If You Score a 2300+, You Have a 99% Admit Chance at HYPM

Applying to College
41

<p>If you look at the number of kids in a given year with 2300+ on their SATs and the number of acceptances in those schools, of kids with those stats, that is just a preliminary figure. You then have to filter for multiple apps; and many do apply across the board to those schools. You also somehow have to exclude those who have some blemish that would have them dropped. </p>

<p>I know in our area, many kids who applied to a half dozen of the most selective schools with stats like that, who did not get into any of those schools, but got into the next tier of selectivity. It's old news here.</p>

42

<p>It makes even more sense, if you throw the little ivies into the mix. The taking home lesson of this OP is that you could go to a very selective college with high SAT plus good gpa.</p>

43

<p>Yes, the math is faulty. Here is a counterexample that illustrates why.</p>

<p>Suppose you have 81 students, each applying to all nine of these schools. One of them has a 0% chance, one has a 1% chance, and so on up to the one student who has an 80% chance. They have, on average, a 40% chance at getting into each school. And if you run through the calculation, the expected value of the number of them that get into Harvard, say, is 32.4.</p>

<p>However, now consider each applicant's chances of getting into any of the nine schools. The applicant with a 0% chance at each school has a 0% chance of getting into any school. The one with the 80% chance has a 100% chance (minus a rounding error) of getting into any. Sum them up, and you get an expected value of 70.49 students getting into at least one school.</p>

<p>So that's a probability of only 88% that a randomly selected student from this group will get into at least one school, not 99% as you claim.</p>

<p>Now here's a more extreme counterexample. Suppose you have only two students. One has a 0% chance at each school, and one has an 80% chance at each school. For each school, they average a 40% probability of getting in. But for all nine, you can be (almost) assured that one will get in somewhere and the other will get in nowhere. So they average only a 50% probability of getting into any one of the nine.</p>

44

<p>I have an idea. Let's settle this little argument using readily available real-world data. If your local high school has Naviance statistics, please feel free to add them to what I have started below and update the calculations.</p>

<p>Our medium-sized (about 2000 total students) highly competitive suburban high school has Naviance stats on its website. If we apply the 2300/3.8 criteria to the Ivies and MIT, I see the following history there:</p>

<p>Brown: 1 admit, 1 waitlist did not attend, 1 reject - P(reject)=0.667
Columbia: 2 waitlist did not attend, 2 rejects - P(reject)=1.0
Cornell: 4 admits, 1 reject - P(reject)=0.2
Dartmouth: 2 admits, 3 rejects - P(reject)=0.6
Harvard: 1 waitlist did not attend, 6 rejects - P(reject)=1.0
MIT: 1 reject - P(reject)=1.0
Princeton: 1 admit, 2 rejects - P(reject)=0.667
U Penn: 1 admit, 2 waitlist did not attend, 2 rejects - P(reject)=0.8
Yale: 1 admit, 1 waitlist did not attend, 1 reject - P(reject)=0.667</p>

<p>If we use the method that blithely assumes statistical independence, we would have
P(admit somewhere) = 1.0 - (0.667)(1.0)(0.2)(0.6)(1.0)(1.0)(0.667)(0.8)(0.667) = 0.972
Not 99% but not terribly far off.</p>

<p>If we go with the title and use just HYPM, we get</p>

<p>P(admit somewhere) = 1.0 - (1.0)(0.667)(0.667)(1.0) = 0.556</p>

<p>Obviously, this is not enough data to make a statistical argument. Please feel free to add to this.</p>

<p>Anecdotal: There was one easily-identified applicant in this data with 2380/4.6 weighted GPA who applied to Princeton, Penn, Harvard, Columbia, Cornell, Dartmouth (plus Duke and a couple of other big names not considered on this thread) and got into none of them. He or she wound up at Rutgers.</p>

