Las metodologías activas en la enseñanza de la filosofía

when the car is started. Some manufacturers are now equipping cars sold in the United States with running lights. Will running lights reduce accidents by making cars more visible?

(a) Briefly discuss the design of an experiment to help answer this question. In

particular, what response variables will you examine?

(b) Example 6 discusses center brake lights. What cautions do you draw from

that example that apply to an experiment on the effects of running lights?

6.7 Red wine and a long and happy life. A New York Times article

reported that according to a study conducted by researchers at Harvard Medical School and the National Institute of Aging, a sub- stance in red wine could extend life. In the study mice fed a high-fat diet and a large daily dose of resveratrol, a substance found in the skin of grapes and in red wine, were found to live as long as mice on a healthy diet without resver- atrol. The article stated that the mice receiving resveratrol “had all the plea- sures of gluttony but paid none of the price.” The article also reported that the mice were fed doses of resveratrol that would require humans to drink 10 to 20 bottles of red wine a day to get a similar dose. Briefly discuss the ques- tions that arise in using this experiment to decide the benefits of resveratrol for humans.

6.8 Fatty acids and depression. A group of medical researchers studied the

effects of the intake of omega-6 fatty acids relative to omega-3 fatty acids on depression. They randomly assigned 88 highly stressed and depressed subjects to either a diet high in omega-6 fatty acids relative to omega-3 fatty acids or a diet with a much lower amount of omega-6 fatty acids relative to omega-3 fatty acids. They found that subjects generally showed increased symptons of depression on the high omega-6 diet compared with those on the low omega-6 diet. The researchers themselves cautioned against interpreting these exper- imental results as a general warning that diets rich in omega-6 fatty acids increase depression. Why?

6.9 Beating sunburn with broccoli. Some recent studies suggest that com-

pounds in broccoli may be helpful in combating the effects of overexposure to ultraviolet radiation. Based on these studies we hope to show that a cream con- sisting of a broccoli extract reduces sunburn pain. Sixty patients suffering from severe sunburn and needing pain relief are available. We will apply the cream to the sunburn of each patient and ask them an hour later, “About what percent of pain relief did you experience?”

(a) Why should we not simply apply the cream to all 60 patients and record the

responses?

(b) Outline the design of an experiment to compare the cream’s effectiveness

with that of an over-the-counter product for sunburn relief and of a placebo.

(c) Should patients be told which remedy they are receiving? How might this

Chapter 6 Exercises 117

(d) If patients are not told which treatment they are receiving, the experiment

is single-blind. Should this experiment be double-blind also? Explain.

6.10 Testing a natural remedy. The statistical controversy presented in this

chapter discusses issues surrounding the efficacy of natural remedies. The Na- tional Institutes of Health is at last sponsoring proper clinical trials of some natural remedies. In one study at Duke University, 330 patients with mild de- pression are enrolled in a trial to compare Saint-John’s-wort with a placebo and with Zoloft, a common prescription drug for depression. The Beck Depression Inventory is a common instrument that rates the severity of depression on a 0 to 3 scale.

(a) What would you use as the response variable to measure change in depres-

sion after treatment?

(b) Outline the design of a completely randomized clinical trial for this study. (c) What other precautions would you take in this trial?

6.11 The placebo effect. A survey of physicians found that some doctors give

a placebo to a patient who complains of pain for which the physician can find no cause. If the patient’s pain improves, these doctors conclude that it had no phys- ical basis. The medical school researchers who conducted the survey claimed that these doctors do not understand the placebo effect. Why?

6.12 The best painkiller for children. A Washington Post arti-

cle reported a study comparing the effectiveness of three common painkillers for children. Three hundred children, aged 6 to 17, were randomly assigned to three groups. Group A received a standard dose of ibupro- fen. Group B received a standard dose of acetaminophen. Group C received a standard dose of codeine. The youngsters rated their pain on a 100-point scale before and after taking the medicine.

(a) Outline the design of this experiment. You do not need to do the random-

ization that your design requires.

(b) You read that “the children and physicians were blinded” during the study.

What does this mean?

(c) You also read that there was a significantly greater decrease in pain rat-

ings for Group A than for Groups B and C, but there was no significant differ- ence in the decrease of pain ratings for Groups B and C. What does this mean? What does this finding lead you to conclude about the use of ibuprofen as a painkiller?

6.13 Comparing corn varieties. New varieties of corn with altered amino

acid content may have higher nutritional value than standard corn, which is low in the amino acid lysine. An experiment compares two new varieties, called opaque-2 and floury-2, with normal corn. The researchers mix corn-soybean meal diets using each type of corn at each of three protein levels: 12% protein, 16% protein, and 20% protein. They feed each diet to 10 one-day-old male chicks and record their weight gains after 21 days. The weight gain of the chicks is a measure of the nutritional value of their diet.

