[burger]

As a "mathlete" one would have hoped Mr. Urschel would have been aware of his sample size problem.
Comparing a sample of 64 with 3,420 poses a few problems for comparing proportions. In the football player sample a shift of 1 player across categories would lead to a 3% shift in differences across categories suggesting the statistical "significance" is not particularly meaningful. Further,there's no a-priori reason to believe the sample of football players would be representative of the full student body; as an obvious example,  women probably represent more than half of the student body, yet there are none on the football team. Point being that pulling out any relatively homogeneous group from the whole will yield differences.  You know what they say about statistics and lies...😉

There is absolutely nothing wrong with comparing a small population with a large population.  In fact, if I had to choose the more reliable of two comparisons, one between two small populations and one between a small population and a large population, I would go with the latter hands down.  More data are always better.

...except in one sense: when you have a large sample size (on the order of thousands or tens of thousands), probability values from the statistical tests used in the article need to be taken with a grain of salt because even small differences between groups are likely to appear to be enormously unlikely.  So, the 1 in 600 billion statistic is a joke because a much smaller difference between football players and the rest of the student body in STS majors would probably produce a probability on the order of 1 in millions because of the sample size.

It's obvious that STS majors are more common among football players than among non-football players.  But the probability values the article quotes are overstated.

[burger]

As a "mathlete" one would have hoped Mr. Urschel would have been aware of his sample size problem.
Comparing a sample of 64 with 3,420 poses a few problems for comparing proportions. In the football player sample a shift of 1 player across categories would lead to a 3% shift in differences across categories suggesting the statistical "significance" is not particularly meaningful. Further,there's no a-priori reason to believe the sample of football players would be representative of the full student body; as an obvious example,  women probably represent more than half of the student body, yet there are none on the football team. Point being that pulling out any relatively homogeneous group from the whole will yield differences.  You know what they say about statistics and lies...😉

There is absolutely nothing wrong with comparing a small population with a large population.  In fact, if I had to choose the more reliable of two comparisons, one between two small populations and one between a small population and a large population, I would go with the latter hands down.  More data are always better.

...except in one sense: when you have a large sample size (on the order of thousands or tens of thousands), probability values from the statistical tests used in the article need to be taken with a grain of salt because even small differences between groups are likely to appear to be enormously unlikely.  So, the 1 in 600 billion statistic is a joke because a much smaller difference between football players and the rest of the student body in STS majors would probably produce a probability on the order of 1 in millions because of the sample size.

It's obvious that STS majors are more common among football players than among non-football players.  But the probability values the article quotes are overstated.