In: Statistics and Probability
In this study, researchers were interested in knowing if the amount of coffee (none, one cup, 4 cups) and the time coffee was ingested (am v. pm) affected student exam performance (exams were in the evening). This study took place over a 3-day period. Students were randomly assigned to either ingest coffee in the morning (AM) or the evening (PM). On day one, students were given no coffee; on day two, students were given one cup of coffee; and on day three, students were given four cups of coffee. Below are the data from this experiment. Exam scores could range from 0-100, higher scores indicate better exam performance.
| 
 Participant  | 
 Amount of Coffee  | 
 Time coffee was ingested  | 
 Exam Score  | 
| 
 1  | 
 None  | 
 AM  | 
 75  | 
| 
 One cup  | 
 AM  | 
 84  | 
|
| 
 4 cups  | 
 AM  | 
 70  | 
|
| 
 2  | 
 None  | 
 PM  | 
 70  | 
| 
 One cup  | 
 PM  | 
 84  | 
|
| 
 4 cups  | 
 PM  | 
 50  | 
|
| 
 3  | 
 None  | 
 AM  | 
 60  | 
| 
 One cup  | 
 AM  | 
 90  | 
|
| 
 4 cups  | 
 AM  | 
 78  | 
|
| 
 4  | 
 None  | 
 PM  | 
 70  | 
| 
 One cup  | 
 PM  | 
 80  | 
|
| 
 4 cups  | 
 PM  | 
 62  | 
|
| 
 5  | 
 None  | 
 AM  | 
 70  | 
| 
 One cup  | 
 AM  | 
 87  | 
|
| 
 4 cups  | 
 AM  | 
 69  | 
|
| 
 6  | 
 None  | 
 PM  | 
 62  | 
| 
 One cup  | 
 PM  | 
 79  | 
|
| 
 4 cups  | 
 PM  | 
 46  | 
|
| 
 7  | 
 None  | 
 AM  | 
 75  | 
| 
 One cup  | 
 AM  | 
 96  | 
|
| 
 4 cups  | 
 AM  | 
 81  | 
|
| 
 8  | 
 None  | 
 PM  | 
 68  | 
| 
 One cup  | 
 PM  | 
 92  | 
|
| 
 4 cups  | 
 PM  | 
 63  |