A two-way ANOVA for a two-factor factorial design has 4 levels of factor 1, 3 levels of factor 2, and 5 observations per cell.
-In testing the significance of interaction,the numerator and denominator degrees of freedom for the ANOVA F test are:
A)5,12
B)5,60
C)5,48
D)6,48
E)12,48

Question

Quizplus · Accepted Answer

The numerator degrees of freedom for the ANOVA F test of interaction is the product of the degrees of freedom of the two interacting factors, which in this case is 2x3=6. The denominator degrees of freedom is the product of the degrees of freedom of the error term, which is (n-1) for each cell, and the number of cells, which is 2x3x8=48. Thus, the correct choice is D, with numerator and denominator degrees of freedom of 6 and 48, respectively.

A Two-Way ANOVA for a Two-Factor Factorial Design Has 4