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In answering any given statistical question, there are many appropriate possible ways to collect and analyze the necessary data. However, not all study designs will be equally good, even if they are technically feasible. Students should be able to compare various proposed designs for studies to determine which among them would be the best choice.

Option (B) is the correct answer. Because runners are randomly assigned to wear either light or heavy shoes, this is an experiment. This randomization should result in two groups of size 10 that have runners of approximately the same skill levels; i.e., it is unlikely that all of the fast runners would be randomly assigned to one group and all of the slow runners would be randomly assigned to the other group. Therefore, we can treat these two groups as equal for purposes of making a comparison. (Note that the twenty runners do not need to be randomly selected; they could even be volunteers. Without a random sample we cannot make claims about the size of the effect of using lighter shoes in the population, but we can still make claims about whether lighter shoes cause one to run faster or not without describing how much faster.) The times of the runners in the light group and the heavy group are compared based on measurements from the same activity. This study design is appropriate for answering the question and is the best among the four choices.

Option (A) describes an observational study. A good aspect of this study is that it includes the same individuals wearing both lighter and heavier shoes, but there are still several key problems. Because the runners might choose when to switch from heavier shoes to lighter shoes, the effect of the lighter shoes may be obscured by the effects of other factors, e.g. training or overall health. (For example, it is possible that as a runner trains more and gets better they may be more willing to invest in more expensive equipment like lighter shoes. Any gains they make after switching to lighter shoes might just be due to their training and not to any effect of the shoes.) Furthermore, this answer only calls for looking at the records of the top runners who wear light shoes - it is possible that there are many runners who are faster that choose to wear heavy shoes. So, (A) is not correct.

Option (C) does not present an appropriate experimental design because the effect of shoe type (light vs. heavy) cannot be distinguished from the gender of the runner. (In this situation the variables are referred to as being aliased.) If, among the twenty runners, there were no statistical differences between the women’s times and the men’s times, then testing light vs. heavy shoes would be possible in this way. We do not have data to support this assumption, and thus any differences that were observed between the two groups could not be definitely attributed to the effect of the shoes. That the runners were selected randomly can be viewed as a positive aspect of this study, but it is not a necessary aspect (see Option (B)) and does not redeem the fatal flaw.

Option (D) presents an observational study. There are many possible confounding variables that may have an influence on both the runners’ times and their decision to wear light or heavy shoes. For example, the fastest runners may be offered sponsorships by a company that sells light shoes; these runners may wear the shoes as part of their marketing agreement even if they have no effect. The slower runners may know from deep familiarity with their sport that the lighter shoes truly have no effect and thus choose to not spend extra money on this piece of equipment for no added benefit. Therefore, (D) is not correct.