<p>
[quote]
Here is a ranking of the Ivies based on the SAT scores of the top 1000 students in the freshman class. If you don't believe me, see a mathematician.</p>
<p>(1) Cornell
(2) Harvard
(3) Penn
(4) Yale
(5) Brown
(6) Columbia
(7) Princeton
(8) Dartmouth
[/quote]
</p>
<p>collegehelp,</p>
<p>where did you find data detailed enough for this list? I have not seen anything nearly precise enough to know the distribution of SAT scores at this precision for most of these colleges. Did you actually find numbers of students with each SAT score, or are you using medians and interquartile ranges, then interpolating based on an assumed distribution? If assumed distribution, did you assume linear, normal, or something else? Do you also have data for other numbers of students (top 500, top 250, bottom 1000, bottom 500, etc)?</p>
<p>By the way, ranking the Ivies is silly. No one school could possibly be best for all students. All this passion about ranking is misguided- when you are there getting an excellent education, why should you care what the admissions stats were?</p>
<p>afan-
My calculation was based on the assumption of a normal distribution, areas under the normal curve, the median and interquartile range. The calculation starts with the 25th and 75th percentile SAT scores. It is possible to determine the z-score of the 75th percentile, then go from there.</p>
<p>I've looked into the shape of the distribution of SAT scores and came away with the impression that most SAT score distributions approximate normality except for schools like Caltech and a few others which are near the ceiling and skewed left. But, the method produces a good estimate even for these schools as long as you are not working with the top 2-3%.</p>
<p>The closest we've had to a mathematician weighing in on this particular application of statistics is redbeard, who was/is getting his doctorate in Operations Research- which would be highly relevant expertise, as this field frequently involves use of statistics at high levels of mathematical sophistication.
His comments are in post #47 of that thread.</p>
<p>As for "ranking", that really depends on the criteria. I suggest each applicant formulate their own, based on their own interests & needs. Globalized "rankings" have limited applicability to any one individual. IMO. And restricting one's investigation to these particular schools that happen to play sports in the same league is rather artificially limiting. There are lots of other good schools to consider.</p>
<p>monydad-
How did you find that old post from redbeard? I had forgotten about it.
It would be great if some real statistician/mathematician could take a look at my method. I have had only a few undergrad courses in statistics.</p>
<p>I don't know of anybody else who has ever used my method. I invented it to satisfy my curiosity. But, I am sure I am not the first person to think of it.</p>
<p>One of the differences between the current problem and the one addressed by redbeard is that, in the current problem, I am trying to estimate the SAT score of the 1000th freshman. In the other problem, I was trying to estimate the number of students with SATs over 1500, which is in the very high end of the SAT distribution where the ceiling effect (1600 max) would distort the distribution most. In the current problem, the 1000th student is below the median for every Ivy except Cornell and Penn which places the 1000th student far from the truncated, most distorted end of the distribution.</p>
<p>I think this is an interesting exercise and that the method is approximately correct. Although I can't be sure of the precision of the estimates, I am confident that the basic conclusion is correct: Cornell's top 1000 students are better than the top 1000 at any other Ivy.</p>
<p>Here are my actual estimates of the SAT scores of the 1000th freshmen.
Cornell 1488
Harvard 1443
Penn 1435
Yale 1366
Brown 1355
Columbia 1306
Princeton 1291
Dartmouth 1162</p>
<p>To repeat, it would be great if somebody could check this out. I am not trying to spread misinformation. I think this is simply a surprising implication of the way SAT percentiles and class size are related.</p>
<p>At Cornell, 69% of the SAT scores fall below the 1000th freshman. At Dartmouth, only 7% fall below the 1000th freshman.</p>
<p>?? Someone close enough to a mathematician has already looked at your method, and posted as such. Redbeard already looked, I have posted the link.</p>
<p>As redbeard indicated, you have only summary statistics, little or no data actually detailing the real patterns of the underlying distributions. He speculated that, were data avaialble, one might find that the distributions are not all the same, and not all normal. The implication is that, in this event, your predictions would have dubious accuracy.</p>
<p>The basis for your assumption of a normal distribution that is applicable for each college is satisfying to you, so you have posted.</p>
<p>Others can read the prior thread and form their own conclusions.</p>
<p>Quite possibly your methodology may be fine if a normal distribution actually fits the relevant data.</p>
<p>IF the relevant data is not well described by a normal distribution, then all bets are off, depending on the extent to which it deviates.</p>
<p>The relevant distributions are NOT the underlying population of people in general, which I would agree can probably be described with a normal distribution. Normal distributions are often applicable to random samples of processes occurring in nature. The individual college distributions are culled from the underlying population of people in general, in a process that is far from random, but is itself correlated with SAT scores.</p>
<p>This is ridiculous. The 1000th freshman at Dartmouth is among the lowest 10% in the class, the 1000th freshman at Cornell is in the TOP 25-30% of his/her class!!!</p>
<p>All this list tells you is that Cornell is huge.</p>
<p>footballyus-
I am not trying to pursuade anybody to attend a particular school. I'm simply intrigued by these statistics. I think it is a really interesting problem.</p>
<p>slipper-
