A chi-square test for goodness of fit is used to examine the distribution of individuals across four categories,and a chi-square test for independence is used to examine the distribution of individuals across six categories in a 2 X 3 matrix of categories.Which test has the larger value for df?
A)The 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 four categories,and a chi-square test for independence is used to examine the distribution of individuals across six categories in a 2 X 3 matrix of categories.Which test has the larger value for df?​
A)​The 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 goodness of fit test is calculated as the number of categories minus 1. For four categories, df = 4 - 1 = 3. For a chi-square test for independence in a 2x3 matrix, df is calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (3 - 1) = 1 * 2 = 2. Therefore, the goodness of fit test has the larger df value.

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