Question

When examining a plot of means for a two-way ANOVA, what should you conclude if the two lines completely overlap and have zero slope?

please do not guess, if you do not know carry on. Please show work, thank you :)

Answer 1

There will be no interaction between two factor and no main effect of two factors.

Explanation:

Interaction effect: If the two lines are parallel, it means there is no interaction between two groups. Hence parallel line shows no interaction. This is also the case of overlapping of two line (because overlapping lines are the parallel lines)

Main effect: If the overlapping lines have slope zero, it means there is no main effect of either of the two factors. this point can be better understand by mathematical term. Let the two way ANOVA table is,

	A1	A2	Average
B1	0.1000	0.1000	0.1000	Difference = 0.001
B2	0.1010	0.1010	0.1010
Average	0.1005	0.1005	0.1005
	Difference = 0.000

(here i took slightly different value to visualize both the line in scatter plot)

The scatter plot for the data values is shown below,

The change in average values of factor A, there is no change in the average values of factor B (the difference in zero) which shows no main effect. Hence we can conclude that if the difference in average values is zero there is no main effect.