<p>Thought I’d revive this thread for a moment, for parents of students in the high school class of 2011. Over on the Harvard forum, there is a thread started by Handala92 who was admitted to Yale, Princeton, and Stanford, but not to Harvard. The thread is titled “Appealing a Harvard Rejection.”</p>
<p>To generalize from the results I’ve collected here (small database, self-selection bias, no guarantee of accuracy), I’d say that aside from a very, very small number of students, having qualifications that are truly Ivy-caliber gives a student roughly a 50/50 chance of admission to any particular one of HYPSM (C selects differently)–this might really be 70/30 or 30/70, but it’s far from a slam dunk, even for a student who is highly qualified, in a holistic sense.</p>
<p>Here’s the issue: Student-perceived fit is not necessarily the same as admissions-office-perceived fit. If a student has picked a particular college as the “dream-of-dreams” school, there’s probably no greater likelihood of admission there than at one of the other HYPSM–and collectively, the student is more likely to be admitted at one of the four that is a dream school, but not the student’s very top choice.</p>
<p>I don’t mean to criticize Handala92 (nor serendipityy, who had the same sort of issue). The immediate reaction to a declination is understandable.</p>
<p>Still, in my opinion, a lot of the difficulty students face at the end of March/beginning of April might be significantly reduced by understanding going in that the most realistic scenario for a highly qualified student is about 50/50 odds.</p>
<p>Also, this means that a student who actually is highly qualified, but declined by all of the schools, probably just had a succession of bad “bounces.” Most likely, there is nothing whatever wrong with the student, nor with the student’s application, including parts that parents cannot see (if your hs is like QMP’s).</p>
<p>Also, in the mode of Cato the Elder, who apparently used to end all of his speeches with
“Ceterum autem censeo, Carthaginem esse delendam,” often quoted as “Carthago delenda est”–whether or not he had been talking about Carthage in the body of his speech–I would like to close this comment with: Furthermore, I hope that marite will return.</p>
<p>I have a kid at Harvard and that is certainly a very wonderful thing but I really agree with blossom’s post. There’s just something troubling about this much concern about getting into super elite schools. With my younger one coming up, I honestly don’t care whether she ends up at an Ivy or a very good public. It just isn’t that hugely important, imo.</p>
<p>In general, I agree with you, sewhappy. I myself picked a large public university <em>on purpose,</em> with other choices available.</p>
<p>However, depending on your son or daughter’s high school environment, it’s hard to keep them from becoming at all interested in “top” schools, especially when they have unusually good stats and impressive accomplishments. At least, that is what I see around us.</p>
<p>Another factor at play is the perception of top students that they might have been admitted to public universities while putting out half or less of the effort they actually expended–by comparison with their classmates who are attending these schools. I think it is understandable for the students to expect that differences in effort might well be reflected in differences in outcomes.</p>
<p>Now, here’s the catch about that. I do think that differences in effort <em>are</em> reflected in differences in outcomes, even if the students wind up at exactly the same public schools. The extra effort yields better and deeper preparation for the opportunities at hand. So the outcome is not the same, even if the students are entering the same university.</p>
<p>I posted these data from the standpoint of trying to assist next year’s group with realistic expectations for their stellar sons and daughters.</p>
<p>Superb insight. Yes, that was what made my older one want so much to go to the elite school - simply because just by going there signaled he was a a very high level whereas attending our state schools does not.</p>
<p>Sigh. My last post talked tough but it really is impossible not to get pulled into the mania. I’m just determined to try to keep it sane for kid #2. With first one, we were sort of oblivious.</p>
<p>I agree with sewhappy’s last post, but I think that it’s not just the level, it’s the effort.
Spouse and I got into Princeton and MIT, respectively, without ever staying up working past 1 am in high school.
I couldn’t count the number of times QMP and friends were up past 1 am, working (suburban, public).
I suspect the situation is much the same at many intense high schools.</p>
<p>Thanks to QM for compiling the numbers. Some comments on the statistical analysis.</p>
<p><a href=“mazewanderer:”>quote</a></p>
<p>It will great to do some correlation analysis between the schools, i.e. if a person gets accepted at Harvard, what does it predict about acceptance at other schools etc.
