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If 10 athletes run a race and the winner A beats B by one tenth of a second B beats C by two tenths of a second, C Beats D by three tenths of a second etc... How would you measure whether the winner A was significantly Faster than the other racers? Could you do it without assuming at what speed the race finished? What kind of statistical test would be suitable to determine significance of a sample size?

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    $\begingroup$ It is not evident that a statistical test would be needed. On that particular day in that particular race, runner $A$ was faster than $B$ was faster than $C$, etc. Isn't that the entire point of a race? If by "faster" you mean some generalization like "inherently faster during this race year" or something like that, then please note that one race is a sample of one performance for each racer. Although you can test a sample of one for significant differences, such tests are not very powerful--which means they are unlikely to give you useful information. $\endgroup$ – whuber Jul 7 '17 at 15:50
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It is necessary to know how the time differences are distributed and there has to be enough information to determine if an outlier is identifiable. For example, see How to identify outliers and do model diagnostics for an lme4 model?, which may give you some clues, as well as, What is the best way to identify outliers in multivariate data?

Obviously, this approach would be best to use on Boston Marathon data with many many participants with the alternative being to race the same, more limited number of participants multiple times to establish how each person performs within tighter limits than can be provided in a single experiment.

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