(12-05-2014, 10:51 PM)burger link Wrote:[quote author=cadet84 link=topic=11289.msg107612#msg107612 date=1417841772]
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...ð
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.
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Although I didn't run the numbers, I think the math is fundamentally solid, even if the interpretation was obviously not conveyed very well. What Mr. Urschel was giving us was a p-value, which represents the probability that the numbers are due to random variation (that is, the probability that the observed distribution was due to chance alone). If you started with the student body with declared majors at Stanford, and randomly selected 64 students, what is the probability that 17 (or more) of them are majoring in STS. Because STS is a relatively uncommon major (3% of students), such a discrepancy is exceedingly unlikely to be due just to chance, although it is conceivably possible that you just happened to pick a lot of STS majors. Whether it's 1 in 1000, 1 in a million, or 1 in a billion doesn't matter all that much, we can safely say that football players majors are significantly (in a statistical sense) different than the student body as a whole. You don't need to do the chi-squared test to see that, and Urschel's focus on this detracts from the broader picture.
Note, I don't think it is all that surprising. I bet if you looked at the distribution of majors among, for example, a capella singers, or Daily staffers, or RA's, it would probably significantly differ from the student body as a whole (though probably not showing an excess of STS majors).
There are two important things with regards to the discrepancy. First, are football students going into STS because it is not rigorous. Having considered the major, I can say that is probably not the case. I think a lot of football players go into it because the major is
flexible:
https://sts.stanford.edu/major-sts/core-requirements
The major has very few absolute class requirements; I think only the intro course is required. Beyond that, STS majors must complete 2 courses (out of choice of 8) in each of three "perspectives", complete a capstone course or thesis, and then 50 units from at least 12 classes in a concentration (for BA majors, 8 courses from the humanities and social sciences for BA majors, 4 from science and engineering; for BS, flip the two). But if you look through the courses, they are all real courses.
The second question is whether the major prepares them for life. Here's what the STS page has to say about what people do afterwords: "Graduates of STS have entered top-ranked Ph.D. and MBA programs and have forged successful careers in a variety of fields, including business, engineering, law, public service, medicine and academia. In a world where graduates are called on to have technical, analytical and collaborative skills, the STS major well prepares Stanford students for a wide range of career paths. For more detailed information on our alums, please visit our Alumni page."
BC