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

Step 1: Understanding the Question
The question asks for the calculation of the degrees of freedom (df) for a Chi-square test of independence when applied to a contingency table with 3 rows and 4 columns.
Step 2: Key Formula or Approach
The formula for calculating the degrees of freedom for a Chi-square test on a contingency table is:
\[ df = (r-1)(c-1) \] where \(r\) is the number of rows and \(c\) is the number of columns in the table.
Step 3: Detailed Explanation
The dimensions of the contingency table are given as \(3 \times 4\).
This means:

Number of rows, \(r = 3\)

Number of columns, \(c = 4\)

Now, we substitute these values into the formula for degrees of freedom:
\[ df = (3 - 1) \times (4 - 1) \] \[ df = 2 \times 3 \] \[ df = 6 \] Step 4: Final Answer
The degree of freedom for the Chi-square test is 6.