<p>two comments on the analysis from a numbers geek ...</p>
<p>Strictly speaking the analysis in the original posting does require each admission decision for one applicant to be independent events. If a kid has great scores and grades but is an axe murderer the admissions decisions will not be independent and they will get in nowhere (if they cured cancer they will get in everywhere) ... so these events clearly are not independent. </p>
<p>That said for the average 2300+ 3.8+ applicant I'd bet the results are pretty close to those if they were truly independent ... and the underlying hypothesis is pretty much on. Assuming you have a very solid applicant with no killer wart (axe murderer, recommendation gunned you down, etc) than increasing the number of applications to elite schools increases the odds of getting into <em>at least</em> one elite school.</p>
<p>Everytime I see the 8 application suggestion ... 3 reaches - 3 matches - 2 safeties ... I hope to see the caveat ... this is a strategy for kids NOT applying to the elite schools. If you're shooting for the HYPSM / ASW end of the world more (very well done) applications is better ... YMMV.</p>
<p>
[quote]
The AP statistics teachers who have replied so far are unanimous in saying that the events can't be taken to be independent in the way that they must be independent to apply the multiplicative rule as you have applied it.
[/quote]
Precisely -- there's nothing wrong with the math itself, it's just that the events are not independent.</p>
<p>Hate to be such a nerd but the way you're calculating probabilities here is not valid. These aren't what we call "independent events" because most Ivys are going to look for similar factors.</p>
<p>Hooo weee --- I hope no one submits this rationale in an admissions essay argument -- then you'll REALLY understand the line about independent and not random events -- you'll sink at every school! LOL</p>
<p>I agree that the analysis doesn't really work, because these aren't independent events. However, I do think there may be a valid perception here: that a candidate with very high SATs and other statistics that puts him or her in the center of those admitted to Ivy League schools is highly likely to be accepted by at least one if he or she applies to all of them. For such candidates, the decisions may appear to be independent and random in some ways, because there are so many unknown factors that may go into admission that may differ from school to school: geographical location, gender, major interest, musical instrument, etc. I agree with the observation that a candidate like this who really wants to go to a highly selective school should apply to more, not fewer, schools. (Note: I want to emphasize that I am NOT saying that Ivies "randomly" select some seemingly unqualified candidates.)</p>
<p>I want to reemphasize the point that saying a student is in range for the least selective of the eight Ivy League colleges (whichever college that is) says nothing about whether that student is in range for Harvard (which is the most selective of the Ivy League colleges most years), Yale (another college well above the Ivy average in selectivity), Princeton (probably less selective than H and Y, but not by much), or MIT (not an Ivy League college, but about as selective as the other three colleges mentioned in the thread title). If you would like to attend Cornell, Penn, Dartmouth, or Brown, you are certainly well advised to apply to them, and I certainly acknowledge that they are fine and competitive colleges, but getting (for example) an early decision acceptance from Penn tells you nothing, really, about your chances at HYPM.</p>
<p>Here's one funny comment from an AP statistics teacher who wrote me both on-list and off-list: </p>
<p>
[quote]
What justification does he give for lumping merit-based leader of engineering, science and all things good MIT in with the snobby who-are-your-parents Ivies?</p>
<p>After reading the post in which you said this, I was wondering the same about you. See below...</p>
<p>
[quote]
Do you realize that right now in the world, there are people in Insurance companies calculating the chances you will drop dead of a heart attack tomorrow based on how much you weigh? Or that how much they should charge you extra because of the statistic that RED cars are more likely to crash than silver ones? How do you think Insurance companies assess risk? PROBABILITY. And let's just say if "stats" lied, I'm pretty sure they'd be out of business and not making a profit...
