sonyvaio18 wrote:Thanks for sharing that data!
Warning: useless hypothesizing below...
Can someone who's good at probability chime in on this: is there a formulaic way to calculate probability of getting into yale conditioned on if you've already gotten into stanford and harvard?
My lay person approach on this was that in a vacuum the closest comparison groups are the HS/no Y and HSY group. I say this because before hearing back from Yale at Time 2, both of these groups were HS at Time 1. To the admission gods at HS, they were seen as somewhat similar. So at time 2: 50/(50+71) got into yale, which is around ~41%. I'm probably making a bunch of faulty assumptions here.
If I want to be nicer to myself, I might argue that the 42 HY and 3 YS should also count because maybe if you're good enough to get into harvard/stanford, you can get into yale. so maybe at time 2: (50+42+3) / (50+71+42+3) = ~57%. So it comes out to a wash - the probability of a coin flip.
An aside: I wonder if another important variable is the Time of Response (time submitted/time accepted) variable. I wonder if those who have lower TOR at HS are more likely to hear back from Y.
OK, first I don't know much about how these admissions work. But I do know about probability, so that's the part I'll comment on here.
I think you wrote this in a convoluted way, but it sounds like you're asking: what's the probability that someone admitted to Stanford and Harvard also got into Yale. If that is what you are asking, you were on the right track the first time. 121 people got into both H and S in any form. Of that set, 50 got into HS + Y and 71 got into HS and not Y. Therefore 50 out of 121 people admitted to H and S also get into Yale, or about 41% as you say.
I don't understand what you're doing counting the HY and YS people because that is off topic to your question. They didn't get into H and S, therefore they tell you nothing directly useful about the odds of an HS getting a Y. Please explain if I misunderstand.
All this being said, there are some limitations to the analysis above. Two big ones I can think of are:
1. I'm ignoring timelines here. It may well be that most of the people who got into all three heard from Yale very quickly, so the fact that a candidate hasn't heard yet indicates their odds are much lower than the average figure suggests. (I don't believe this is the case, but it illustrates a theoretical assumption I am making).
2. This ignores where candidates actually applied. We have no evidence that these 71 were rejected
from Yale, maybe they never applied. So I'm assuming (almost certainly erroneously) that all these candidates applied to all three schools.
TL;DR I'd say the odds of someone accepted to H and S getting into Yale are about 41% based on the stats above, knowing nothing else about the candidates, assuming the stats are representative, and assuming that the folks who applied to H and S also applied to Y.