45

<p>Okay man, we get the point. You got a high SAT score and you're going to get accepted to the "better" ivies, and Cornell shouldn't be in the ivy league, superiority complex, etc., etc...</p>

<p>But to add to the thread, you really can't calculate ivy chances given SAT scores with such incomplete data. You would need a random sampling of EVERYONE who applied to all the ivies across different SATs. You also can't automatically assume that SAT is correlated with acceptance. Correlation is not causation. There may be a lurking variable. In fact, there is most certainly more than one lurking variable.</p>

46

<p>The other thing that this theory is ignoring is how many kids are getting in without the 2300+ or high gpa, but has something that is unusual that does not fit with the usual profile. Perhaps homeschooled, non traditional school or college courses, online courses. The top colleges may have break pts that do not coincide with the 2300 mark; a kid may get a top rating score for test scores with lower than that making him indistinguishable from someone who does when the adcoms make the decision on him. From what I understand the ivies tend to count the SAT2s in their equation. Also some schools such as Duke use a numerical scale that will give half the points to non academic issues such as ECs, recommendations and essays. Most kids get a middle of the range score for these things. Only those who have truly phenomonal entries in those areas score above average, and that can mitagate the top academic scores. And if the academic break points are less than what the OP has designated, I can see kids not making the cut. </p>

<p>I've done a similar analysis that Bass Dad did using data from 6 highschools that track their kids' application over the last 5 years, and I see the same results. I also see some kids who get in everywhere so if you just take the number of acceptances to those school without assigning them to a person, the numbers would come out more as the OP presents.</p>

<p>I do agree with the OP that someone with those numbers have an excellent, near 100% chance of getting into highly select school. I 'm talking about schools like Vanderbilt, BC, Northwestern, Tulane, Tufts, Emory, Davidson, CMU, Michigan, Wisconsin, Colgate, Bates, UCh, Georgia Tech, USC, GW. and a number of other schools that are considered very good schools. When you are talking about those schools that are approaching single digits in acceptance rates, and high yield rates, the statistics start taking a curve because of other factors start coming into play.</p>

47

<p>Not sure if you are responding to my post or the OP's, theslowclap. If the former, I will say that I do not have a horse in this race. I am the father of a college junior and a high school senior. None of us has attended or applied to an Ivy or MIT. I realize my data proves exactly nothing by itself. That is why I asked others to add to it. Even with lots of data, the method in my posting may not prove anything, but it can help get us closer to the truth by replacing some assumptions with real data. No slight was intended to Cornell, I am just reporting the numbers from my kids' high school website.</p>

<p>If you were responding to someone else, nevermind.</p>

48

<p>gpa has to be very closer to 4.0 based on our Naviance.</p>

49

<p>BassDad: i was responding to the OP.</p>

<p>On further thought, I realized my post came off as rude again. hahaha, i'm just getting sick of how all these people look down on cornell like it's sub-par and not even worthy of being in the ivy league. I guess there's really no harm in discussing the predictability of SAT scores. I guess I misinterpreted what the OP was saying in his post when he mentioned cornell. I do admit that cornell has a higher acceptance rate, and saying otherwise would be statistically irresponsible. but in cornell's defense, the higher acceptance rate stays true to its mission. don't mind me everyone. do continue =]</p>

<p>If it's any help, I remember reading that the SAT has an r value of 44, meaning that the r-squared is something like 6.33, which is a horrible predictor? This discussion seems to be about the predictability of SAT with admissions on a specific ivy population. I don't know if anyone's actually gone out and found all this data or if it's possible to collect it.</p>

50

<p>uml1958 makes an interesting point. Our Naviance site reports only weighted GPA's and not one of the Ivy admits had anything lower than a 4.5. I have no idea of whether the OP is talking about weighted or unweighted GPA. He is probably a lot closer to being right if he means unweighted GPA's however.</p>

51

<p>To the OP, you can't use that exponential rule because the events are not independent of one an other.</p>

