Solutions to Chapter 2 (except for diagrams)

Section 1: Why experiment?

2.2. Yes, because a treatment was imposed on the subjects. The exercise is the explanatory variable, and change in metabolic rate is the response.

2.5. (a) The students are assigned to a reading program (the treatment) as part of the study. (b) Reading program (regular or computer) is the explanatory variable, change in reading score is the response. (c) Since it is an experiment, the results should be useful in making that decision (assuming that the experiment is otherwise well-designed - random assignment of students, etc.).


2.7. (a) The experimental units are batches
of the product; the response variable is the
yield of a batch. (b) There are 2 explanatory
variables (temperature and stirring rate) and
6 treatments (temperature-stirring rate combi-
nations). Diagram at right. (c) 12 batches - 2
at each of the 6 treatments.

2.10. It is not clear that the breastfeeding mothers' warm attitudes are caused by the fact that they nursed their babies. Their prior attitudes toward their babies which probably influenced their choice of feeding method - is the lurking variable; the effect of the prior attitude is confounded with the effect of the nursing.

2.13. The placebo effect strikes again. The tea-drinking residents' better health may simply have been because of the attention they got from the students.

2.21. Use a randomized comparative design with three groups and 200 volunteers in each group; the diagram is below. (Equal group sizes are convenient but not essential.) The response variable can be as simple as whether or not a subject gets flu during the winter. In Section 3, it will become clear that this experiment should be double-blind.


2.23. The answer will vary with the portions of Table A chosen. Students should specify these.

2.29. The experimental subjects were 3262 heart attack patients. Two treatments, TPA versus TPA plus angioplasty, were compared. Half the subjects got each treatment, but the article does not state that they were randomly assigned. The response variable was whether or not a subject had another heart attack in the six weeks following treatment. If we assume that random assignment was used (it certainly was, but the news article omits this important detail), the design is as shown below, and we can trust the result.

[In the language of Chapter 8, the result is "no significant difference." That is, there is no reason to think that angioplasty helps. Yes, we need to know something about the power of the test to draw that conclusion, but that's beyond us here.]

2.30. (a) There were three treatments: weight loss, exercise, and nothing (the control group). The response variables mentioned in this excerpt (there were others) are "good" cholesterol levels and blood pressure. (b) The experiment had a control group. The article also gives the number of subjects (replication). (To interpret the conclusions, we also need the information about the ages and weights of the subjects.) (c) No mention is made of randomization; it- simply says the men were divided into three groups. (d) Assuming that an equal number of subjects were assigned to each group, the outline would be similar to that shown below.

2.43. Label the rats in each strain separately 0, 1, . . . 9. Then reading line 111, rats 8, 1, 4, 6, 9 of strain 1 get diet A. It is best to separately randomize strain 2. Continuing in line 111, rats 4, 8, 7, 6, 0 of strain 2 get diet A. [This is a randomized block design, but the blocks are not complete - they do not each contain exactly as many units as there are treatments.]

2.45. Each subject will be presented with a glass of each cola and asked to choose which he/she prefers. It is essential that the colas not be identified to the subject. The cola tasted first should be assigned at random.