in its simplest form, birthdate bias theory says that when an athlete was born matters. that's date of birth, not time of birth.

to test whether this applies to my sport I collected data on around 4000 athletes from a dozen countries, and...

1. assigned them to birth categories based on the start of the scholastic year in their country
2. calculated number and percentage of athletes in each category who achieved, "success" in the sport (note: "there are several definitions of "success" which we do not need to go into)
3. this results in a table, an example of which I include here:

code / event / sum(s) / win(s) / sum(m) / win(m) / solo / multi
USA 400m 122 (44.4%) 153 (55.6%) 243 (41.9%) 337 (58.1%) 275 580
USA 800m 133 (48.2%) 143 (51.8%) 293 (48.8%) 307 (51.2%) 276 600
USA 1500m 139 (48.3%) 149 (51.7%) 343 (52.4%) 312 (47.6%) 288 655
USA 5000m 149 (51.2%) 142 (48.8%) 300 (46.4%) 346 (53.6%) 291 646
USA 10,000m 169 (52.0%) 156 (48.0%) 362 (53.0%) 321 (47.0%) 325 683
USA total 712 (48.9%) 743 (51.1%) 1541 (48.7%) 1623 (51.3%) 1455 3164

this table is of athletes reaching the final of the united states national championship
the top row shows, from left to right, in the 400m, 122 finalists were born in summer, 153 finalists were born in winter. the summer-born athletes made 243 appearances in finals, the winter-born athletes made 337 appearances in the finals. a total of 275 athletes appeared in the finals of the 400m, and they made 580 appearances in those finals.

my question is: how do I calculate whether any of these results are statistically significant ?

I have tried to study this topic online and the process seems to be:

1. guess what statistical significance would mean
2. collect your data and run the numbers
3. compare the data with your guess from step 1

this does not strike me as being particularly rigorous, but I am prepared to admit that some part of, "guess what statistical significance would mean," may have eluded me.

if anyone is able to offer advice on how to do this I would be very grateful.


thank you.