How are the degrees of freedom computed for each test listed below?(a) a chi-square goodness-of-fit test df = k − 1 df = N − 1 df = n − 1 df = (n1 − 1)(n2 − 1) df = (k1 − 1)(k2 − 1)(b) a chi-square test for independence df = k − 1 df = n − 1 df = N − 1 df = (k1 − 1)(k2 − 1) df = (n1 − 1)(n2 − 1)

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Solution to the problem

Let's define some notation:

N= Total number of individuals for a population

n = Total of individuals selected from a sample

n1= number of objects/individuals with characteristic 1

n2= number of objects/individuals with characteristic 2

k1= number of levels for the variable or factor 1

k2= number of levels for the variable or factor 2

Part a

For a chi square goodness of fit test the degrees of freedom are given by:

[tex]df= k-1[/tex]

Where k represent the total number of categories on the godness of fit test.

Part b

For a chi square test of independence the degrees of freedom are given by:

[tex]df= (k_1-1)(k_2-1)[/tex]

Where k1= number of levels for the variable or factor 1, k2= number of levels for the variable or factor 2 for the chi square test for independence.