<p>I think SAT scores are continuous enough…</p>
<p>but you cant score a 791 or a 457 on SAT. maybe GPA is an example of a continuous data. if not, then i dont think anything school record related is continuous.</p>
<p>“Continuous enough” LOL. The mathematician in me shivers.</p>
<p>But the smallest difference in an SAT score is less than 1/20 the total range. It really is “continuous enough”. And besides, I think that cellardweller was refering to USAMO as being non-continuous, not SATs. </p>
<p>Look at it this way. Anyone would agree that height is continuous, right? For all practical purposes, it is. But in the “literal” sense, it’s not, because you can’t have half a proton. </p>
<p>The mathematician in you may shiver, but the physicist in me is warm and cozy.</p>
<p>i hope this thread doesnt into a debate of infinite divisibility…</p>
<p>I answer to your question, I think you can use a multi-linear regression based on SAT scores and GPA for an initial admission probability.</p>
<p>Where the regression model falls apart are for binary choices such as AMC/non-AMC, AIME qualifier, Intel finalist, valedictorian etc.. or for non-continuous variables such as AP scores, AIME scores etc.. Regression model are also poor predictors unless you have a much larger number of data points as compared to variables. They are also fairly poor binary classifiers i.e when you seek to use the model to predict if the result is either in or out of a target group (such as admitted students/rejected students).</p>
<p>Bayesian models are on the other hand very robust binary classifiers and work well with limited data sets. They are used routinely in medicine to assess the reliability of various tests at detecting a disease. </p>
<p>You can get a brief summary of the method andother binary classifiers here:
[Binary</a> classification - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Binary_classification]Binary”>Binary classification - Wikipedia)</p>
<p>You essentially compute a sensitivity and specificity for each test based on your data sample. (Such as AIME qualifier yes/no). The sensitivity is the probability that the student has the characteristic given that he is admitted. (few false negatives). The specificity is the probability that the student does not have the required characteristic given that he is rejected. (Few false positives) A good example of a sensitive test would be a score of 5 on AP Calc BC. It is known that the majority of MIT students have a 5 on AP Calc BC as they get credit for single variable calculus. But is not a very specific test: a lot of rejected students also have a 5 on AP calc BC. Being a USAMO medalist on the other hand has high specificity (most rejected applicants are not USAMO medalists). On the other hand it is not very sensitive as most admitted students do not have that characteristic. Unfortunately or maybe fortunately, no admission test is both sensitive and specific for MIT; if there was one it would be the sure test for admission, pass it you get in, fail it you are rejected. </p>
<p>By using a series of successive tests, each with their own operating (sensitivity/specificity) characteristics, you can progressively refine the admission probability. You start with your initial admission probability (determined by linear regression for instance). You then apply the first test using your initial probability and obtain a post-test probability which is very useful as it tells what the probability of admission is given that you passed the test (scored a 5 on AP Calc or whatever). This value is then used as pre-test probability for the next test and so on. In some cases you may see a major rise in admission probability (high AIME score for instance) or a big drop (got a bad score on AP Calc BC). </p>
<p>As far as including your model as part of your application, I would not recommend it for several reasons: first, adcoms will not read it as they neither have the time nor the technical competency to understand what your are sending them; second, they are extremely unlikely to forward it to somebody in the math or economics departments. They would not do that for published research let alone unpublished work. There is on the other hand a specific section in your application where you are asked if you have ever invented or created something. There you could mention that you like developing statistical models in your spare time and that one actually involved computing the probability of admission to MIT.</p>
<p>Well, I more wanted to include it as a supplement just so they’d appreciate the irony, not necessarily because they’d dwell on the statistics.</p>
<p>They would still get the irony from you discussing the model in the application. Unnecessary supplements tend to burden the application.</p>
<p>
well i think that’s a bit of an understatement</p>
<p>oh and WOW that’s some advanced statistics there!</p>
<p>if you say MIT gives more importance to SAT IIs, will a 680 from your sophomore year of honors chem hurt you?</p>
<p>of course, I’m just an applicant, so I’m not the most qualified person to answer said question, but: </p>
<ol>
<li><p>680 isn’t that bad</p></li>
<li><p>My data uses the highest science subject test score, which is usually from chemistry, but occasionally came from BIO</p></li>
<li><p>MIT admissions is holistic, so they’d probably consider the fact that most of the test-takers were Juniors/Seniors, and not so much hold that score against you</p></li>
</ol>
<p>no, it shouldn’t but it’s a bad idea to take the SATII’s before you take the AP class.</p>
<p>^no. my school encourages the opposite. but then again our honors classes > most ppls AP classes so whatever. i took both bio and chem after freshman and sophmore classes and got 800s without studying.</p>
<p>Well, ok, for most people “sophomore honors” is like a warm-up for the AP. So that’s why I said that. Many people take honors chemistry and then AP chemistry the following year.</p>
<p>im taking it in my senior year, as well as AP bio. i wonder how i will finish up my science sat IIs..i guess i have no choice but to go with physics</p>
<p>
This thread, and the formula in it, do not imply that MIT gives more weight to SAT IIs than to other factors in the application.</p>
<p>You really have a lot of time on your hands hahaha. Or you enjoy math so much you have to find a formula for everything–including chancing sometimes very unpredictable admissions decisions. It takes so much work for the numbers. I think I’ll just let the admissions committee tell me if I qualify or not. I don’t want to give myself some false hope lol.</p>
<p>So… I think by the third statistical model, the top someone can really get is something around 50%. Like Tongchen, who got 50.5. So, while the model doens’t overpredict, it’s still not capturing the essence of what admissions entails.</p>
<p>For most people, I think. Admissions isn’t going to be able to be accounted for even in some sort of correlation because they may be barely related to the variables one would apply to such a model. </p>
<p>I agree. I think being a USAMO finalist almost automatically puts a huge flag on your application. From there on, as long as you don’t screw up something majorly, you’re basically in. Same with finalist in a bunch of other olympiads and Intel or Siemens. I mean, I am a firm believer that a good number of people have something to show along those lines. Either, outperforming in academics or doing something major, community service-oriented (though these people are probably looking at Harvard - which seems to place leadership of that kind on a pedestal). Eh, I could just be tired from shoveling all this snow.</p>
<p>tongchen, i’m too lazy to check my math, but I got a 105% according to this. </p>
<p>I am currently a freshman, but I honestly think MIT would take an IMO participant with 150 less SAT points, .5 less GPA points, and 5 less APs than me.</p>