Problems with acceptance rates for SAT ranges

Colleges and Universities A-Z Princeton University
21

<p>everyone, the key word is PERCENTAGE. the key fact is sample size DOES NOT affect PERCENTAGE. </p>

<p>Let me give yet another analogy. We have balls, each labeled with a certain number from 1-20. Say there are 100 balls in the 1-10 range and 900 balls in the 11-20 range. </p>

<p>In this case we have NO bias toward any particular number or any particular number range. In essence, we now somehow magically cover up the numbers on the balls for the time being, and we throw all 1000 balls into a huge magical random ball selector machine. </p>

<p>(Note: We can choose randomly if 1) we ignore distinguishing characteristics, like covering up the numbers since it it assumed that numbers make no difference, and 2) we assume that all other characteristics of the balls are roughly similar i.e. colour, texture) </p>

<p>So the ball selector is programmed to randomly and blindly select 100 balls out of the 1000 balls in one single process. What do you think is each ball's chance of being selected? P = 100/1000 = 1/10 = 10%. This applies to every single ball, regardless of number.</p>

<p>Now we take the 100 randomly selected balls and reveal the numbers printed on them. We can all agree now that if the selection is at complete random, 10 balls will be from 1-10 range and 90 balls from 11-20 range.</p>

<p>So what percentage of 1-10 range balls in the machine were selected? ** 10/100 = 10% **
So what percentage of 11-20 range balls in the machine were selected? ** 90/900 = 10% **</p>

<p>Surprise, surprise. Sample size does not affect probability if we assume that the numbers from 1-20 don't matter. Now replace "numbers from 1-20" with "SAT scores from 2200-2400". </p>

<p>But that isn't the case with Princeton's stats, or any other school's stats. There is a positive correlation between SAT scores and acceptance rates.</p>

<p>Now you are going to say that correlation does not mean causation. So name me the cause of the correlation. </p>

<p>Higher scores = usually a stronger all-round applicant? I could also say that, if anything, higher scores = more time spent on academics = less time spent on ECs = negative correlation. Why not? There is no proof either way. This is simply a wild assertion. </p>

<p>Now this thread just seems like a bout of weak rationalization and self-denial. Funny how the statistics are easier to digest if I don't mention the words "SAT score", don't you think? The weak understanding of mathematics - the kind needed in the SATs - exhibited on this thread is probably the very reason for the self-denial that gave rise to this thread.</p>

<p>And oh, if anyone needs to take AP Stats, it's probably not me.</p>

22

<p>Question: Last month, I scored a 1,950 on the SAT. (The real one, not one from a prep-school.) Is that where I should be right now if I hope to score 2,300+?</p>

<p>I had:
680 Critical Reading
570 Math
700 Writing, 9 essay</p>

<p>I'm in Geometry, so I didn't understand a lot of the Math.</p>

<p>Also, I'm Asian. What do Asians at least need to score? (Since Princeton is obviously racist.)</p>

23

<p>"We have balls."</p>

<p>lmao that made my day</p>

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<p>Sample size does make a difference. If you have to pick 100 balls and you keep adding more balls to choose from, then the percentage that you pick goes down.</p>

25

<p>^ How do you get through AP Calc?</p>

<p>If there is no difference between people of different score ranges, then an equal PROPORTION of people from each score range will be admitted. I.E. 10% of 2350's would get in and 10% of 2200's would get in (which would mean very few high scorers because there are so few to begin with).</p>

26

<p>^</p>

<p>you're assuming that there is NO DIFFERENCE between people of different score ranges, which is an unfounded and fallacious assumption</p>

<p>it can be observed through various ways (including chance threads) that overall strong applicants typically have really high SAT scores (2300+)...therefore, higher SAT scores have some sort of correlation with the strength of an applicant, which could be the reason why the acceptance rate is higher for 2300-2400 range applicants....think about it, the people who are USABO and USAPHO etc. finalists are people who also get perfect scores, the people who get 2200 and below can be strong, but usually not as strong as the 2300-2400 people</p>

