A chi-square test for independence is used to evaluate the relationship between two variables.If both variables are classified into two categories,then what is the df value for the chi-square statistic?
A)df = 1
B)df = 2
C)df = 3
D)The value of df cannot be determined from the information provided.

Question

A chi-square test for independence is used to evaluate the relationship between two variables.If both variables are classified into two categories,then what is the df value for the chi-square statistic?​
A)​df = 1
B)​df = 2
C)​df = 3
D)​The value of df cannot be determined from the information provided.

Quizplus · Accepted Answer

When both variables are classified into two categories, there are four possible combinations of responses. However, the total number of responses is fixed and can be calculated by summing the number of observations in each category. Since knowing the frequency in three categories gives us enough information to determine the frequency in the fourth category, we end up with two degrees of freedom. Therefore, the df value for the chi-square statistic is 1.

A Chi-Square Test for Independence Is Used to Evaluate the Relationship