Question

In addition, answer the following question:

• In an experiment investigating the effect of sleep and eating breakfast on exam scores, researchers classified students into one of 3 sleep groups: less than 3 hours of sleep, 3-6 hours of sleep, and more than 6 hours of sleep, and 2 different breakfast groups: ate breakfast and didn’t eat breakfast. Below is a table of hypothetical data from that experiment. The dependent variable is the score on the exam.

	Hours of Sleep
	< 3 hours	3-6 hours	>6 hours
Breakfast Eaten?	M=65	M=70	M=75
	M=55	M=60	M=65

• What kind of ANOVA is this? Indicate the type (between, within, mixed design), and the numbers associated with the factors (e.g. 2x2).
• Did the results indicate that there is likely a significant main effect of breakfast? If so, explain the effect of eating breakfast on exam scores.
• Did the results indicate that there is likely a significant main effect of sleep? If so, explain the effect of the number of hours of sleep on exam scores.
• Did the results indicate that there is likely a significant interaction between breakfast and sleep? If so, explain the effect of eating breakfast and hours of sleep on exam scores.
• Graph the means in a table. Put Hours of Sleep on the X axis and Breakfast on separate lines.
• How would you interpret the interaction based on the graph? Does this match up with your answer from part iv.?

Answer 1

	< 3 hours	3-6 hours	>6 hours
Yes	65	70	75
No	55	60	65

This is ANOVA two-way

	< 3 hours	3-6 hours	>6 hours
Yes	65	70	75	70
No	55	60	65	60
	60	65	70	65

Did the results indicate that there is likely a significant main effect of breakfast? If so, explain the effect of eating breakfast on exam scores.

Yes, as marginal means are not same

Eating breakfast increases the mean

Did the results indicate that there is likely a significant main effect of sleep? If so, explain the effect of the number of hours of sleep on exam scores.

Yes, as marginal means are not same

as time increases, mean increases

Did the results indicate that there is likely a significant interaction between breakfast and sleep? If so, explain the effect of eating breakfast and hours of sleep on exam scores.

No, as lines are parallel