Interpreting Results from a Two-Factor Analysis with no Interaction Present

Let's consider a 3x4 independent groups design with n = 20. Suppose that we are interested in the impact of a drug on rats' performance on mazes of varying difficulty. The Maze factor can take on 3 levels (Easy, Moderate, Difficult) and the Drug factor can take on 4 levels (None, Low, Medium, High dosage). The dependent variable is the number of trials to error-free performance on the maze (so lower scores represent quicker learning). Below you will see the StatView analysis of the data.

Given the lack of a significant interaction, you would turn your attention to the main effects. In this case, we have a main effect of Drug and a main effect of Maze. Because both of those factors have more than two levels, we would need to conduct a Tukey's post hoc test to determine which specific means differed. The computations are seen below.

Given the four means for Drug (None = 12.35, Low = 11.983, Medium = 11.533, High = 10.350), we could then conclude that a High dosage of the Drug led to significantly faster learning than Medium, Low, or No Drug. No other differences were significant.

Given the three means for Maze (Easy = 5.15, Moderate = 9.613, Difficult = 19.9), we could then conclude that Easy Mazes are learnedsignificantly faster than Moderate Mazes and Moderate Mazes are learned significantly faster than Difficult Mazes. (By implication, though you could state it explicitly, Easy Mazes were leaned significantly faster than Difficult Mazes.)

Interpreting Results from a Two-Factor Analysis with an Interaction Present

Suppose that you ran the same experiment, but came up with the StatView results seen below.

Because the interaction is significant, you would focus your attention on interpreting the interaction. To that end, I would first look at a graph. StatView will line up the levels on an axis alphabetically, so I'll give you the graph produced by another program.

To my eyes, it appears that the levels of Drug had little or no effect on rats running the Easy maze. It does appear that there may be some small effect of higher levels of Drug on rats running the Moderate maze, leading to slightly fewer trials to correct performance on the maze for Medium and High levels of Drug compared to None and Low levels of Drug. However, it does appear that Drug has an impact on rats running the Difficult maze. It appears that as the dosage increased, performance on the Maze also improved. With that interpretation of the results in mind, I would now proceed to a post hoc analysis.

With the HSD value, I'd be able to conclude that: The effects of all levels of Drug were the same for the Easy maze. The effects of all levels of Drug were also the same for the Moderate maze. (Note that the little dip that my eyes saw was not significant, so the Easy and Moderate mazes were similarly affected by the levels of Drug.) However, No Drug (M = 21.3) didn't differ from Low Drug (M = 20.7) but produced significantly poorer performance than Medium Drug (M = 18.45) and High Drug (M = 16.35). Low Drug produced significantly poorer performance than High Drug. No other differences were statistically significant.

Thus, everything else being equal (level of side effects, etc.) it appears that rats can be led to better maze performance on Difficult Mazes by the introduction of Medium or High levels of Drug (compared to No Drug). However, administering any level of the Drug appears to have little to no effect on performance on Moderately Difficult Mazes nor on Easy Mazes.