c08Exploration8

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Exploration 8.1 Recruiting Organ Donors 195 Exploration 8.1 Recruiting Organ Donors STEP 1: Ask a research question. In Example P.1 we considered a study that investigat- ed how to encourage people to be more likely to become organ donors. At the time, we did not formally analyze the data from the study. Now we are studying methods for comparing three groups, so we can further analyze the data and draw inferential conclusions from this study. STEP 2: Design a study and collect data. Recall that researchers asked volunteer sub- jects to imagine they moved to a new state, applied for a driver’s license, and needed to decide whether to become an organ donor. Researchers created three different versions of the survey, each with a different donor recruiting strategy. Subjects were randomly assigned to one of the three types of recruiting strategies: • The default option is to be an organ donor, and individuals have to opt out of organ dona- tion (opt-out group) • The default option is to not be an organ donor, and individuals have to opt in to organ donation (opt-in group) • There is no default option, and individuals have to choose whether they will be an organ donor (neutral group) 1. What are the observational units? What are the variables? Are the variables categorical or quantitative? If categorical, how many categories do they have? Also, identify the roles (explanatory or response) of the variables. Observational units: Explanatory variable: Type: Response variable: Type: 2. Did this study make use of random sampling, random assignment, both, or neither? Also describe the implication of your answer in terms of scope of conclusions that can potentially be drawn from this study. 3. Did this study pair subjects in one group with subjects in another group or are the subjects in the different recruiting groups independent of each other? 4. Let’s write out the hypotheses. a. Write the appropriate null and alternative hypotheses (in words) using the language of association between the explanatory and response variables. b. Express the null hypothesis in symbols. ( Hint: Remember that hypotheses are always about parameters, so define and use appropriate symbols for parameters.)
196 CHAPTER 8 Comparing More Than Two Proportions STEP 3: Explore the data. 5. Researchers found that 23 of 55 subjects in the opt-in group chose to be organ donors, 41 of 50 in the opt-out group chose to be organ donors, and 44 of 56 in the neutral group chose to be organ donors. a. Based on these counts, produce a two-way table of counts, putting the explanatory variable in columns. ( Hint: You have seen this table earlier in this chapter!) b. For each of the three groups, calculate the conditional proportion who agreed to become an organ donor. c. Produce a segmented bar graph (by hand or with the Multiple Proportions applet) to compare these conditional proportions across the three groups. d. Comment on what your calculations and graph reveal about whether the default option used in the question appears to affect how likely the person is to become an organ donor. STEP 4: Draw inferences beyond the data. We see some differences in the sample pro- portions of individuals who chose to be organ donors across the three treatments, but are these differences large enough to be statistically significant? In other words, do these data provide strong evidence of an association between donor recruiting strategy (opt-in, opt-out, neutral) and choosing to become an organ donor in the population? 6. Suggest two possible explanations for how these observed proportions could have turned out to be as different from each other as they are. ( Hint: Think about what our null and alternative hypotheses are.) Applying the 3S Strategy To investigate, we will see how we can apply the 3S strategy to these data. Because researchers are attempting to minimize (or at least control) the proba- bility of Type I errors, in cases with multiple groups they first do an overall test (see the Unit 3 introduction for more discussion on this). However, this requires computing a single statistic and considering the null distribution of that statistic. Let’s look at this approach now.
Exploration 8.1 Recruiting Organ Donors 197 1. Statistic 7. What statistic would you propose? a. Propose a formula for a statistic that could be used to measure how different the three sample proportions are. ( Hint: The key here is that the statistic needs to provide a single number that somehow focuses on differences between/among the observed sample proportions.) b. For the statistic you propose, would a large value or small value give evidence for the alternative hypothesis that at least one recruiting strategy has a different probability of someone agreeing to be a donor? When we compared two proportions in Chapter 5, we used the difference in two propor- tions as the statistic. In this chapter, though, there are multiple proportions. There are actually several reasonable ways of summarizing the differences among the groups in one number. Once you have settled on a statistic, you apply the 3S strategy as before—simulate the distri- bution of the statistic under the null hypothesis and then see where the observed value of the statistic falls in that distribution. 8. One possible statistic is p max p min . Review the conditional proportions you determined in #5(b) and calculate the observed value of this statistic for these data. Why might this be a less than satisfactory choice? However, this statistic ignores some of the groups. Another reasonable statistic to cal- culate is the mean of the absolute values of group differences for each pair of conditional proportions. (We could call this statistic Mean Group Diff for the mean of group differences.) 9. Let’s construct the Mean Group Diff statistic for these data by going through the following steps. a. Review the conditional proportions of organ donors you determined in #5(b) and calculate the group differences in these proportions for each pair: Opt-out minus opt-in: Opt-out minus neutral: b. Opt-in minus neutral: Calculate the mean of the absolute values of these group differences. So which statistic should you use? And how can you use the statistic to estimate a p-val- ue? We’ll consider those questions Section 8.2.
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