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.