the successful athletes are divided into two groups, those born in summer and those born in winter, where winter is defined as the first six months of the school year in their country.

the hypothesis is: the proportion of successful athletes born in winter will increase as race distance increases.

we have three variables: sum = number born in summer, win = number born in winter, T = total (sum + win)

since we have a different number of athletes at each race distance, the calculation I am doing is: (Abs(sum-win)/T)*100

so this is the difference between sum and win, as a percentage of their total.

my question is: is this an appropriate measure for testing this hypothesis. or would it be more appropriate to just use the absolute percentage of winter born athletes, or something else altogether.

thank you.