Question

A two-factor between-subjects design is evaluated. The F-value for Factor A has df = 1, 40 and the F-value for Factor B has df = 3, 40. Based on this information, what are the df values for the A x B interaction?

Answer 1

The df values for the A x B interaction are also 3,40

Explanation:

The F-value for Factor A has df = 1, 40

The F-value for Factor B has df = 3, 40.

The df values for the A x B interaction are also 3,40

This is because the source of variation between columns has ( c- 1); rc(n-1) degrees of freedom and the source of variation between rows has (r-1); rc(n-1) degrees of freedom and the source of variation of interaction

(between rows and columns) has ( c-1) ( r-1); rc(n-1) degrees of freedom.

Therefore

Factor A: ( c- 1); rc(n-1) = 1,40

Factor B: (r-1); rc(n-1) = 3,40

Interaction : ( c-1) ( r-1); rc(n-1) = 3*1,(40)= 3,40

where c refers to columns , r refers to rows and n refers to the total sample size.