<p>I, for one, have know idea about whether the underlying distributions of applicants to colleges fit a generic normal distribution around SAT scores.</p>
<p>These estimates do not have the same likelihood of being accurate if the underlying distributiuons are different from that which is assumed.</p>
<p>I still recall the points I lost in an exam in my first grad school statistics class. I was marked off because I had made estimates that were only valid if the underlying distribution was a normal distribution. Instead of looking at the actual data to see what the distribution really was. It was not close to normal, in actuality. I was wrong.</p>
<p>gellino-
I considered doing this for LACs but I don’t think it would be as interesting. The thing about universities is that they vary dramatically is size from 33,000 at Texas to 913 at Caltech. It is therefore difficult to imagine the number of high SAT students without doing the calculation. There is an interplay between SAT range and enrollment size that is hard to see with the naked eye.</p>
<p>LACs, on the other hand, are more or less uniform in size so the only thing that varies much is the SAT range. You can simply rank LACs by SAT range and get a rough idea where the most high SAT students go. It would be a lot of work for information that is not quite as enlightening.</p>
<p>monydad-
The normality assumption is kind of important. I asked a relative check the SAT distribution at their large, second-tier, private university and it closely approximated normality. I have no way of knowing for sure, but I suspect SATs are like IQs, normally distributed.</p>
<p>SAT scores may well be normally distributed in the general population at large.</p>
<p>This has no bearing at all, that I can see anyway, as to whether the scores in a poulation consisting of selected and enrolled students at a particular college is normally distributed. </p>
<p>These are completely different populations. One is random and naturally occurring. The other is non-randomly selected from the overall population pool, in two directions, and therefore is not random.</p>
<p>I can understand how being able to make this assumption can be helpful to get “the easy answer”, since a lot of underlying math and tables are derived for cases of when the underlying data can be considered to be normally distributed. However, because it is easy to compute does not mean that the easy answer is correct.</p>
<p>There are software programs such as “At Risk” where the underlying distribution can be explicitly specified, and results obtained via simulation using these distributions. One still must be able to specify the underlying distribution though. Meaning one must have some samples of underlying data to have a reasonable basis to make these predictions.</p>
<p>Regarding the Florida-UTA anomoly…an extra 1500 students at UTA has little to do with the computed difference of almost a thousand extra 1500+ students at UTA (2516 vs. 1639). It really comes down to the validity of the asumption of a normal distribution. I do believe your math is likely correct, but it is hard to believe UF has higher average SAT scores, equal or higher 75th percentile scores, yet presumably has <em>far</em> fewer 1500+ scorers. Clearly UTA is being boosted by fact the 25th percentile scores are <em>lower</em> than Florida’s.</p>
<p>Sorry, I just don’t buy it…even if the math is correct.</p>
<p>Hey look, HYPSMC, then “tier 2” elites Dartmouth, Duke, Columbia, Brown…I guess kind of predictable since most undergrad rankings usually have these 10 stacked at the top - strong correlation with US News Rankings, THES, WSJ Feeder, Number of National Merit Scholars Attending, Rhodes scholarship winners, etc. etc. etc. </p>
<p>Of course, exceptions are Penn, which seems too high on US News but just right on the other ones, and Brown, which seems too low on US News but just right on the other ones, and of course Rice, which has an extremely strong student body statistically but is ranked some notches below its peer schools based on SATs</p>
<p>Looks like SATs are a good predictor of overall student body strength, though not perfect</p>
<p>I sympathize with the intent of this exercise, though.</p>
<p>There was another thread someplace where someone was suggesting that a particular state university had an insignificant number of high-achievers in attendance. Data of this type might show that, though a small percentage of the student body, the absolute number of high achievers at this huge school was actually reasonably high. Then- if it were the case that such students congregated in separate Honors programs, or they elected difficult majors such that only people like themselves were in most of their classes- under those circumstances the big state u may not look so bad to a particular high-achiever. Alternatively, the facts might prove the contention that virtually no high-achievers are in attendance there.</p>
<p>Perhaps one can get to a similar place, more accurately, by using destinations of National Merit Semi-finalists? If this data is available.
