<p>And I think "vast majority" is an exaggeration in both cases. In any case, we know for sure what the vast majority of cross-admits do who are admitted to both Columbia and Harvard.</p>
<p>there was once a time when columbia and harvard where regarded as the top two schools in the country</p>
<p>Harvard's hegemony has been for about ~50 years. before then the ivies were pretty much an old boy's club/</p>
<p>the selectivity at columbia and harvard are identical. the same with princeton and yale and brown, and quite possibly some other ivies, MIT, stanford, some other great schools. the kids who make up the top 25%, qualifications-wise, of the applicant pools at these schools are very similar. in many (if not most) cases, they are the same applicants applying to more than one school. if you think that harvard's applicants are "from another eschelon of high school students" or that it's applicant pool is any more competitive than these other schools', you are sadly mistaken...the only real difference in the schools' entering classes is those who decide to matriculate, because it can be shown that harvard, yale and princeton win out most of the cross-admits with other schools, and harvard comes out at the top of the list most of the time, based on brand name alone.</p>
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[quote]
if you think that harvard's applicants are "from another eschelon of high school students" or that it's applicant pool is any more competitive than these other schools', you are sadly mistaken
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</p>
<p>How would you prove that point with detailed data? </p>
<p>By the way, the spelling is "echelon."</p>
<p>The question is, how would you prove the opposite? How could you POSSIBLY go about proving such a normative statement as "Harvard's applicant pool is more competetive that School X," especially when a large chunk of the applicant pool applied to the other schools as well? It's simply an arrogant, haughty, pompous thing to assume that Harvard, with it's illustrious name and hallowed traditions, is just SOO much better than other schools. It simply is not. It's a great school. You know what? There are at least 30 other schools who will educate you as well or better. Harvard does not have a secret Harvard potion that they feed you that makes you Superman. Just sitting in the room with a Nobel Prize winner (which probably won't happen anyway) does not make you a Nobel Prize winner. You could be in a one room school house in Topeka, if you're with a great teacher and you work hard, you will be educated as well or better than any Harvard grad.</p>
<p>By the way, the "s" key is right next to the "e" key, Mr. Deputy of the Spelling Police. Sorry my typo wrought displeasure from your super-literate eye.</p>
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The question is, how would you prove the opposite?
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<p>There have been studies before in which cohorts of high school students have been followed by researchers as they apply to and are admitted to (or not) to different colleges. If the data show that the most competitive applicants (the applicants with the highest admission test scores, highest grades, most challenging high school curricula, and most state and national extracurricular awards) apply more to one college than another, that would be an issue to consider, as well as base acceptance rate, in deciding which college "was the most selective this year." Post #15 includes a factual assertion, with which I disagree, that "Columbia College was the most selective this year!" I have said above that Columbia College is selective, undoubtedly, but I doubt very much that it is the MOST selective college in the United States, and I have called for evidence on that point. </p>
<p>Perhaps an example will make the issue clearer. If Podunk Community College started a more vigorous marketing campaign, and encouraged many more applications than it has received before, it might find that the number of applications submitted was far above its capacity to enroll students, and thus find, even taking into account less than 100 percent yield of admitted students who actually enroll, that it could not admit all applicants. If Podunk has a 10 percent yield, a new first-year class size of 1,000, and receives 200,000 applications, it might issue a press release, after it admits 10,000 applicants, saying "Podunk admission rate down to 5 percent, lower than any Ivy League college." But a thoughtful reader of that press release, even one who believes everything that Podunk reported, might still have genuine doubts that Podunk is more selective than Columbia, not to mention Harvard. Base acceptance rate is one interesting statistic about a college's annual admission cycle, but it is not the sole competent evidence about which college is most selective.</p>
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In any case, we know for sure what the vast majority of cross-admits do who are admitted to both Columbia and Harvard.