[/quote]
</p>
<p>Unfortunately, even with the full data on all applicants, that can’t quite be done. Add to that the small size of the actual sample, and the between-school correlations are dominated by noise. There are also some biases from restricting to cross-admits, such as inflating the results of MIT-or-Caltech admits (students cross admitted to those schools and non-engineering schools will be relatively strong in humanities AND good enough in science to be admitted to one of the top two tech schools).</p>
<p>JHS’ analysis (#26, p.2) is insightful, and is a more meaningful sort of calculation to make than looking at correlation coefficients. It seems to indicate that multiple admissions arise at comparable rates from luck (students who are credible but typical applicants at several schools, and have rolled the dice enough times to get several YES outcomes) and from overqualification. That is, the populations of “expected” and “unexpected” cross-admits are of similar size.</p>
<p>Unlike correlation, something that can be quantified from the cross-admit data is relative difficulty of admission to the different schools (at least for cross-admits). You can do this by subtracting QuantMech’s Harvard-for-MITadmits effect from the same thing with Harvard and MIT reversed,and the same calculation for all other pairs of schools. It is better if you do this exercise without the waitlistees, but one can nevertheless directly perform this subtraction on QuantMech’s numbers as posted, to get an idea of the admissions difficulty ranking and whether it is linear.</p>
<p>mazewanderer asked about correlations between admissions at Harvard and other schools. […] of the students who were accepted by Harvard:</p>
<p>11 of 19 who applied to Yale were accepted […& similar 50+% figures for other schools…]
[/quote]
</p>
<p>There are problems with the correlation assertions, as I mentioned in the other thread. </p>
<p>More on that below, but first, a more specific breakdown of the numbers. I’ll do the exercise for Harvard and Yale, but a fuller analysis should consider more pairs of schools. </p>
<p>The results of the 53 applicants who applied to Harvard and Yale are as follows.</p>
<p>What stands out here is the high acceptance rates:</p>
<p>entire group – 22/53 accepted at Harvard (41%) = 22/53 (41%) accepted at Yale
of Yale admits – 12/22 (55%) accepted at Harvard, up from 10/31 (32%) for Yale non-admits
of Harvard admits – 12/22 (55%) accepted at Yale, up from 10/31 (32%) for Harvard non-admits</p>
<p>This suggests identical admissions difficulty at Harvard and Yale. The only difference seen in this table is in the handling of non-admits, with Harvard using the waitlist more often, and Yale the rejection letter, which is consistent with one having Early Admission and the other not, but could also occur for any number of reasons including the small sample size. </p>
<p>
</p>
<p>The rate of Harvard or Yale admission seen in this sample was 41%, not 5-10%. The rate at each school was higher and lower by factors of approximately 1.3, not ten, in the subset of students admitted (resp., rejected or waitlisted) by the other. That’s not an enormous effect, but it would be perfectly meaningful if a similar effect held for larger samples, as it probably does. The discussion that follows is NOT about the limitations of small samples or the difference between ratios of ten and 1.3, but the subtler question of what it means to say that there is “correlation” if Harvard admits (as a population) have elevated admission rates to Yale. </p>
<p>As covered with some precision in the other thread, a reasonable, and in some sense the only possible, model of an individual, ordinary applicant’s admission results (regular, Jan 1 cycle, no special athletic recruitment or other consideration that could correlate the results between schools) is the assignment of a set of admission probabilities for each outcome at each school: Prob[Joe accepted at Harvard], Prob[Joe waitlisted at Yale], Prob[Joe rejected at MIT], and so on. Joe’s probability of admission at Harvard and UC Berkeley may differ, and Jane’s probability at any school may differ from Joe’s. The different schools generate their own random outcomes independently — there is no correlation between events like “Joe admitted to Princeton” and “Joe waitlisted at Stanford”, and the probabilities of such events can be combined by multiplication. </p>
<p>Given this, in theory there could be “correlation” between probabilities for acceptance to different schools. For example, 100 percent correlation of Harvard and Yale probabilities would mean that each applicant’s chances are the same at H and Y (but a superstar might have 80 percent chance at both schools, an underqualified applicant a 0.1 percent chance at each – it varies from applicant to applicant). </p>
<p>The trouble is that these “correlations” are not something that can be measured from data. This is because each applicant only applies once to each school, per cycle, and we would need to re-run the process many times to pin down Prob[Joe in at Harvard] and P[Joe in at Yale] before seeing whether these numbers are the same. Each applicant is a source of more uncertainty than data. </p>
<p>More specifically, if you had the entire set of results for all joint applicants to Harvard and Yale, or the cross-admit results (the number admitted to H-only, Y-only, and H+Y), there is no specific concept of “correlation” between the individual applicants’ probabilities (such as the correlation coefficient, “r”, used in basic statistics) that can be calculated from the table or, equivalently, from the full set of H/Y admission results for all joint applicants.</p>