(b) How many explanatory variables are there? How many treatments? Use a

diagram like Figure 6.1 to describe the treatments. How many experimental individuals does the experiment require?

(c) Use a diagram to describe a completely randomized design for this experi-

ment. (Don’t actually do the randomization.)

6.14 Peanut brittle. A food scientist wishes to study the effect of the type of

pan and amount of sodium bicarbonate used in preparing peanut brittle on the flavor of the peanut brittle. In an experiment, peanut brittle is baked in four types of pans (iron, aluminum, stainless steel, and nonstick stainless steel) us- ing 0, 2, or 4 grams of sodium bicarbonate in the recipe. Ten batches of peanut brittle are prepared at each combination of pan type and amount of sodium bicarbonate. A panel of tasters scores each batch on the intensity of peanut, sweet, and buttery flavors.

(a) What are the explanatory variables and the response variables for this

experiment?

(b) Make a diagram like Figure 6.1 to describe the treatments. How many treat-

ments are there? How many batches of peanut brittle are needed?

(c) Explain why it is a bad idea to bake all 10 batches for one treatment at

once, then bake the 10 batches for the second treatment, and so on. Instead, the experimenters will bake the batches in a random order.

6.15 Comparing hand strength. Is the right hand generally stronger than

the left in right-handed people? You can crudely measure hand strength by placing a bathroom scale on a shelf with the end protruding, then squeezing the scale between the thumb below and the four fingers above. The reading of the scale shows the force exerted. Describe the design of a matched pairs experiment to compare the strength of the right and left hands, using 10 right- handed people as subjects. (You need not actually do the randomization.)

6.16 Does charting help investors? Some investors believe that charts of

past trends in the prices of securities can help predict future prices. Most economists disagree. In an experiment to examine the effects of using charts, business students trade (hypothetically) a foreign currency at computer screens. There are 20 student subjects available, named for convenience A, B, C, . . . , T. Their goal is to make as much money as possible, and the best performances are rewarded with small prizes. The student traders have the price history of the foreign currency in dollars in their computers. They may or may not also have software that highlights trends. Describe two designs for this experiment: a completely randomized design and a matched pairs design in which each stu- dent serves as his or her own control. In both cases, carry out the randomization required by the design.

6.17 Mozart and manual dexterity. A researcher is interested in the effect

of music on the performance of tasks requiring manual dexterity. She chooses playing Symphony no. 41 (the Jupiter Symphony) by Mozart as background music and playing no background music as treatments. The response variable is the time it takes to accurately cut out a complicated pattern on a piece of paper with scissors.

Chapter 6 Exercises 119

(a) Outline a completely randomized design to compare dexterity at the differ-

ent treatments. Twenty subjects are available.

(b) Because individuals differ greatly in dexterity, the wide variation in indi-

vidual scores may hide the systematic effect of presence or absence of music unless there are many subjects in each group. Describe in detail the design of a matched pairs experiment in which each subject serves as his or her own control.

6.18 Comparing cancer treatments. The progress of a type of cancer differs

in women and men. A clinical experiment to compare four therapies for this cancer therefore treats sex as a blocking variable.

(a) You have 500 male and 300 female patients who are willing to serve as

subjects. Use a diagram to outline a block design for this experiment. Figure 6.2 is a model.

(b) What are the advantages of a block design over a completely randomized

design using these 800 subjects? What are the advantages of a block design over a completely randomized design using 800 male subjects?

6.19 Comparing weight-loss treatments. Twenty overweight females have

agreed to participate in a study of the effectiveness of 4 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

Birnbaum 22 Hernandez 25 Moses 34 Smith 42

Brown 34 Jackson 33 Nevesky 28 Stall 33

Brunk 30 Kendall 28 Obrach 30 Tran 35

Cruz 25 Loren 32 Rodriguez 30 Wilansky 29

Deng 24 Mann 39 Santiago 27 Williams 35

The response variable is the weight lost after 8 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 5 blocks of

4 subjects each by grouping the 4 least overweight, then the next 4, and so on.

(b) Use Table A to randomly assign the 4 subjects in each block to the 4 weight-

loss treatments. Be sure to explain exactly how you used the table.

6.20 In the cornfield. An agronomist (a specialist in crop production and soil

chemistry) wants to compare the yield of 4 corn varieties. The field in which the experiment will be carried out increases in fertility from north to south. The agronomist therefore divides the field into 20 plots of equal size, arranged in 5 east-west rows of 4 plots each, and employs a block design with the rows of plots as the blocks.

(a) Draw a sketch of the field, divided into 20 plots. Label the rows Block 1 to

Block 5.

(b) Do the randomization required by the block design. That is, randomly as-

sign the 4 corn varieties A, B, C, and D to the 4 plots in each block. Mark on your sketch which variety is planted in each plot.

6.21 Speeding the mail? Is the number of days a letter takes to reach another