If You Score a 2300+, You Have a 99% Admit Chance at HYPM

Applying to College
61

<p>BassDad: I think you're right that technically, the admissions decision are statistically independent. The problem in the math is a bit more subtle than that, and it doesn't depend at all on the definition of statistical independence.</p>

<p>OP's calculation involves averaging out the chances at each school over a large pool of students, then using the result to calculate the chances of a student from that pool getting into at least one school. This doesn't work; see my other post. What you must do instead is calculate the chances of getting in somewhere for <em>each</em> student in the pool, and then average them over the whole pool.</p>

62

<p>
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I think you're right that technically, the admissions decision are statistically independent.

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<p>That's what I learned by asking statistics teachers about it: the decisions are NOT independent in the statistical sense of that term (as I mistakenly said early on), because they are correlated. (That is, colleges can agree in their admission decisions even if they do not collude.) Not perfectly correlated, to be sure, but strongly correlated. A flip of a fair coin has NO correlation to the next flip, but an admission decision by one college about a particular student is a reasonably strong predictor of another college's decision about the same student.</p>

63

<p>Token, if you flip the coin 10 times and get all heads, then this is a strong predictor that you may get tail next time. It is very similar to what you mentioned about useing one college's decision to predict another's.</p>

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<p>Actually, i'm taking a guess here, but doesn't the Central Limit Theorem says that the average will eventually come out to 50%, but just because you have 10 heads does not say anything about your next coin. You may even have 1000 heads and it doesn't say anything except you got really "lucky" in the non-mathamatical, intuitive way of thinking.</p>

<p>I say we all assign ourselves a bit of homework and ask our college statistics professors about SATs and admissions into the ivy leage =) hahaha.</p>

65

<p>"Token, if you flip the coin 10 times and get all heads, then this is a strong predictor that you may get tail next time. It is very similar to what you mentioned about useing one college's decision to predict another's."</p>

<p>No, it is 50% no matter what.</p>

66

<p>BassDad: i agree that independence does not require a normal distribution, but the reason i said a normal distribution is required is because in order to calculate probabilities for an individual, then you need a normal curve. this could be solved by sampling correctly because then the curve will automatically distribute itself about the mean. otherwise you end up with the average chance of a person with 2300/3.8/750 etc., and that information is really useless if you ask me. what does that establish? high scores and high gpa will get the average smart guy into the ivy league 99% of the time? how do you know if you are this average smart guy? this leaves the individual back to square one.</p>

67

<p>No, I was saying that the decisions are NOT independent. Statistical independence is what allows you to multiply together the individual probabilities to get the joint probability. However, in some situations, multiplying together the probabilities may not be terribly far off even when the events are not completely independent, or the OP may have poorly estimated the individual probabilities in such a way as to get something close to the right answer even though the method was wrong. It is hard to disprove what he is claiming without having real-world numbers to work with. While he has not provided a rigorous proof of his claims, nobody has provided conclusive evidence that his conclusion is more than, say, a factor of five off.</p>

<p>If you flip a fair coin and get heads ten times in a row, the probability of getting heads on the next flip is still 0.5. Those previous ten flips have no influence on the outcome unless the process is somehow rigged. If you flip a coin and get heads 1000 times in a row, I would suggest checking to see if the coin has heads on both sides.</p>

68

<p>From the other thread truazn started, someone argued that admissions wants "**real people **with real passions," not people who were academic superstars. </p>

<p>You know, I think the butchering of probability theory on this thread illustrates the value of doing extremely well in class. The point of doing well in class is to integrate the theory into your intuition, and to recognize when and where an equation or theory should be applied and what its limitations are. It is not about just spitting out something back on a test and being obsessive about memorizing a list of equations.</p>

<p>So, it's not that people with perfect stats and grads are not real people, it is that perhaps they would actually be able to use the things they learn in class years later.</p>

69

<p>As I see it, it boils down to chance. By chance I mean this... we don't know in what order our apps are being evaluated. So, if they have reviewed mostly girls that particular day and you happen to be a boy then you may have a better chance that day (provided the scores are quality scores and all applicants are pretty equal). We just never know when our apps are being evaluated.</p>

70

<p>
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if you flip the coin 10 times and get all heads, then this is a strong predictor that you may get tail next time.

