Question

1) In a two-way ANOVA, what are main effects?

2) In a two-way ANOVA, what are interaction effects?

Answer 1

1. In factorial experiments combinations of two or more levels of more than one factor are the treatments. For example with two factors (i) nitrogen fertilizer at three levels, denoted by n0, n1 and n2 and ii) irrigation at two levels, I0 and I1 in an agricultural experiment we can for the following six combinations taking one level from each factor I0n0, I0n1, I0n2, I1n0, I1n1 and I1n2. Such combinations form treatments in factorial experiments

The comparisons required in this type of experiments are not the pair comparisons as in varietal trials but a special type of comparison call main effects and interactions.

The contrast obtained from the difference of the totals of the first 3 and the last 3 of the above six combinations gives the main effect contrast for irrigation.

Similarly, two independent, comparisons among the totals, I0n0+I1n0, I0n1+I1n1 and I0n2 + I1n2 represent the main effect of nitrogen

2. We can get an effect of irrigation of presence of say n0 from I0n0-I1n0. Two more such effects can be obtained from the other two levels of nitrogen, namely, I0n1 - I1n1 and I0n2 - I1n2. Comparison among these three contrasts indicates the equality or otherwise of the effects of irrigation at the different levels of nitrogen. This sor of comparison, indicates if the factors act independently or they interact ot influence the yield of the experimental unit on which they appear simulationsly. Such contrasts are called interaction effect.