<p>This article contains a fairly deep/fundamental logical flaw, but is worth a read.</p>
<p>Aren’t you going to share the flaw with us? Seems there are a few oddities to me (not too many cc’ers would agree that there are 113 elite schools in the same category as Harvard and Stanford), but the general crux of the argument is correct. I’ve said it many times, there is no such thing as a 5-10% student. Most applicants are either below 1% or much higher than 10%.</p>
<p>Here the key excerpts from the article: </p>
<p>1) They don’t, however, represent the true odds of a well-qualified student’s being admitted to a top school.</p>
<p>2) top students have been sending out more applications.</p>
<p>3) But while the best students are sending out more applications for the same number of slots at elite colleges, the slots themselves aren’t becoming more scarce and the number of students competing with one another isn’t growing.</p>
<p>4)It’s the percentage of top students who are admitted to at least one top school. </p>
<p>5)Sure enough, 80 percent of top students were accepted to at least one elite school.</p>
<p>6) If you work hard and get good grades and test scores, there is very likely a place in the best schools for you.</p>
<p>The article can be summarized with a tautology: if you are a top student, you will get into an elite school. This is best seen in #3 where we are told that there is some sort of pigeonhole principle in the background: we have n-slots and n-students so the top n will map to the top n. The article also uses an equally weighted binomial assumption which doesn’t apply to this context…qualifications don’t create binomial sortings and colleges don’t use binomial decision points.</p>
<p>It IS a tautology of sorts; that is the point of the article, not a flaw, that people don’t see this obvious fact. I’m probably misunderstanding your point, sorry. I’ll just say that the qualifications of the admitted students at these schools has not increased as much as the falling admit rates might suggest at a glance. People greatly exaggerate the increase in difficulty of admission (over let’s say 10ish years ago) for a given student. I agree with this, generally, and I think that is the article’s main takeaway.</p>
<p>Now if you shrink that 113 down to 10, I think a good case can be made that entrance is considerably more difficult for a given student (the number of perfect ACT scores, just to pick one data point, has increased 10 fold) than it was years ago. I think that is the main flaw in the article. Most parents around these parts do not care very much at all about school #113.</p>
<p>I guess we’ll have to agree to disagree: when an article is titled as this one was, I expect insight, not a statistical tautology. Students want to know how to get into “that” school and this article won’t go very far to slake that thirst.
So, yes, your point is taken, that there is less here than meets the eye, but my take was that the author could have avoided what I note: “The article also uses an equally weighted binomial assumption which doesn’t apply to this context…qualifications don’t create binomial sortings and colleges don’t use binomial decision points.” In other words, using point #5, some kids may come away with a variant of the ecological fallacy that if they simply multiply the number of submissions they will correspondingly multiply the probability of admission, which is patently false. So the article really addresses the need of “top” students, but doesn’t waste much time on defining “top”, addressing the concerns of the 20% of the “top” students who don’t get in or addressing the needs of non-“top” students. So, other than those features, it is a great article.</p>