Question

Two Way Analysis of Variance results:
Responses: Recall
Row factor: Vivid
Column factor: Length

ANOVA table

Source	DF	SS	MS	F-Stat	P-value
Vivid	1	0	0	0	1
Length	1	32	32	10.666667	0.0309
Interaction	1	8	8	2.6666667	0.1778
Error	4	12	3
Total	7	52

Means table

	1	2
1	5	3	4
2	7	1	4
	6	2	4

1. Is there a significant main effect? If yes, is it a main effect of vividness, length, or both?
2. Based on the means table, do the main effects results surprise you? Explain. In your explanation, clearly state the marginal means. (Helpful Hint: Vividness means are presented in the rows, and length means are presented in the column).
3. If there is a significant main effect, state which level of the factor had higher recall scores. (Helpful Hint: You will need to look at the means table).
4. Is there a significant interaction?
5. Based on the interaction plots, does the interaction result surprise you? Explain.
6. In thinking about statistical power, discuss a possible reason for why you received these interaction results? What could be done to improve your chances of finding significant results?
7. Based only on the interaction plots (not the F-statistic results), describe the results of the interaction.

Answer 1

a. Since the p-value corresponding to Length is less than the level of significance if considered 0.05, hence the main effect of Length if significant.

b. The mean effects of vividness levels are surprising because they are the same for both levels.

c. There is a significant main effect of Length and level 1 had a higher recall.

d. Since the p-value corresponding to interaction is greater than the level of significance if considered 0.05, hence there is no interaction effect.