(Not Scholarship winners, but semifinalists).</p>
<p>One problem is that many midwestern students take the ACT and do not take the SAT at all.</p>
<p>svalbardlutefisk-
I know that the SAT scores have an approximately normal distribution at one university. It is possible that the distributions are not normal at other institutions but my gut feeling is that they are approximately normal. Schools like Caltech may have hit the ceiling on the SATs, so the distribution is skewed. My sense is that most of the students at a university have SAT scores near the mean with fewer students far above and far below the mean. This is consistent with a normal distribution. New students certainly are not selected randomly, but I think the net outcome of the admissions process is a normal distribution of student ability, including the SAT measure.</p>
<p>If you can find any statistics out there that state “X% of the students at Lutefisk University have SAT scores above Y”, then I can test this method. It is possible to determine empirically how well this technique works. So help me find statistics to test it. </p>
<p>Maybe other schools publish a more detailed chart of the distribution of SAT scores. Look at the distribution and see if it appears normal (bell-shaped).</p>
<p>I typed “distribution of SAT scores” on the google search engine.</p>
<p>Maybe the admissions offices or institutional research offices could tell me the actual percent over 1500 so I could verify some of these schools. On the other hand, they might consider it a nuisance call.</p>
<p>rogracer-
I have sent an email to U Florida and to U Texas asking them to verify my estimates of over-1500 SAT students. I will be surprised if they reply, but you never know.</p>
<p>What a great way to procrastinate for a math geek … while I’m not sure what to do with this analysis it is fun to think about.</p>
<p>
</p>
<p>I have no idea if each individual school distribution of SAT scores is normal or not but I would guess there is a pretty good chance they are NOT at a lot of State Us … and that the distirbution is bi-modal with an extra bulge of high scores … why? Honors programs … I would think they create a second smaller (and higher scoring) normal curve that overlays on the general student population. Depending on how big the honors program is compared to the rest of the school might determine if it makes the overall distibution look bi-modal. Back to much less fun work.</p>
<p>Interesting. But I want to point out 2 fallacies in the methodology which maybe be mentioned by others but I don’t have time to read all the posts here. </p>
<ol>
<li><p>The distribution may not be normal. For public schools with honor programs, and private schools with a lot of merit-based scholarship, there will be a peak on the high end of the scores.</p></li>
<li><p>For some schools, students take 5-6 years to get their degrees. I reasonalby believe most of 5-6 year students are low-scoring. For some big schools, there are high percentage of transfers whose scores are hardly crossing 1400 line, let alone 1500. So the better way may be to multiply the freshmen enrollment by the percentage you got, then times 4 (school years).</p></li>
</ol>
<p>I think your reason to believe 5-6 year students are lower scoring is false. I knew many in that category and instead of being on their parents dime, they were paying all or most of their schooling and working 20-30 hours a week. So they only took 9-12 hours a semester and maybe even took one off every once in awhile. That sort of assumption is insulting to kids that happen not to have upper class backgrounds.</p>
<p>For the last 3 years, UF and UTA have swapped places for the largest number of enrolled National Merit Finalists for all public schools, and are only surpassed by Harvard (and sometimes Yale) in that regard.</p>
<p>I believe the students who are in their 5th or 6th year are usually the smartest students. They are the engineering and science students whose courses were so heavily scheduled that they couldn’t fit in all the requirements. Or, they took time for internships and co-ops.</p>
<p>I do not think honors colleges create a bimodal distribution at public universities. I think the honors college students simply comprise the upper tail of a normal distribution. I don’t think honors colleges are very attractive to top students who realize they can get into a much better university than the one that houses the honors college. Just about all publics have an honors college or honors program, so the effect is equalized across the publics.</p>
<p>Let’s see what happens to UF’s National Merit numbers after the substantial cut in payment to those kids takes effect. Maybe Harvard will get a few bumps up?</p>
<p>Instead of all the estimates based on third-party sources (USNews) why not simply go the the Common Data Set for any schools you like and calculate a much closer estimate based on the actual distribution of FTIC kids’ SAT scores from the reported CDS data? </p>
<p>May not be as much fun, math-wise, but I guarantee it’ll be more accurate.</p>
<p>Further, I suspect any kid that’ll take the time to prepare for the SAT to the level of 1500 performance (math and English) will be quite a bit more focused and directed and tend to graduate in an appropriate time.</p>
<p>What you might have more fun with is calculating the correlation of high IQ scores to success and satisfaction (whatever that is) later in life. I think a couple guys at Harvard spent a few hours doing that and maybe wrote a book about it.</p>
<p>How about - the correlation of where 1500 SAT score kids go in relation to the money they get from a school?</p>
<p>parent2noles-
I don’t think you can get the number or percent over 1500 SAT from the common data set. The US News figures come from the US Department of Education IPEDS data, the most authoritative source.</p>
<p>However, I did use the common data set to help verify the accuracy of my technique. I was able to find from the common data set the proportion of recent freshmmen scoring over 1400 at Princeton (.735). My mathematical technique estimated the proportion at .701, a virtual bullseye.</p>
<p>This is strong support for the validity of my data.</p>
<p>The answers to the questions you asked would be very interesting indeed.</p>