<p>siserune, at the beginning of the thread, I mentioned that I only included the cross-applicants who were at least waitlisted by one of the “top” schools, HYPSM+C. I did not include students who were rejected by all of the schools.</p>
<p>This might affect some of your remarks, concerning the high acceptance rates. You raise some other interesting points, which I will think about.</p>
<p>What other thread? Obviously, if you are going to accept as proved that the outcomes aren’t correlated, then you are going to decide that they aren’t correlated.</p>
<p>Adding more dual rejects to the table would strengthen the case for identical admissions difficulty, and would increase the odds ratio somewhat (the purported “change in odds of admission”, though again, there is no quantitative interpretation of this concept that corresponds to a statistical model that can be calculated from data). For there to be a large effect on the odds ratio, the number of H+Y rejects would have to be very substantial. The new 2x2 table, if there were X double rejects omitted from the list, would be</p>
<p>12 (a/a) 10 (H-a)
10 (Y-a) 21+X (not admitted to either H or Y)</p>
<p>This would imply a “change of odds” that is higher by 2*X percent than the one given in my posting. How big do you think X was, based on having gone through the RD results thread?</p>
<p>For the point about correlation, I should note that certainly some specific hypotheses about “correlation of probabilities” can be ruled out given enough data. The idea that Harvard probability is exactly 1.1 times lower than Yale probability can be tested by calculating the number of H admissions minus 1.1 times the number of Y admissions in a group of dual applicants and seeing whether it’s statistically different from zero. You can, I think, also test whether correlation of probabilities is zero. But any question where there is some unknown parameter that we try to find from the data, such as the “true” individual-level ratio of the H and Y admission rates, the (hypothetically nonzero) correlation coefficient between probabilities at H and Y, or a “change in odds” associated with admission to one of the schools, then this cannot be calculated no matter how large the sample. </p>
<p>The implication is that, whatever the philosophical framework for considering and discussing probabilities – frequentist, Bayesian, or something else – the concepts of “correlation of probabilities” and “change in odds” don’t have any quantifiable meaning. Which is to say that they are, at least in this context, meaningless probability-flavored jargon.</p>
<p>It is certainly meaningful to discuss (and compute) correlation between predicted admissions probabilities for individuals, in specific models of admission based on SAT score, GPA, zipcode, gender, race, or any other variables that are given for each individual. But this is a different concept altogether.</p>
<p>There was a long and somewhat entertaining dissection of a thoroughly wrong “FAQ” posted many times (but never recanted!) by tokenadult. The short version is that you have to define precisely what “correlated” means in order to avoid nonsensical statements. There’s a big difference between talking about correlation of Joe’s outcomes at Harvard and Yale ---- they are independent and in a clear quantifiable sense, uncorrelated — and the question of whether Joe’s H-admission probability is correlated to his Y-admission probability. The answer to the latter question, somewhat subtly, is that the latter “correlation” is a nebulous concept unless you start discussing specific models of admission, such as taking the presumed common causes leading to correlation (SAT scores, grades, etc) and using them to estimate chances.</p>
<p>“Data” source: I just went through a cross-applicant thread that had been posted, where people gave multiple results at HYPSM+C and other highly selective schools. I didn’t go through the individual RD threads. If someone wanted to do that, it would probably give an interesting set of results for the CC denizens. Also, it would probably be more representative than the cross-applicant thread.</p>
<p>Also, look for my upcoming paper, “The Implications of Hugh Everett’s Many-Worlds Interpretation of Quantum Mechanics for the Existence of Correlations in Admissions Probabilities at Highly Selective American Universities.” I plan to submit it to the Journal of Irreproducible Results.</p>
<p>Don’t want to revive the arguments from the thread about increasing admissions chances by applying to multiple Ivies–can’t really add to what I’ve said there. I think tokenadult’s remarks do have a sensible probabilistic interpretation, though siserune clearly doesn’t. I somewhat doubt that proponents of either viewpoint will change their minds any time soon.</p>
<p>It might just be a coincidence, but for some reason, my school is having an unprecedented amount of people turning down Harvard for Yale or Stanford. In past years, pretty much everybody who got into Harvard went no question, but this year I would say a majority of the students that got in are not going. I guess that’s a good thing, because it means people are increasingly choosing which school to attend based on the atmosphere rather than the name.</p>