Thoughts about Statistics, Misconceptions, and Stupidity in Admissions

greeniguana00
Sun, 14 Dec 2008 11:50:13 +0000

As much as I subconsciously don’t believe what I am about to say, I know it is true: the university doesn’t make the people, the people make the university. As a dogma, it is perhaps the most important thing to understand when it comes to college admissions. But what does it really mean?

Well, starting at a basic level, a university is not the buildings or the campus, but rather the people there, professors and students. Eh, I guess we can throw in admissions counselors too. When accepted, you are forming part of the university. It is not this great privilege you are receiving; you are simply a part of the university. But what does this really mean?

Let’s look at a single cell. You have your endoplasmic reticulum (English department), your ribosomes (Computer Science department), your vacuole (Philosophy department), etc. Each of these is composed of many proteins (people) all working together to form something great. Usually you would expect such an analogy to be made for the purpose of relating a fundamental characteristic of whatever is being discussed, but instead I am using it to illustrate what I don’t mean. First, why would you want to be a protein in this cell? It would be completely unrewarding - you are simply part of a whole, and nothing more, not of any individual importance, for no one cares about a protein but with respect to what it does in the cell. Second, why is the whole so dependent on the parts? Would not a university continue to exist without the existence of an English department? Yet a cell would certainly fail without an endoplasmic reticulum. (interestingly enough, a university would fail without the existence of endoplasmic reticulums, and a cell would be perfectly fine without an English department :)) So, I have tackled one extreme of misconception of what it means to be part of a university. It is not a selfless act of contribution of your awesomeness (and money), as much as admissions counselors would love to believe this is your motivation for applying to Chicago.

Also, however, it is not merely an opportunity for you to serve as a leech in the college community to advance yourself. You are not trying to deceive the admissions officers in order to gain access to this great supply of knowledge. As much as students would love to believe that by drinking the sacred milk of Chicago they will become great, it’s simply not the case, for it is the people that make the university, not the university that makes the people.

Okay, now to get to the main point: it really doesn’t matter what university you end up going to. There is this idea that if you get into University of Chicago, you will suddenly become the type of person who would be an intellectual at heart, the kind who has a shot at a Nobel prize. If you go to Yale, you will be a leader. If you go to your local community college, you will end up as a store manager living a miserable existence, hated by all those under him, and disrespected by all those above him, peerless, lonely, until one day he finds true love in a place so unexpected: the dry cleaners. Finding Beatrice changes him: she is a devout catholic and he soon finds God pulsing through his veins - veins of vengeance, for there was corruption in the company, and now he is finally going to clean it up. With guns, lots of guns. But it’s not like that at all.

All college professors are horrible teachers. This is true across the board. They are very knowledgeable, yes, but teachers they are not. They will profess to you what they know, but you have to put it together yourself and make what you can of it. At the end of four years, the changed person you are will not be the result of the University shaping you, but from you using the University to shape yourself. While some tools may be more refined and others more crude, the chisel used by Michelangelo is no better a tool to use than any other.

Now, we can explore yet another facet of “the people make the university.” What appeals to you about Chicago? Sure, the architecture is sexy, and the core curriculum is a balanced way to pursue your education, but when it comes down to it, it is all the great people associated with the University that gives it its appeal. These great people draw more great people into the university with time, and the whole thing builds upon itself until the university seemingly becomes greater than the sum of the Nobel prize winners - it becomes a Nobel prize-winner factory in the minds of applicants. But it is not, and this is the other half of the leeching coin. The University has no desire to pick you up off the street and shape you into a great person. Not only would that be incredibly difficult, but it would be incredibly, incredibly, incredibly difficult. They are looking for people who have the drive already to become great themselves, and then all they must do is provide the tools - the buildings, the libraries, the professors, and the scalpels for brain modifications. They are looking to admit people who will draw more people to the university.

I think this should make it incredibly clear what is and isn’t important to admissions officers. Community service, while commendable, is not important if you are doing it begrudgingly. Let’s put it this way: would you want to be around people who do community service for many hours for an ulterior purpose? Well, kind of - you’d like the cleaner parks and contented homeless people, but wouldn’t you much rather have people who will talk to you about philosophy at 2am? Who will be enthusiastic about the things you are interested in? Who will be as dedicated to a club as you are? Who will love you unconditionally? Who will do something amazing? Who are absorbing knowledge like a sponge and then using it to form their own ideas about the world, ideas that may change it? Or would you rather be with the people who want to get a degree from a prestigious university so they can make more money?

That being said, the process of forming yourself can start a little late for some people. Perhaps you didn’t fully realize your love of knowledge until senior year of high school, so your GPA does not reflect the level of dedication you truly have. Perhaps you are incredibly stupid, and hence your SAT scores are not quite what you would have hoped. Well, you may want to get an idea of how appealing your new-found self is in the context of the self that is portrayed by your grades and scores. So, what do you look to? The statistics, of course!!!

