Final answer:
To detect an interaction in a factorial design graph, observe the lines representing each factor's levels. Lack of interaction is indicated by parallel lines, while interaction is suggested by lines that converge, diverge, or cross.
Step-by-step explanation:
To determine if there is an interaction on a factorial design graph, you should look for lines that are not parallel. In a factorial design graph, each factor of the experiment is represented by a different line. If these lines are parallel, it indicates that there is no interaction between these factors on the dependent variable being measured; however, if the lines converge, diverge, or cross, this is indicative of an interaction effect. Interaction implies that the effect of one factor on the outcome depends on the level of the other factor.
For example, consider a graph with two factors and their respective levels plotted on the x-axis and the response variable on the y-axis. If Factor A has levels A1 and A2, and Factor B has levels B1 and B2, we might have two lines: one for Factor A at level A1 combined with Factor B at levels B1 and B2, and the other line for Factor A at level A2 combined with Factor B at levels B1 and B2. The absence of interaction would be shown by two lines that are parallel to each other; the presence of interaction would be shown by the lines crossing or not being parallel.