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.