# If there are 10 racers, and Racer A beats B by 0.001 seconds and B beats C by 0.002 seconds, how would you measure?

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?

• 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. – whuber Jul 7 '17 at 15:50