Do swimmers go faster in the finals?
1. Do swimmers go faster in the finals?
Now that you have had some practice quantifying swimming results, you will use data to investigate some concrete questions.2. Michael Phelps's personal bests
Anecdotally, it seems like swimmers swim faster in the finals. For example, all of the personal best times of the great American swimmer Michael Phelps occurred in the final round of a competition.3. Sarah Sjöström's personal bests
Similarly, as of summer 2017, the personal bests another great swimmer, Sarah Sjöström of Sweden, all occurred in a final, except for one semifinal.4. Your question
This raises the question, do swimmers swim faster in the finals than in other rounds? At face, this seems like a reasonable question, but we have to be more precise. Let's think about some issues we need to resolve to make our question clear. First, which swimmers are we talking about? For example, we could compare average swim time in the finals versus in the semifinals. But only the best swimmers swim in the finals, so on average, they will be faster. So, we should compare the performance of individual swimmers from round to round. Second, against what rounds will we compare? A problem is that elite swimmers sometimes do not give everything they have in the heats because the competition is weak and they want to have more energy for the finals. So, a better comparison is for individual swimmers between semifinals to finals. Finally, do we want to make this comparison for a given stroke, or for all strokes together? And for what distances? So, we see that posing the statistical question is a crucial, and sometimes difficult, first step in an analysis. Let's be more specific in our question, then.5. Your question
Do individual female swimmers swim faster in the finals compared to the semifinals? Implicit in this question is that we will include all events that have semifinals, which are the shorter distance events in each of the strokes.6. Diff'rent strokes
We are almost ready to do the analysis, but we have another issue to think about. As I mentioned before, each stroke is swum at a different pace, as we can see here by ECDFs of the swim times of the semifinals for the women's 200 m events. Furthermore, the improvement from semifinals to finals for each distance may vary as well, with larger gains possible at longer distances. So, we have to come up with a metric for improvement from semifinals to finals that is unaffected by these inherent differences in events.7. Fractional improvement
A reasonable metric is the *fractional improvement* from the semifinals to the finals. By normalizing the difference in time by the semifinal time, we mitigate the effects of different strokes and different distances.8. Your question(s)
So, we no longer ask the original yes or no question, but a quantitative one. "What is the fractional improvement of individual female swimmers from the semifinals to the finals?" You will answer this question in the exercises by computing the mean fractional improvement with a confidence interval. This is the heart of what we are after. The icing on the cake is the hypothesis test. "Is the observed fractional improvement commensurate with there being no difference in performance between the semifinals and finals?" This process of carefully posing a question to ask of your data is a key part of any analysis. My goal for you in this case studies course is to develop some of these question-posing skills, in addition to honing your technical skills with hacker stats.9. Let's practice!
Ok. Your tasks are clear. Now go answer these well-posed questions in the exercises!Create Your Free Account
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