The Cornell freshman class is three times the size of Dartmouth's class. If you divide the Cornell class into thirds, then only 40% of the Dartmouth class would fal into the top third of the Cornell class. Most of the Dartmouth class is in the middle third of the Cornell class. In other words, if Cornell shrunk its freshman class to same size as Dartmouth's (1100 approx) by keeping the best students, the resulting Cornell class would be much better than Dartmouth's. It just helps put things in perspective. I am not trying to disparage Dartmouth.</p>
<p>monydad-
I actually have looked at the raw data for one large school (thanks to a relative who is employed there). The SAT distribution at that school was not normal. The shape of the distribution deviated significantly from normal. A normal distribution is symmetrical (skewness=0) and has a certain "form" (kurtosis=0...kurtosis is like peakedness). The distribution at this large school had skewness=-.47 and kurtosis=1.19.</p>
<p>The interesting thing is that when I applied my method I was able to nevertheless estimate the SAT score of the 1000th student within 5 SAT points. So this method can work accurately even when the distribution deviates somewhat from normal. The problem is this school is not an Ivy-caliber school and probably did not have a pronounced ceiling effect.</p>
<p>collegehelp: so what you're saying is, Cornell has a larger student body, but it has a subset of very strong students, yes? (I think that's the same case with Berkeley and many other colleges.)</p>
<p>Collegehelp, Cornell's colleges of Agriculture, Human Ecology, Architecture, ILR and Hotel Management don't count when comparing it to other Ivies because other Ivies only have colleges of Arts and Sciences and Engineering. That's not to say they aren't excellent programs mind you. Cornell's colleges of Architecture, ILR, Hotel Administration, and Agriculture are generally considered #1 in the nation by a wide maring. But including students in those colleges when comparing Cornell to a school that does not have those colleges is pointless since each colleges attracts and accepts students of a different sort. </p>
<p>So to compare apples to apples, if you want to compare Cornell to say Dartmouth, you should look at the SAT range of the students in the colleges of A&S and Engineering. Those two colleges at Cornell enroll roughly 7,000 undergrads and the SAT scores of students in those two colleges is quite high (mean of roughly 1440).</p>
<p>kyledavid-
Yes, that is what I am saying. And, what's more, I am saying that the number of very strong students in this subset at Cornell is as large or larger than the entire freshman classes at many schools who claim higher selectivity. And, yes, it is the same at many large schools like Berkeley, Michigan, UVA, and so on. Their freshman classes probably contain one or more Harvard freshman classes. It would be interesting to expand my method to the top 100 universities to see how they all stack up. Just for fun.</p>
<p>Alexandre-
Yes, you are right. If you really want to compare apples and apples you would have to exlude the Cornell specialty colleges. I wish I had access to the statistics that would allow me to do that.</p>
<p>Collegehelp, that seems completely convoluted to me. You take Cornell's best 1100 and compare them to Dartmouth or Princeton, but this isn't fair as you're basically saying that the top 33% of Cornell's student body is better than Dartmouth or Princeton's ENTIRE student body. Using the same logic I could say that Ohio State's top 500 students are better than Amherst's top 500 (its entire class). True, but completely irrelevant.</p>
<p>When you compare based on percentages, Dartmouth and Princeton students are MUCH stronger, to the tune of almost 70 points on the SAT. </p>
<p>Cornell has many more mediocre students than Dartmouth or Princeton. This just is all a bunch of statistical manipulation to make Cornell look strong. Its clearly size biased. You can't compare the worst 7% of a student body with the top 33% of another school.</p>
<p>However, it is important to keep in mind that the Cornell statistics include Architecture students, who are known to have lower SATs since Architecture admissions don't weigh SATs nearly as heavily as the respective committees for A&S or Engineering. After all, what good is a 1570 SAT if you can't maintain a half-decent portfolio?</p>
<p>Cornell's middle 50% for the ACT was 28-33, Dartmouth's is 28-34 (again, includes Architecture).</p>
<p>So... Dartmouth does not have 70 points up on Cornell, nor are its students "MUCH stronger" than Cornellians.</p>
<p>
[quote]
...statistical manipulation to make Cornell look strong
[/quote]
</p>
<p>How dare you imply that one of the nation's top schools needs to "look" strong? You insult Cornell.</p>
<p>slipper-
There is more to it than you point out. Dartmouth's 1100 is the best 1100 they could enroll. I am comparing these to the best 1100 that Cornell enrolled.</p>
<p>It is rather convoluted but there is some validity to it.</p>
<p>LaptopLover,
Please remember that those numbers are for ADMITTED students. Every school, including several ranked well below Cornell, have impressive numbers for admitted students. The trick is getting them to enroll. </p>
<p>I'm with slipper on this comparison. Both are terrific schools, but pound for pound (which is what really counts), Dartmouth has the stronger student profile.</p>
<p>Dartmouth's yield is about 5 points higher than Cornell (53 vs. 48%). </p>
<p>Collegehelp, Dartmouth and Princeton enrolled the most well rounded classes possible, as all top school do. That includes the top 30% who might be stats heavy and the bottom 30% stats wise who might be legacies, athletes, URMs, applicants who wrote a book, etc. Its silly to compare a whole class with the top academic portion of another class.</p>
<p>As I mentioned the worst 1000 students at Cornell on average are significantly worse than the worst 1000 at Dartmouth or Princeton.</p>
<p>OK... so when Cornell matches up with Dartmouth stat-wise, we have huge similarities:</p>
<p>SAT range is almost identical (Cornell's endowed range includes AAS)
Yield difference is 5% (not exactly big like Cornell vs. Harvard)</p>
<p>I do agree with you slipper, that we can't compare Cornell's best 1000 against Dartmouth's 1000 (which is pretty much its entire class). The stats I cite are overall averages.</p>
<p>My point is just that Cornell is a peer institution with the likes of other ivies and top schools and should not be shafted to the side.</p>