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<p>I hope you don't really believe that statement as you have typed it out here. A belief system like that could really burn you in the stock market or at a casino.</p>

71

<p>Theslowclap,</p>

<p>can you formulate your post #66 mathematically? I don't understand what you are trying to get at from your statement above. </p>

<p>I will try to explain my point again: The OP has made a statement about the average smart guy not about any individual person. That is a limitation of a statistical approach - it works much better for predicting the outcome for a large group of people than it does for predicting the outcome for an individual. In effect, he is saying that your average smart guy has a 1% chance of rejection if he applies to these nine schools. People are disproving all sorts of things that he did not say and claiming that he is therefore wrong. It ain't necessarily so.</p>

<p>I do agree that the information is useless, but for different reasons. How many applicants with those stats apply to all nine of these schools? Someone that smart is looking for world-class programs in their major (or should be) and I doubt that there is a single major that is world-class at every one of those nine schools. I did a quick check and I think there are only ten to twelve majors that exist at every one of the nine. They are all great schools, but they all have relative strengths and weaknesses. I can understand that there might be a handful that are only looking at the prestige aspect, but I give most people who can score 2300 on their SAT a bit more credit than that.</p>

72

<p>"That's what I learned by asking statistics teachers about it: the decisions are NOT independent in the statistical sense of that term (as I mistakenly said early on), because they are correlated. (That is, colleges can agree in their admission decisions even if they do not collude.) Not perfectly correlated, to be sure, but strongly correlated. A flip of a fair coin has NO correlation to the next flip, but an admission decision by one college about a particular student is a reasonably strong predictor of another college's decision about the same student." </p>

<p>Take a biased coin. Therefore, its heads/tails probabilities are NOT 50/50, but say you do not know what they are. You flip the coin ten times. You get ten heads. Since you do not know the actual probabilities involved with this biased coin, the first ten flips all coming up heads are a reasonably strong predictor that the eleventh flip will come up heads. </p>

<p>However, it is quite obvious that the coin flips are independent. Clearly, P(heads on first try)*P(heads on second try) = P(heads on first and second tries).</p>

73

<p>
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Since you do not know the actual probabilities involved with this biased coin

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<p>Then how, pray tell, will you do any calculations with those unknown probabilities? </p>

<p>That's actually the general problem in this thread with calculating the probability of one individual's getting into some subset of colleges applied to. Since the applicant doesn't know his or her own probability of getting into any college, there is no way for the applicant to calculate how probable it is for that one applicant to get into at least one of the several colleges. </p>

<p>I would hope after this many posts that all readers of this thread can think of many ways in which flipping coins is NOT like applying to colleges. Nassim</a> Nicholas Taleb writes about the "ludic fallacy"--treating real-world decision-making as if it is perfectly modeled by games of chance--and I see that he identifies a genuine problem.</p>

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<p>I never said this scenario would allow for calculations.</p>

<p>However, it is quite clear that P(heads on first try)*P(heads on second try) = P(heads on first and second tries) is true. It is just that we do not know the probabilities involved. </p>

<p>In any case, you are missing the point. I have demonstrated that even if the outcomes of several events are strong predictors of the outcomes of other events, the results can nevertheless be independent. This directly contradicts what you appeared to be asserting with the statement I quoted- that if the outcomes of several events influence our predictions as to how likely certain outcomes of another event are, than the events cannot be independent. If my example if flawed, please explain why.</p>

<p>It is not my intention to demonstrate that real life and college admissions are perfectly modeled by mathematical models of chance such as flipping coins. The example I proposed above was merely to disprove your reasoning in the statement you made.</p>

75

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I have demonstrated that even if the outcomes of several events are strong predictors of the outcomes of other events, the results can nevertheless be independent.

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<p>No you haven't. If the events are strong predictors of the following events, the following events are NOT "independent" in the sense that allows the multiplicative rule. I think what I will deny here is that you have shown me an example in which the preceding events are predictors of the subsequent events. Then maybe you'll see your mistake in definitions. </p>

<p>After edit: Have you taken an AP statistics course or a college course using one of the "fab five" textbooks? Have you ever studied conditional probability or Bayesian</a> analysis?</p>

76

<p>I don't know why this is a big discussion. Its obviously not independent to anybody that knows anything about probability and the real world.</p>

<p>If student A gets admitted to Havard Yale And Princeton, the chances of him then getting admitted to Cornell with be virtually 100%! in the event that they were independent the LAW OF INDEPENDENCE would have to hold up and the probability of him getting in to cornell would remain about 40% or whatever.</p>

<p>But the OPs "conclusion" is almost correct because somebody with a 2300+ SAT, 4.0 GPA, and decent ECs, probably stands a 60% chance of getting into cornell and thus a 60% chance of getting into at least one ivy. The way he went about it and the theory behind it were just bogus.</p>

