Na_Swatch wrote:Actually Haribo, the gap between 43% and 68% is significant enough that, factoring in the difference in class sizes, you still display a higher preference for H versus Y.
Basically, for simplification purposes, assume like you did that 200 Yale admits also got into Harvard and Stanford. (A generalization based on the 75% Yale yield. If you use the actual 75%, the math is more complicated but you get the same results.)
With class sizes being (slight rounding here):
200 Yale
200 Stanford
550 Harvard
This means that
Harvard, at 68% yield, admits = 810
Stanford, at 43% yield, admits = 465
810 - 200 Yale Admits - 550 Harvard Admits = 60 turn down Harvard (Excluding Yale Admits)
465 - 200 Yale Admits - 200 Stanford Admits = 65 turn down Stanford (Excluding Yale Admits)
Thus you have more people turning down Stanford than Harvard, even though the Harvard class is more than double that of Stanford. Again the difference is not as exaggerated as it appears, due to the fact that Stanford's smaller class size means that there are more people who are only accepted to Harvard out of HYS than people only accepted to Stanford out of HYS.
However, this definitely illustrates basic yield choice between a person facing Harvard or Stanford is not equal. If it was, then the ratio to fill a portion of the class would be same for the first 200 students at each school. This means that to fill the first 200 of Stanford (entire class) you would need to accept 265 students (excluding the Yale 200). Similarly to fill the first 200 Harvard students you would need to accept 265 students (excluding the Yale 200). At this point, that would mean the remaining yield on the last 300 Harvard students accepted would be over 100%, illustrating that a 1:1 choice selection ratio given both Harvard and Stanford as options is not the case.
Anyways, some confounding factors such as Yale is actually 75% and the effect of say schools like Columbia with scholarships will skew these results slightly and obviously the gap between H and Y is much, much narrower than the outward appearance of 68% vs 43% yield. Just wanted to show that mathematically, these numbers still indicate at least a slight preference for Harvard over Stanford.
Also, I am utterly bored waiting for my Megavideo 50 minute to be over so I can continue watching my movie which is why my analysis got so long.
Well, first of all I think both of our analysis are flawed by rounding. Since we'll never know exactly how many Yale students were dual-enrolled at Harvard and Stanford, neither can be perfect. However, your analysis shows some pretty heavy-duty rounding errors.
Anyway, I was bored as well so I decided to run the actual numbers based on LSN.
Stanford: 171 attending/398 admitted
Harvard: 558 attending/834 admitted
Yale: 189 attending/249 admitted
Calculations:
Stanford: 398-189-171 = 38 students chose to enroll elsewhere
Harvard: 834-189-558 = 87 students chose to enroll elsewhere
These numbers are quite different from your own
Of course, we should correct them for class size. Stanford now has a 78% yield rate, and Harvard is sitting at 84%. Harvard still has a slight edge, but I'd argue at 6% it's not worth writing home about.
Obviously, this is kind of a stupid, nit-picky little pet peeve of mine, but I don't get to play with numbers nearly enough anymore. Thanks for your reply, it was fun
