Question

What is the degree of freedom for a Chi-square test used in a \(3 \times 4\) contingency table?

• A. \(6\)
• B. \(8\)
• C. \(9\)
• D. \(12\)

Hint:

For a Chi-square test using a contingency table: \[ df = (r-1)(c-1) \] where \(r\) is the number of rows and \(c\) is the number of columns.

Answer 1

The Correct Option is A

Concept:
In a Chi-square test for independence using a contingency table, the degrees of freedom are calculated using the formula: \[ df = (r-1)(c-1) \] where:

• \(r\) = number of rows
• \(c\) = number of columns

Step 1: Identify the number of rows and columns.
Given contingency table: \[ 3 \times 4 \] Thus, \[ r = 3, \qquad c = 4 \]
Step 2: Apply the formula for degrees of freedom.
\[ df = (r-1)(c-1) \] \[ df = (3-1)(4-1) \] \[ df = (2)(3) \] \[ df = 6 \]
Step 3: State the conclusion.
\[ \therefore \text{The degree of freedom is } 6. \]