6.25 Comparing weight-loss treatments. Twenty overweight females have agreed to participate in a study of the effectiveness of four weight-loss treatments: A, B, C, and D. The researcher first calculates how overweight each subject is by comparing the subject’s actual weight with her “ideal” weight. The subjects and their excess weights in pounds are
| Alexander | 21 | Murray | 34 |
| Barrasso | 34 | Nelson | 28 |
| Bayh | 30 | Pryor | 30 |
| Collins | 25 | Reed | 30 |
| Dodd | 24 | Sanders | 27 |
| Franken | 25 | Schumer | 42 |
| Hatch | 33 | Specter | 33 |
| Kerry | 28 | Tester | 35 |
| Leahy | 32 | Webb | 29 |
| McCain | 39 | Wyden | 35 |
The response variable is the weight lost after eight weeks of treatment. Because a subject’s excess weight will influence the response, a block design is appropriate.
(a) Arrange the subjects in order of increasing excess weight. Form five blocks of four subjects each by grouping the four least overweight, then the next four, and so on.
(b) Use Table A (or statistical software) to randomly assign the four subjects in each block to the four weight-loss treatments. Be sure to explain exactly how you used the table.