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<p>How do you know for sure? What is this vast majority? You appear to be citing but not understanding the Revealed Preferences article, a mistake made by several posters here in CC.</p>
<p>I take it you mean that saying that Harvard wins "tournaments" in the revealed preferences study sense as against Columbia is not the same as saying that a majority of students who are admitted to both Columbia and Harvard go to Harvard. I will grant that point, because of course some students are admitted to quite a few different colleges, and each prefers a particular college out of all the varied sizes of sets of colleges that admit each student. It's not clear, as I noted above, that there even is an absolute majority of Harvard applicants who are also applicants to Columbia--I wonder how someone could definitely answer that question for this year's class of high school seniors. For readers following along in this discussion, I will cite the revealed</a> preferences study, which would be an interesting study design to replicate with a current data set. </p>
<p>Returning to the issue brought up by another participant in this thread, what would be good, persuasive evidence that </p>
<p>a) Harvard is more selective than Columbia, </p>
<p>or that </p>
<p>b) Columbia is more selective than Harvard?</p>
<p>woah...THREE people got into Harvard from my high school... I just assumed it accepted more people than usual</p>
<p>Um... actually, comparing regular action programs between these particular schools is completely unrevealing, since they both have a substantial early program that admits (at a much higher rate) almost half of the matriculating class.</p>
<p><a href="tokenadult%20wrote:">quote</a> I take it you mean that saying that Harvard wins "tournaments" in the revealed preferences study sense as against Columbia is not the same as saying that a majority of students who are admitted to both Columbia and Harvard go to Harvard.
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<p>No, I meant that the study doesn't support conclusions about the results of dual-admit contests between specific universities. We don't really know from the article alone whether, in Harvard-Columbia admission battles (admitted to both, matriculated at one), Harvard wins 90 percent of the time, or 52 percent, or whether Columbia wins 60 percent.</p>
<br>
<blockquote> <p>How do you know for sure? What is this vast majority?<<</p> </blockquote>
<br>
<p>According to this 91% of applicants admitted to both Harvard and Columbia choose Harvard over Columbia. I'd say that qualifies as a "vast majority."</p>
<p>Thanks, coureur, that is the user-friendly presentation of the same calculations shown in a different format in table 3 of the revealed preferences study paper.</p>
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According to this 91% of applicants admitted to both Harvard and Columbia choose Harvard over Columbia.
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<p>That's incorrect. The NY Times chart is an extract from the Revealed Preferences article, not data from real applications. The New York Times did not clearly explain that these are the parameters from a computer model that does not purport to predict the result of cross-admit battles between any two specific schools, including Harvard and Columbia. As stated above, we don't know from the article alone whether Harvard even wins 50 percent of its tourneys with Columbia, much less 91 percent. We all probably believe that it's higher than 50 percent, but that belief precedes the article and is only vaguely supported by it.</p>
<p>Siserune, I don't think that is the correct interpretation of the study.</p>
<p>The revealed preference ranking is a survey based on preselected 3000+ high school students actual college matriculation data. It is a medium sized survey that attempts to rank colleges based on the assumption that if Student X choses college A out of the number of colleges he has been accepted to, College A wins a match against B,C,D,E... </p>
<p>Thus, to tabulate the cumulation of "matches", the researchers proposed a model (the computer model you are referring to) to come up with a ranking on based on total number of matches played out.</p>
<p>What it means: </p>
<p>The survey indicates that FROM the 3000+ high school students, 91 percent would choose Harvard over Columbia with a certain uncertainty - can't remember the number, its in the report.</p>
<p>HOWEVER, since the survey is only that of 3000+ students, it cannot be called totally representative. Therefore, the best statement one can make from the report is: According to 3000+ students, and not students from the whole nation, Harvard would win 91 percent of the cross admits.</p>
