In the fixed effects model with interaction, assume that there are 3 levels of factor A, 2 levels of factor B, and 3 observations for each of the six combinations of levels of the two factors. Then the critical value for testing the null hypothesis of no interaction between the levels of the two factors at the .05 significance level is
A) 3.49
B) 3.89
C) 3.00
D) 3.55
E) 3.11

Question

Quizplus · Accepted Answer

The critical value for testing the null hypothesis of no interaction between the levels of the two factors in a fixed effects model can be found using an F-distribution table or calculator, given the degrees of freedom for the interaction and the significance level. Here, the degrees of freedom for the interaction term are calculated as (levels of A - 1) * (levels of B - 1) = (3-1) * (2-1) = 2. With 3 observations for each combination, the total number of observations is 3 * 6 = 18, leading to degrees of freedom for error as total observations minus the number of groups, which is 18 - 6 = 12. Looking up the critical value for F with (2, 12) degrees of freedom at the .05 significance level typically yields a value around 3.89.

In the Fixed Effects Model with Interaction, Assume That There