Question

You intend to conduct a test of homogeneity for a contingency table with 5 categories in the column variable and 2 categories in the row variable. You collect data from 72 subjects. What are the degrees of freedom for the χ 2 χ 2 distribution for this test?

Answer 1

we will conduct a test of homogeneity for a contingency table with 5 categories in the column variable and 2 categories in the row variable. You collect data from 72 subjects.

therefore the total number of column of contingency table are 5 (i.e. c=5) and total number of row of contingency table are 2 (i.e. r=2).

we know that the degrees of freedom for chi distribution test are, df=(c-1)(r-1)

in given case, the degrees of freedom are,

df=(c-1)(r-1) = (5-1) * (2-1) = 4*1 = 4

the degrees of freedom for the χ 2 χ 2 distribution for this test are 4.