# What should I do when found no interaction in two way ANOVA (2x2) but I have both significant main effects of factors!!

I ran a two way ANOVA to find effect of interaction between drug and food on size of plant. I found no significant interaction but both drug and food were significant, Now, should I switch to type II ss and just report F? or perform t-tests (as each factor has two levels)? please guide me on this

• The interaction test is the same for Type II and Type III sums of squares. Commented Feb 28, 2017 at 22:30

First, I don't think you need to "do anything" about not having found an interaction. You will report that as not significant. It means that the drug factor had the same effect no matter what the food factor.

I don't know why you would change the calculation of SS. For example, sometimes people fold non-significant interactions into the error term. But you've already shown that both main effects are significant so there is no point.

Your next step would normally be to conduct post hoc tests but with two groups in each factor, you don't need post hoc tests to tell you which means are different. If drug1 ad drug2 are the means for the drug factor, they differ. Similarly for the food factor.

• Thanks Alan, I got it. It was short but really useful.
– Non
Commented Feb 23, 2017 at 4:26
• One more thing! How should I plot my data? separately? or on one single plot?
– Non
Commented Feb 23, 2017 at 4:50
• You could plot a main effects plot and an interactions plot. The interactions plot would simply confirm the results which were already statistically determined. Commented Feb 23, 2017 at 8:50
• @Moh I think your plot(s) should support your argument/interpretation and because you didn't find an interaction I'd say that two independent plots would be most clear. But I'm sure you could be clear in the text whether you produced a single plot with both variables, or a plot with panels (a) and (b) (i.e., two plots in one) or two independent plots. If failing to find an interaction is important or surprising then I might be inclined to produce the interaction plot which Tavrock says will show the "practical significance" of the non-interaction. Commented Feb 23, 2017 at 14:47