Chapter 4: Designing Studies

Magnets and pain Refer to the chapter-opening Case Study (page 205). The researchers decided to analyze the patients’ final pain ratings. It also makes

sense to examine the difference between patients’ initial pain ratings and their final pain ratings in both groups. Here are the data:

(a) Construct a comparative dotplot of the data. Describe what you see.

(b) Calculate the mean (average) change in pain rating for each group. Find the difference in the average changes for the two groups (Active – Inactive).

(c) Describe how you could use index cards to randomly reassign the subjects to the treatment groups.

(d) Suppose we used your method in (c) to redo the random assignment 50 times. The Fathom dotplot displays the difference (Active – Inactive) for the average change in pain rating for each of these random assignments. What conclusion would you draw about the effect of magnets on pain relief? Explain.

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 as follows:

The response variable is the weight lost after 8 weeks of treatment. Previous studies have shown that the effects of a diet may vary based on a subject’s initial weight.

(a) Explain why a randomized block design would be better than a completely randomized design in this setting.

(b) Should researchers form blocks of size 4 based on subjects’ last names in alphabetical order or by how overweight the subjects are? Explain.

(c) Use technology or Table D to carry out the random assignment required by your design. Explain your method clearly.

Carbon dioxide and tree growth The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO2 into a 30-meter circle of the forest. We want to compare the growth in the base area of trees in treated and untreated areas to see if extra CO2 does in fact increase growth. We can afford to treat three circular areas.46

(a) Describe the design of a completely randomized experiment using 6 well-separated 30-meter circular areas in a pine forest. Sketch the circles and carry out the randomization your design calls for.

(b) Areas within the forest may differ in soil fertility. Describe a matched pairs design using three pairs of circles that will reduce the extra variation due to

different fertility. Sketch the circles and carry out the randomization your design calls for.

Students as customers A high school student the newspaper plans to survey local businesses about the importance of students as customers. From telephone book listings, the newspaper staff chooses $150$ businesses

at random. Of these, $73$ return the questionnaire mailed by the staff. Identify the population and the sample.

A sampling at the mall You have probably seen the mall interviewer, approaching people passing by with a clipboard in hand. Explain why even a large sample of mall shoppers would not provide a trustworthy estimate of the current unemployment rate.

A researcher studied a group of identical twins who had been separated and adopted at birth. In each case, one twin (Twin A) was adopted by a low-income family and the other (Twin B) by a high-income family. Both twins were given an IQ test as adults. Here are their scores:

$100$ IQ and twins (3.1) How well does one twin’s IQ predict the other’s? Give appropriate evidence to support your answer.

A researcher studied a group of identical twins who had been separated and adopted at birth. In each case, one twin (Twin A) was adopted by a low-income family and the other (Twin B) by a high-income family. Both twins were given an IQ test as adults. Here are their scores:

IQ and income (1.3) Do identical twins living in low-income homes tend to have lower IQs later in

life than their twins who live in high-income homes? Give appropriate evidence to support your answer.

Random sampling versus random assignment Explain the difference between the types of

inference that can be made as a result of random sampling and random assignment.

Foster care versus orphanages Do abandon children placed in foster homes do better than

similar children placed in an institution? The Bucharest Early Intervention Project found that

the answer is a clear “Yes.” The subjects were $136$ young children abandoned at birth and living in

orphanages in Bucharest, Romania. Half of the children, chosen at random, were placed in foster

homes. The other half remained in the orphanages.$55$ (Foster care was not easily available in Romania at the time and so was paid for by the study.) What conclusion can we draw from this study? Explain.

Frozen batteries Will storing batteries in a freezer make them last longer? To find out, a company that produces batteries takes a random sample of $100AA$ batteries from its warehouse. The company statistician randomly assigns $50$ batteries to be stored in the freezer and the other $50$ to be stored at room temperature for $3$ years. At the end of that time period, each battery’s charge is tested. Result: Batteries stored in the freezer had a higher average charge, and the difference between the groups was statistically significant. What conclusion can we draw from this study? Explain.