Here we are: [University of Chicago College Admissions | Incoming Class Profile](http://collegeadmissions.uchicago.edu/admissions/classprofile.shtml)

Okay, so I am male: 49% were male.
I went to a public school: 66% went to a public school
I have a 1560 (out of 1600) SAT: 37% had 1500-1600
I am white: 42% were white

What do we do with these numbers? Well, we are trying to find the probability that they all occur concurrently. 0.49 x 0.66 x 0.37 x 0.42 = 0.05025636 = 5%. Wow, that’s pretty bad compared to the average admission rate of 28%. I shouldn’t even bother apply, right? Right?!??!

Well, no, because the number I came up with is not even close to my actual probability of being admitted, but this is the type of thing most people do when they look at statistics like this. No, they don’t actually calculate anything like this, but they see a statistic like “Only 8% weren’t in the top 15% of their high school class.” and then assume that that means their chance of admission based on that statistic is 8%. Unfortunately, most people don’t understand the statistics enough to draw any reasonable conclusions about their actual chances of being admitted. So, how would we actually calculate it?

Well, you need more statistics than University of Chicago provides on their website. First, you need statistics not only for those admitted, but for those who applied. (Actually Chicago’s website has neither - only the statistics for the incoming class). Let’s do a theoretical example:

Fake Statistics:
1/4 of applicants had an SAT from 1500-1600
1/3 of those admitted had an SAT from 1500-1600
1/3 of applicants were in the top 15% of their class
2/3 of those admitted were in the top 15% of their class
1/3 of applicants were admitted
1/1 of those admitted were admitted

Now, what we can form are ratios of admitted to applied. For example, if 1/2 of all the applicants were human, but 1/1 of those admitted were human, then the admitted-applied ratio for humans would be (1/1)/(1/2) or 2. This means by being human, you are two times more likely to be admitted than the typical applicant. The ratio for non-humans would be (0/1)/(1/2) or 0, which would mean by being non-human you are 0 times as likely to be admitted. Sorry! So, the ratios for our fake statistics are:

SAT 1500-1600: (1/3)/(1/4) = 4/3
Top 15% of Class: (2/3)/(1/3) = 2
Admission in General: (1/3)/(1/1) = 1/3

So, by having an SAT from 1500-1600 and being in the top 15% of your class, you would be 8/3 as likely as the typical applicant to be admitted. You simply multiply all the ratios together. Since the admission rate in general is 1/3, your overall chance would be 8/9, or about 88%. This is about as close as you could get for a good predictor of your chances with easy math and no actual data. Or is it?

What is the problem with the method? Well, this calculation assumes that the factors are independent. In other words, it assumes that your SAT scores are your ranking are completely unrelated. In truth those with a higher SAT score are also likely to be ranked higher in their class. What does this mean? Well, it means that this 88% is a high number. For example, say there were 100 different tests exactly like the SAT that everyone had to take for college admission. For SAT-1, the admitted-applied ratio would be 4/3, and same with SAT-2, SAT-3, SAT-4, etc. so the combined ratio for all of these would end up being (4/3)^100, or about 3,117,982,410,208. In reality, you wouldn’t have THAT much more of a chance of being admitted than the average applicant.

So, either you do some really awful math, get the actual data and compile your own statistics, or you change the simple calculations a little bit to give a more accurate probability. To compile the statistics on your own, you would just look at the ratio of those in the applicant pool to those admitted pool who shared all your characteristics, of course, we don’t have the data, unfortunately. So…

You should only look at one factor at a time.

The SAT ratio is 4/3, so then according to that, 44% chance of being admitted.
The Rank ratio is 2, so according to that, I have a 66% chance of being admitted.

Now I have 2 numbers: 44% and 66%

I can’t say for sure which number is closer to the actual probability, but I can be certain that it lies somewhere around those numbers. If you wish, you can take the average, so I’d say 55%. So, if you want a quick number that is more accurate than looking at the numbers without understanding them at all:

(Total Admission Rate) * (Number of Admitted with Characteristic) / (Number of Applicants with Characteristic)

So, for that person worried about not being in the top 15%, while only 8% of those admitted weren’t in the top 15%, if only 4% who applied weren’t in the top 15% of their class, then with an overall admission rate of 28%, an applicant not in the top 15% of the class would have a 56% chance of getting in! Pretty good, eh? Well, it would be. Unfortunately, University of Chicago doesn’t provide statistics for the applicants, so there is really no way to get a meaningful number after all.

What was the point of all this talk of statistics then? Well, do you want to think about the statistics of college admission after reading all of that? I didn’t think so. That it my point - the statistics will not help you at all. As long as you are true to yourself in your application and work to shape yourself with whatever tools you have, you will do well in life, no matter what happens. The best thing you can do is stop worrying about college in this senior year and start enjoying it, because this is the last time you’ll see many of your friends. It is not the admissions officers deciding your future, believe me, it is yourself.

Stop trying to use numbers to measure yourself, because if you go for the numbers, you’ll miss the bigger picture. When you are 60 years old and realize that you have done nothing for the world but used it, you will look upon your SAT scores, your GPA in high school and college, and your salary with contempt, for they will have taken away true self-actualization.

Now, I need to go to my school with two large lenses and do something awesome to help out the performance of Macbeth. What are you going to do?