Question

For the following 2 x 2 ANOVA tables, decide whether or not there appears to be (a) a main effect for IV1, (b) a main effect for IV2, and/or (c) an interaction effect IV1-A IV1-B Row Mean IV2-A 5 10 7.5 IV2-B 15 20 17.5 Column Mean 10 15 Both IV1 and IV2 have main effects. There is also an interaction effect. Both IV1 and IV2 have main effects. There is no interaction effect. Neither IV1 nor IV2 have a main effect. There is an interaction effect. There are no main effects. There is also not an interaction effect

Answer 1

The question is incomplete. Still I am helping out as much I can.

First of all, ANOVA table can not be 2x2. It can be a 2-way ANOVA table.In that case the effects would be written as:

Theory: Let there be two factors A and B where A₁,A₂,.....,A_p are the levels of A and B₁,B₂,......,B_q are the levels of factor B. Thus we have pq level combinations (A_i,B_j);i=1,2,....,p; j=1,2,....,q.

And, y_ij is the observation of (i,j)th cell.