'Smoking': ['Smoker', 'Smoker', 'Non-Smoker', 'Non-Smoker'], 'Disease': ['Yes', 'No', 'Yes', 'No'], 'Count': [30, 70, 10, 90]})
contingency = survey.pivot(index='Smoking', columns='Disease', values='Count')
chi2, p, dof, expected = chi2_contingency(contingency)
print(round(p, 4))

B

import pandas as pd
from scipy.stats import chi2_contingency

survey = pd.DataFrame({'Smoking': ['Smoker', 'Smoker', 'Non-Smoker', 'Non-Smoker'], 'Disease': ['Yes', 'No', 'Yes', 'No'], 'Count': [30, 70, 10, 90]})
contingency = survey.groupby(['Smoking', 'Disease']).sum()
chi2, p, dof, expected = chi2_contingency(contingency)
print(p)

C

import pandas as pd
from scipy.stats import chi2_contingency

survey = pd.DataFrame({'Smoking': ['Smoker', 'Smoker', 'Non-Smoker', 'Non-Smoker'], 'Disease': ['Yes', 'No', 'Yes', 'No'], 'Count': [30, 70, 10, 90]})
contingency = survey.pivot(index='Disease', columns='Smoking', values='Count')
chi2, p, dof, expected = chi2_contingency(contingency)
print(round(p, 4))

D

import pandas as pd
from scipy.stats import chi2_contingency

survey = pd.DataFrame({'Smoking': ['Smoker', 'Smoker', 'Non-Smoker', 'Non-Smoker'], 'Disease': ['Yes', 'No', 'Yes', 'No'], 'Count': [30, 70, 10, 90]})
contingency = survey.pivot_table(index='Smoking', columns='Disease', values='Count', aggfunc='sum')
chi2, p, dof, expected = chi2_contingency(contingency)
print(round(p, 4))

💡 Hint

Use pivot_table with aggfunc='sum' to create the contingency table correctly.

Option D correctly creates the contingency table summing counts by Smoking and Disease, then runs chi2_contingency and prints rounded p-value.

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