Question

In Vienna, Eliud Kipchoge became the first athlete to run a marathon in less than two hours. Kipchoge wore a special type of shoe developed by Nike called Vaporfly that is different than all previous running shoes. It has a much thicker midsole and has a layer of carbon fiber to bounce back as much energy as possible. Nike engineers claim that Vaporfly is significantly faster than any other shoe. Specifically, they claim that Vaporfly improves anybody’s running time by 4% compared to the company’s best running shoes.

A) Design an experiment to validate Nike's claims of 4% improvement.

B) Suppose you have running times for 1275 runners who completed the Boston Marathon in 2017 and 2018. Of the 1,275 runners who run Boston for both years 52 switched to Vaporflys in 2018. You have compared 2018 vs 2017 running times for all 1275 athletes and it is clear that most of those 52 runners who switched to Vaporflys have faster times in 2018 compared to 2017. On average the persons who switched to vaporflys improved their time by 5%. Do you conclude that wearing Vaporfly makes you run faster or do you need additional information to back Nike's assertion of 4% improvement? If you do need additional information state what additional calculations you need to do.

Answer 1

A) The claim made by Nike is that Vaporfly increases running time by 4%. To check if this claim is valid, a controlled experiment is needed.

A certain set of random individuals should be sampled. They should be divided into two groups, with each individual being assigned to one of the groups randomly. Both of these groups should be then made to run and their run time be evaluated. This should be then followed by providing both groups with a shoe. One of the groups should receive Vaporfly while the other group can receive any other shoe. However, the members should not be informed a priori if the shoe that they have received is Vaporfly. This is to ensure that the subjects are not biased. Then the run times should be measured for both the groups.

The first task would be to see the ratio of run time with and without Vaporfly. And then this ratio should be compared with the run time with and without the dummy shoe. If the difference is significant and the ratio for the Vaporfly group is indeed 4%, then the claim of Nike holds, otherwise it fails.

B) Here, the runners were analyzed with an year long interval. There is no evidence to say that the runners themselves haven't practiced hard throughout the year to improvise their speeds. Hence a controlled experiment like the one mentioned in A is required.