In a two-factor ANOVA,where a is the number of factor A levels and b is the number of factor B levels,the number of degrees of freedom for the interaction term is
A)(a − 1)(b − 1)
B)ab − 1
C)(a − 1)+ (b − 1)
D)Unknown; need to know the number of replicates.

Question

Quizplus · Accepted Answer

The number of degrees of freedom for the interaction term in a two-factor ANOVA is equal to (a-1)(b-1). This is because there are (a x b) cells in the design, but only (a-1) main effects for factor A and (b-1) main effects for factor B, leaving (a-1)(b-1) degrees of freedom for the interaction term. The number of replicates is not necessary to determine the number of degrees of freedom for the interaction term.

In a Two-Factor ANOVA,where a Is the Number of Factor