<p>Chances are if you were admitted to Harvard you stand a far better chance that you were admitted to the other 8 schools you were talking about. </p>

<p>Your method relies on the assumption that Ivy league schools shuffle all students with a 2300+ together and admits 40% of them. </p>

<p>Too many outside variables are confounding your data, making it virtually useless.</p>

52

<p>It will be interesting to see what part of the OP's argument people are actually disagreeing with. It seems that a lot of people are disagreeing with his assumption that most people with good stats have reasonably good ECs, but then again I could be wrong. A lot of people are really confusing in the way in which they prove that the events are not 'independent'.
So let me propose this scenario and see how many disagree:</p>

<p>Based on grades, essays, ec's, extracurriculars, and everything else (not just numbers), Bob definitively has a 10% chance at Harvard, 20% chance at Yale, 30% chance at princeton, and 40% chance at UPenn. He therefore has a 0.9<em>0.8</em>0.7*0.6 chance of being admitted to at least one of these.</p>

<p>Who disagrees and why?</p>

53

<p>Because if you are admitted to Harvard, the chance that you are also admitted to Cornell is virtually 100%, not 60% or whatever probability you assign to Cornell.</p>

<p>And if you are rejected from Cornell, the chances of you getting accepted into Harvard are virtually 0 not 10% still.</p>

<p>In the event that all of the Ivys were the same school, and all applicants with 2300 SAT and 4.0 gpa were exactly the same and all of the ivys always admitted 40% of them, independent of eachother and completely random, then what the OP said would be true.</p>

54

<p>Tyler09: I would buy this argument if we are talking about comparing normally distributed admissions for each separate college that are separated by statistically significant differences. The way I think you envision the admission curves for each college is that there is Cornell at 0 (arbitrary scale for explanation purposes), Columbia at 20, and Harvard at 100. I don't think the curves are that far apart. We are talking about an SAT range from 2000 to 2400. A lot of the curves overlap so much that it's really ridiculous to try to see the relationship between a 50% chance of acceptance at Harvard and the corresponding chance of acceptance at Brown. EVEN IF we had all this information, and EVEN IF these data are normally distributed, and EVEN IF sats were the only indication of acceptance, and EVEN IF we control for all the individual confounding variables, and EVEN IF we assume there are no lurking variables, we can't calcuate the probability of AN INDIVIDUAL because we need to know the area under the curve that is at least as extreme as the cut-off of interest.</p>

<p>It appears that we are analyzing these numbers with the assumption that SATs alone predict admissions. Did anyone yet establish the necessary statistical conditions required to analyze data based on a correlation? Did anyone yet make sure that the data comes from a representative population? Did anyone even check if SAT scores are even linearly associated? Did anyone control for the differences in personality? Do you know if colleges admit people along a normal curve (it's most likely skewed)?</p>

55

<p>Actually, I do not think that statistical independence requires that the probability density functions be normally distributed. The probability density function for a coin flip is 50% heads and 50% tails if the coin is fair. Successive outcomes are independent but the pdf is uniform, not normally distributed.</p>

<p>If I remember my probability and statistics courses from way back when, the definition of statistical independence was that the knowledge that one event has already occurred has no bearing on the probability that another event is going to occur. In mathematical terms</p>

<p>P(A|B) = P(A)</p>

<p>where P(A) is the probability of event A occurring given no knowledge of event B and P(A|B) is the probability of event A occurring given the knowledge that event B has already occurred. This leads directly to </p>

<p>P(A&B) = P(A) x P(B)</p>

<p>where P(A&B) is the probability of both A and B occurring. By extension, if several events are all independent, then we can say that</p>

<p>P(A&B&C&D&...) = P(A) x P(B) x P(C) x P(D) x ...</p>

<p>If we choose event A to be "applicant rejected by Brown", event B as "applicant rejected by Columbia", etc. down to I as "applicant rejected by Yale", then the OP is stating that the probability of being accepted by at least one school of the nine mentioned is approximated by the equation</p>