77

<p>"No you haven't. If the events are strong predictors of the following events, the following events are NOT "independent" in the sense that allows the multiplicative rule."</p>

<p>So you're essentially arguing that coin flips are not independent events? To clarify, are you arguing that P(heads on first try)*P(heads on second try) is not equal to P(heads on both first and second tries)?</p>

78

<p>Truanz, since I do not know anyone who applied to every single ivy plus MIT, it really is a moot point to argue this. I doubt that you know very many who have done this either. It would be interesting to get a group that fits your criteria do this and see the results. I have not seen anywhere near this accept % with kids with close to and some exceeding your parameters, but they are anecdotal, and though they applied to colleges with close numbers to those you gave, they are not exact. You would not need a large sampling for this as you assert 99%. I</p>

<p>Actually "A is for Admissions" pretty much says the same thing for Dartmouth admissions. The spoiler is the class rank, and when ECs and personal factors come into play. </p>

<p>The actual cases I know that are very close to your requirements caused a huge brougha about Asian discrimination. A family with two very bright daughters had them both declined at a bunch of schools with only their safety, and MIT accepting them. They really wanted to go to an ivy or other less tech school. They had near perfects SATs, took APs up the wazzoo and had all kinds of academic honors. They were state level string and piano musicians. Two things were drawbacks. Great grades, but not top 5 in rank, because of some college courses they took and "B"s in PE that counted for rank in that district; also not so generous weighting. The other big issue was that they were very quiet, hard to engage and had little experience being with people. They interviewed for all of their schools, and I doubt it went well since they are so withdrawn. They were actually very sweet and interesting once you got them out of the shell but that takes time. Also their parents kept them cloistered and they did not show well in terms of appearance. I think it was a mistake that they were denied as they would have so benefited from those schools as they are bright, creative adults today, now that they have the polish that they did not have in highschool, and should not have been a factor for college.</p>

<p>The third girl was also Asian and did get into Brown off the wait list after much pursuit by the gc at the school. She was again tops in academics, but because of ranking method did not make top handful, and was in the usual musical ECs, and was a quiet interviewer and definitely not a leader type. But, at college that did change. Again, just a late bloomer. From what I have read, this happens a lot in Asian populations, mainly with males.</p>

<p>The spoilers with the #s I have is that I do not have SAT2 numbers, and I do know that they count heavily in admissions to the ivies. I do know too many top kids who did not get into Duke even with great #s because their ECs, essays, recs were just average, and with their point system, that may not cut it. Also the class rank can cut kids at times. I can see why schools do away with that.</p>

79

<p>
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So you're essentially arguing that coin flips are not independent events?

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<p>I'm arguing you can't have it both ways: if the first flip predicts the next, they aren't independent. Or, if they ARE independent, you can't know anything about the second flip from observing the results of the first. </p>

<p>College admission decisions are NOT independent, in the statistical sense, because, as an AP statistics teacher taught me when I asked him about this, if you observe how several other admission committees act on an applicant's applications, you can gain information about how the next applications you observe will turn out. You MIGHT be surprised, but you will be less surprised than if you knew nothing about any of the decisions. Even when college admission committees don't collude, which is most of the time, they judge individual admission applications in strongly correlated manners.</p>

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<p>"I'm arguing you can't have it both ways: if the first flip predicts the next, they aren't independent. Or, if they ARE independent, you can't know anything about the second flip from observing the results of the first."</p>

<p>In my example, the first twenty flips makes you change YOUR OPINION as to the probabilities of the twenty-first flip- but it doesn't actually change the probabilities of the twenty-first flip.</p>

<p>Independence only applies to the true probabilities of events occurring- not your perception of them.
The probabilities in P(A and B) = P(A)*P(B) all reflect true probabilities of events occurring and not what you think they are, or what your predictions are.</p>

<p>I'll use the dice example. Say the odds of the coin coming up heads are x%- but you do not know this value of x. The first twenty flips of the biased coin may all come up heads- and this will make you think that the twenty-first flip will likely come up heads as well. However, what people predict and think is irrelevant- only the true odds of the coin landing heads matters. What you think x is is irrelevant. Only the actual value of x matters.</p>

<p>This is the same way in college admissions. Say Bob gets rejected from Cornell. You may change what you think the odds of Bob getting into Harvard are- but this does not actually change the odds in real life that Bob will get into Harvard.</p>

<p>Please don't tie my post into the OP's argument. I am only attempting to demonstrate that college admissions are independent, and nothing else.</p>