[/quote]
</p>
<p>If you've taken probability/stats, then you should know better than most how stats can be done badly, and distorted. Everyone else in this thread has already poked the obvious hole in your "proof", so I won't bother. Instead I'll poke different holes.</p>
<ul>
<li><p>Claiming that 750 is the 99th %ile for SAT IIs is just silly, because the score distributions between tests aren't the same. For example, a 750 on the English Lit test will put you in the 94th %ile, a 750 on Math IIC will put you in the 78th %ile, and a 750 on Chinese will put you in the 21st %ile. I also question that a 3.8 GPA will put you in the 99th %ile, but that depends more on the school.</p></li>
<li><p>You don't read your own data right. If you look at the chart, the actual 99th %ile SAT acceptance rates are: MIT, ~40%; Harvard, ~15%; Yale, ~25%; Princeton, ~18% (incidentally, thank you for the link, Princeton has a really strange curve there).</p></li>
<li><p>Your so-called proof fails to take rather major factors into account, for example whether the applicant is domestic vs. international. I know that at MIT, for instance, where there's a cap on the percentage of admits who are international, domestic applicants are something like three times more likely to get in.</p></li>
<li><p>Correlation does not imply causation. There is a correlation between high SAT scores and admittance at HYPM. There might be one or more causal factors correlated with high SAT scores that you're overlooking, and an applicant with high scores but without these causal factors would be unlikely to be admitted regardless of score.</p></li>
</ul>
<p>
[quote]
5400 in US with 2300+ SATs? This is not true.. people superscore.. so that figure should be much higher.
[/quote]
</p>
<p>It is a frequently made assertion here on CC that the number of students with a specified score level on the SAT is "much" higher by superscoring (considering each student's best section scores from multiple sittings section by section) than by considering single-sitting scores (which is what College Board reports). </p>
<p>I doubt that the number of superscored 2400s, say, is any higher than 150 percent of the number of single-sitting 2400s, and likewise down the scoring scale. I think I will have time today to write to a College Board representative I met last week and ask him some questions to pass on to his colleagues in the research offices of College Board. Maybe after a while we will have a definitive answer to this question from the primary source.</p>
<p>To achieve 2400 by superscoring means that the score on one or more sections must go down from a previous sitting. I suspect that it doesn't happen all that often.</p>
<p>You can't objectify admissions like this. I had a friend last year who scored a 2350 in one sitting and had one of the highest GPAs in the school (no rank available) and still got rejected/waitlisted at every Ivy except for Cornell.</p>
<p>Also, your point about the 17000 acceptances from the Ivies going out per year doesn't make sense--you're making the assumption that the accepted pools at all the Ivies are mutually exclusive, which they are most definitely not.</p>
<p>you realized ur logic is terribly flawed. Yes statistics speak. But you know there are some people who suck at everything besides school and tests. How many kids are there at harvard that have absolutely no ECs...NONE!</p>
<p>most people who are that stellar in everything usually have decent EC's as well, and the few exceptions are statistically significant but not 'enormous' at all.</p>
<p>The applicant pools at the ivies are extremely similar and surely contain many of the same applicants. Therefore, many of the most qualified applicants will recieve multiple acceptances from the Ivies (explaining why those 17,000 acceptances go to a much lower number of actual applicants).</p>
<p>You're looking at the admissions process as though, once you have a 2300+ and a 3.8+, the admissions committee will just roll dice to see who they accept, when this is clearly not the case. They have other ways to differentiate between these applicants (ECs, essays, recs, etc.). Someone with a 2300/3.8 who gets into Princeton and Harvard will most likely get into all of the other Ivies, while someone with a 2300/3.8 who gets rejected at Cornell and Penn will most likely be rejected at all the other Ivies (when, according to your logic, they would still have over a 95% chance at getting into one of the six other Ivies).</p>
<p>haha this is a highly entertaining post. no sarcasms really.
however, i do wish you can play with numbers a bit and tell me that i have 99% chance to get into princeton. :P
i stayed on campus for five days and the ambience is shockingly favorable.</p>
<p>"Someone with a 2300/3.8 who gets into Princeton and Harvard will most likely get into all of the other Ivies, while someone with a 2300/3.8 who gets rejected at Cornell and Penn will most likely be rejected at all the other Ivies (when, according to your logic, they would still have over a 95% chance at getting into one of the six other Ivies)."</p>
<p>I suspect this is true, but how true is it? How many people, in fact, get into one or more of HYP but are rejected at other Ivies? I agree that the decisions are not random, but they may LOOK random if criteria other than clear stats are being used.</p>