<p>P(acceptance somewhere) = 1 - P(rejection everywhere)
= 1 - [P(A) x P(B) x P(C) x P(D) x P(E) x P(F) x P(G) x P(H) x P(I)]</p>

<p>for a fairly small subset of the general pool of applicants. He then makes some handwaving arguments to come up with P(A), P(B), ... P(I), does the math and states that the answer is about 0.99.</p>

<p>To me, the interesting question is not whether this equation is exactly correct, but rather how far off it is. As slowcap points out, there are a lot of variables that are not being accounted for. As Tyler points out, the variables that we are considering are certainly not independent over the general pool of applicants and we have no real reason to expect that they should suddenly become independent given the arbitrary limits imposed by the OP. However, even if you believe that the OP's methods are imprecise, there is still the possibility that he may have hit upon the right answer (or something reasonably close to it) by accident.</p>

56

<p>This is bs...I can think of 18 kids at my high-school, out of a total of 24-26, that fit into this criteria, including myself, who did not get into HYPM.</p>

<p>I remember 5-7 cases where they had this criteria and didn't get into any ivies.</p>

57

<p>Counter-proof truazn's argument:</p>

<p>Here is USNWR top 10 schools admission rate:
P-10%
H-9%
Y-9%
S-11%
CalT-17%
Upen-18%
MIT-13%
Duke-23%
Columbia-12%
UChicago-38%
The rejection rate is then: 90,91,91,89,83,82,87,77,88, and 64 %
Based on truazn's logic, here is an average guy's (SAT>1980) chance of getting into one of the top 10 schools if she applies to all 10:</p>

<p>p=1-.9<em>.91</em>.91<em>.89</em>.83<em>.82</em>.87<em>.77</em>.88*.64=83%</p>

<p>That is too high!</p>

58

<p>Cornell is unusual because there are special consideration for entry in some of their schools. The hotel school, for example, looks for experience, aptitude and interest in the hospitality industry rather than test scores and grades. There have been kids rejected there because of its specialty emphasis, not because they are not good students. I am not certain about out of state status for the land grant colleges, whether state residents have preference, but they are predominently filled with Nyorkers. I would guess that the kids going to Arts and Science, Engineering, and Architechture would be right up there with kids at Brown, Dartmouth, Upenn. But being a larger school would make it a bit less selective. I think the kids there are as motivated and sharp as any of the kids in the top schools, and I understand the work load is very demanding.</p>

59

<p>The OP was referring to the ivies. However when you do the math, you need to adjust for those kids who were accepted with lower stats than the top kids because they had something the school wanted. You also have to adjust for those kids accepted at multiple schools. That reduces the number of seats available and you need to increase the number of kids in the 2300+ pool to include those who got the SAT score through multiple seatings. Also some of those kids may have not scored that high on SAT2s which would bring down their appeal a bit. You then have to adjust for the number of kids that are considered top range for academics and SAT scores, though they are not at the OP's level because the schools top category cutoff is below the 2300+ number, and grades. This is reality since since those kids will be equally considered as top candidates academically. Schools don't tend to split hairs on a few points on the SAT if they are within clusters that are designated. Also there will be kids whose grades may not be that high but they have high class rank due to a rigorous grading standard, and those kids who go to private school who are rated on a whole different chart again because of the non weighted tough grades.</p>

60

<p>Now, now, in all fairness we should consider what the OP is claiming. He has said nothing about the general population of applicants, only those whose scores are 2300/3.8/750 or better who have applied to all of a set of nine particular schools. I rather doubt that there are many people out there who meet all of those criteria so his result is not going to be very useful in any case. Nonetheless, to refute his argument with numbers based on probabilities for the general pool of applicants, or with numbers based on applications to a different set of schools, or with ancecdotal evidence based on applications to a subset of those schools is to refute a different argument than the one he is making.</p>