Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 2■ Example 1.3: Effectiveness of a diet pillThe weight-loss supplement ephedra was popular until its risky side effects became betterknown. Because of its side effects, ephedra was removed from sale in Canada and theU.S. Its effectiveness is also in question, although in combination with caffeine ephedrais widely thought to work well. The Muscletech company commissioned a number ofstudies in the year 2001 to see if its ephedra-based product, Hydroxycut, was effective forweight loss. One study found that Hydroxycut users lost 15 pounds of fat mass in 12weeks, while those taking a placebo (a sugar pill) lost 10.Even before asking whether the results are statistically significant, a skeptical observermight ask several questions about the trial. We know who funded the trial. Did this factaffect the outcome? Were the groups randomly assigned or chosen to favor the company?Were those in the placebo group aware that they were taking a placebo? Were theresearchers aware of who was in the placebo group? Is the difference in weight lostattributable to chance and not the ephedra pill? Is the ephedra pill safe to use?A randomized experiment is used to measure effectiveness. An idealized one wouldbegin with a group of subjects, or experimental units. These would be randomly allocatedinto possibly several treatment groups, one being the control group. A treatment isapplied to each subject, with those in the control group receiving a placebo. In theexample, there are just two groups—those who get a dosage of ephedra and those whoget a placebo. After the treatment, observations are made and recorded for furtheranalysis.The role of the randomization is to avoid bias, or a “stacking of the deck.” Sometimes,to cut down on variations, the subjects are matched in groups with commoncharacteristics, so that similar treatments would be expected to yield similar results. Toensure that subjects do not improve because they expect they should, a blind experimentmay be used. For this, a control group is given a treatment that appears to be the same butis really not. To further eliminate the chance of bias, a double-blind experiment is used.In a double-blind experiment, the researchers themselves are unaware of which treatmentgroup a subject is in. This sounds like a lot of work, but it is necessary to try to eliminatethe effects of other variables besides the treatment (confounding variables) that mayaffect the results. This is the only way a cause-and-effect relationship can be drawn.Assume for the moment that the industry-sponsored research on ephedra wasunbiased. Was the reported difference significant? Not according to a New York Timesarticle from June 2003:In an internal memorandum accompanying the study, a Muscletechofficial warned, “None of these results can be deemed significant,” addingthat “Hydroxycut can’t be claimed as superior” to the placebo. To getaround that, the official proposed that copy writers simply say, “Lose 15pounds of fat in 12 weeks with Hydroxycut and exercise!”How one chooses to compare or present results can have a dramatic effect on what isimplied.■ Example 1.4: The impact of legalized abortion on crime Does abortion cut downon crime? Steven Levitt, a University of Chicago economist, and John Donohue, aStanford University law professor, concluded in a paper in the May 2001 Quarterly