Question

Describe the pattern in a line graph that indicates the presence of an interaction effect in a factorial design.

Answer 1

To detect an interaction effect of two or more than two factors from the graph we would have to look at the slope of the line of all factors. If the lines are parallel in the graph then there is no interaction whereas if two lines intersect or appear to intersect then it can be said that there is a chance of interaction between the factors.

Here, I found a line plot from a study of factorial design. Which is very relevant to visualize.

The graph is only to understand the interpretation of the interaction effect. In this plot, those lines which are not parallel that is either intersect or appear to intersect have significant interaction. Whereas lines which are parallel no matter how steep those are they are not significant. Here steepness tells that how significant is the individual factor.

Note: Plots can display non-parallel lines that represent random sample error rather than an actual effect. P-values and hypothesis tests help you sort out the real effects of the noise. So drawing a conclusion on looking at the graph only is not free from mistake.