A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories,and a chi-square test for independence is used to examine the distribution of individuals in a 2 X 2 matrix of categories.Which test has the larger value for df?
A)The test for goodness of fit has the larger value.
B)The test for independence has the larger value.
C)Both tests have the same df value.
D)The df value depends on the sizes of the samples that are used.

Question

A chi-square test for goodness of fit is used to examine the distribution of individuals across three categories,and a chi-square test for independence is used to examine the distribution of individuals in a 2 X 2 matrix of categories.Which test has the larger value for df?​
A)​The test for goodness of fit has the larger value.
B)​The test for independence has the larger value.
C)​Both tests have the same df value.
D)​The df value depends on the sizes of the samples that are used.

Quizplus · Accepted Answer

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as the number of categories minus one. In this case, with three categories, df = 3 - 1 = 2. For a chi-square test for independence in a 2x2 matrix, df is calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1. Therefore, the test for goodness of fit has the larger value for df.

A Chi-Square Test for Goodness of Fit Is Used to Examine