In a chi-square test of independence with five rows and two columns, what is the degrees of freedom?

In a chi-square test of independence with five rows and two columns, what is the degrees of freedom?

• A. (5-1)(2-1) = 4
• B. (5-1)+(2-1) = 5
• C. 4
• D. 10

Answer: (A)

The concept being tested is how to determine degrees of freedom for a chi-square test of independence in a contingency table. For a table with r rows and c columns, the degrees of freedom are calculated as (r−1) × (c−1). This reflects how many cell counts can vary independently once the row and column totals are fixed. With five rows and two columns, the degrees of freedom are (5−1) × (2−1) = 4 × 1 = 4. Intuitively, you can freely set the counts in four cells, and the remaining counts are determined by the row and column totals, leaving four independent pieces of information. Adding the row and column reductions would overcount the constraints, and using the total number of cells (which is 10) ignores the margins entirely, so it isn’t appropriate for calculating degrees of freedom.

The concept being tested is how to determine degrees of freedom for a chi-square test of independence in a contingency table. For a table with r rows and c columns, the degrees of freedom are calculated as (r−1) × (c−1). This reflects how many cell counts can vary independently once the row and column totals are fixed.

With five rows and two columns, the degrees of freedom are (5−1) × (2−1) = 4 × 1 = 4. Intuitively, you can freely set the counts in four cells, and the remaining counts are determined by the row and column totals, leaving four independent pieces of information.

Adding the row and column reductions would overcount the constraints, and using the total number of cells (which is 10) ignores the margins entirely, so it isn’t appropriate for calculating degrees of freedom.