In a chi-square test of independence with 4 education levels and 3 opinion categories, what are the degrees of freedom?

In a chi-square test of independence with 4 education levels and 3 opinion categories, what are the degrees of freedom?

• A. (4-1)(3-1) = 6 degrees of freedom
• B. (4-1)(3-1) divided by 2
• C. (4-1)+(3-1) = 5 degrees of freedom
• D. (4-1)(3-1) + 1 degrees of freedom

Answer: (A)

This question tests how to determine the degrees of freedom in a chi-square test of independence. For a contingency table with r rows and c columns, the degrees of freedom are (r−1)(c−1). This reflects the number of independent cell counts you can estimate after accounting for the row and column totals. Here, there are 4 education levels (rows) and 3 opinion categories (columns), so df = (4−1)(3−1) = 3×2 = 6. The other options aren’t correct because they either modify the formula incorrectly (dividing by 2, or adding the terms, or adding 1), which doesn’t match how degrees of freedom are defined in this test.

This question tests how to determine the degrees of freedom in a chi-square test of independence. For a contingency table with r rows and c columns, the degrees of freedom are (r−1)(c−1). This reflects the number of independent cell counts you can estimate after accounting for the row and column totals.

Here, there are 4 education levels (rows) and 3 opinion categories (columns), so df = (4−1)(3−1) = 3×2 = 6. The other options aren’t correct because they either modify the formula incorrectly (dividing by 2, or adding the terms, or adding 1), which doesn’t match how degrees of freedom are defined in this test.