<p>Hence, it will not be unusual to find places in which the majority of people would choose Columbia over Harvard. Although the chances are admittedly slim considering the 3000+ higher schoolers were carefully chosen for geographic and racial representation.</p>
<p>You need to read the paper, including the technical parts, to understand what is going on.</p>
<p>91 percent is NOT the measured proportion in the survey. They did NOT have anywhere near 3000 students applying to or choosing between Harvard and Columbia; they had 3000 students applying to 100 colleges, of which a handful were admitted to both Harvard and Columbia and matriculated at one. For a variety of reasons, the paper does not leave us better equipped to guess what the proportion of that handful was that chose Harvard, than we were before the paper came out. The paper does not claim that the cross-admit probabilities are reliable or attempt to make them reliable; they are a mathematical artifact en route to producing the rankings. The confidence intervals in the paper are for the probability that Harvard has higher rank than Columbia, not probability of choosing one school over the other. It is possible in their system for Harvard to lose cross-admit battles to Columbia but end up ranked higher.</p>
<p>The study was based on 3200 high-achieving students at 500 different high schools across the country, so it's a reasonably representative group. The pool of students who apply to places like Harvard or Columbia may number in tens of thousands but not in millions, so the study looks at a good fraction of the relevant subject group. Assuming each student applies to 5-10 schools, which is a reasonable assumption, and since they applied to 100 colleges, and since Harvard and Columbia are very popular schools, it's safe to conclude that the group probably included 500-1000 applicants to Harvard and Columbia, and hundreds who applied to both. </p>
<p>I think that's an adequate sample size. </p>
<p>It's the best objective data available we have, far more objective than people on this board. Does anyone seriously believe siserune's claim that Harvard might be losing cross-admit battles to Columbia? That is so laughable. Even Columbia admissions officers wouldn't claim that.</p>
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it's safe to conclude that the group probably included 500-1000 applicants to Harvard and Columbia, and hundreds who applied to both.
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<p>As discussed in the preliminary report on the survey, about 8 percent applied to Columbia with 108 admitted. This is from 2700 students, with issues of missing data for the other 700 participants that may or may not have been resolved. So the exact number of Columbia admits is between 108 and 140.</p>
<p>Of those, the cross-admit battle with Harvard refers to people who were admitted to Harvard and Columbia and matriculated at Harvard. That is, people admitted to both who attend Yale, Princeton, MIT, Brown, NYU, Duke, etc are subtracted. The raw admit rate for Harvard was about half that of Columbia in this study, so let's say that 50-60 were admitted to both. One has to reduce this estimate, because of self-selection upward for the Harvard admits' application targets, and downward for Columbia's. As you can see from CC admission-results threads, nowhere near 50 percent of people accepted to Harvard are applicants to Columbia. Of those, one has to subtract the people who chose Princeton, MIT, etc over either school. One needs to also take account of strategic admissions by the universities (Columbia rejecting or waitlisting applicants likelier to go to HYP), as discussed in the article. This leaves a rather small number of direct data points on Harvard vs Columbia, and the "91 percent" figure in the study is not a direct reporting of that data. </p>
<p>If you read the paper, you will see that it is quite possible for all of those dual admits to go to Columbia but Harvard to still rank number one. Caltech ranked number two based on just 7 matriculations. </p>
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Does anyone seriously believe siserune's claim that Harvard might be losing cross-admit battles to Columbia? That is so laughable.
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<p>Please quote my exact claim instead of lying. My statement was that there is no basis from the Revealed Preferences article for saying that Harvard beats Columbia 91 or 73 or 21 percent of the time. 91 percent is NOT the result found from the handful of tournaments that Harvard or Columbia won against the other, it's a composite of many different calculations. The only reason we "know" that the real-life result of H versus C is probably above 50 percent is from data that existed before the study, such as the relative yield numbers (roughly 2-to-1 advantage for Harvard, so guess a victory rate of <em>at most</em> 66 percent using the method of the paper).</p>
<p>if nothing else, that study doesn't seem very reliable.</p>