27

<p>I love how people assume that these threads are made by those who are in denial...</p>

<p>Bicyclekick is right in that those with the higher scores (2300-2400) usually have other better qualifications. There are more unqualified 2200-2290 scorers than there are unqualified 2300+ scorers. What I am trying to say is do not mistake cause and consequence. The reason why the admit rates are lower on the 2200-2290 scorers is because of there being more unqualified applicants in that score range applying as opposed to "unqualified" 2300+ scorers. Now, admissions is not based on proportions. You have a set number of spots that is fixed. The thing that varies is how many people apply for that set number of spots. So, if you have 1000 people applying for 100 spots, that is a 10% admit rate to such spots. Now, if 2000 people applied for the 100 spots, the admit rate does not stay at 10%, it goes down to 5%.</p>

<p>The whole point of my original post was that having a SAT score in the 2300+ range as opposed to the 2200-2290 range means nothing. Yes, the admissions rates are higher for 2300+, but the actual score is not the cause of the higher admissions rates. There is only a correlation. And for anyone wondering, I have not yet taken the SAT (taking it in March), but I consistently score 800 for math, 750ish+ for writing, and CR is the only thing I need to up (I'll be happy with a 700 flat on that, but my scores range from 670-730 usually). So now you can stop psychoanalyzing the point of the thread.....</p>

28

<p>
[quote]
you're assuming that there is NO DIFFERENCE between people of different score ranges, which is an unfounded and fallacious assumption

[/quote]

I wasn't assuming anything. That is why my post began with the word "if".</p>

<p>Now since you admit that high-scorers tend to be better applicants overall (and we are done with this ridiculousness about the acceptance rate being higher due to some ghost in the math), wouldn't Princeton be aware of this? Don't they want a student body that will go on to make great discoveries in their fields? Given all of the caveats about the usefulness of the SAT, you can still say with reasonable confidence that higher scorers are, on average, smarter (this is why they tend to be stronger applicants in other areas).</p>

29

<p>bicyclekick: haha, glad that at least someone caught that balls thing! LOL</p>

30

<p>
[quote]
Sample size does make a difference. If you have to pick 100 balls and you keep adding more balls to choose from, then the percentage that you pick goes down.

[/quote]
</p>

<p>cicero, I'm afraid you are still confusing percentage with raw numbers. if you keep adding more of one type of balls, the raw number you don't pick goes down, yes, but the raw number you pick goes UP too, and therefore no change in PERCENTAGE.</p>

31

<p>But there is no change in the number of balls that you have to select...it remains one hundred. If you pick from a pile of 20000000000 balls or just 9000 balls, you still need to pick 100 out of that pile. Therefore, percentages do change.</p>

32

<p>yes you're right percentages change. but percentages will change for BOTH types of balls. what i wanted to say was that percentages don't vary between the two types of balls. both percentages will be the same if you are not biased toward either type. if you need an explanation, just refer to my original working and increase the number of one type of balls. end result will see both percentages change by the same amount.</p>

<p>but thats not the case with princeton's stats. there is a clear bias that should be very obvious to any reasonable person.</p>

33

<p>
[quote]
"A blind sample would yield more 2200-2300 accepts, but since the total possibilities is greater for the 2200-2300 group, it should be the same PERCENTAGE. Your point that we're only looking at the problem from an SAT standpoint is irrelevant, because that's the entire thread is about."

[/quote]
</p>

<p>No my point is right bc there are lurking variables which there are, so that means the entire debate is pointless unless the SAT is the sole factor.
Even if the thread is focusing on the SAT, it doesn't matter, bc the data the OP and others cite comes from the real world where the SAT is not the sole factor.</p>

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<p>So how good was Princeton's math department again?</p>

35

<p>is it really difficult to understand the percentage thing?
its kinda pathetic really...its basic math, the stats clearly show that you're obviously better off having a 2300 as opposed to a 2200</p>

<p>and if the 2300's are more qualified in other areas argument is true, then SAT scores must be a good indication of one's ability and Princeton wud definitely want higher SAT scoring applicants.</p>