Sorry for this self-indulgent post. It will probably be of interest to only 0.1% of you.
I have been interviewing high schools students applying to Harvard College for the past three years. There are twice as many applications today as there were in my day, and the admittance rate has correspondingly dropped by half. None of the applicants that I previously interviewed were accepted, and only one, the top student in a class of 600, was wait-listed. All of the applicants though were very talented and qualified as if the weak students self-selected themselves out. In my past MBA life, I have also read applications for the business school with a similarly low acceptance rate and only one of the 15 applications I examined was accepted.
A new student I just interviewed is promising... She has all the right ingredients and knows how to market herself. I googled her on the Internet and found a web trail of achievement starting from middle school. I probably connected with her because of her perfect ACT score, which she claimed only one in the state and 22 in the nation. I checked this statistic on the ACT website and there are actually 500 perfect ACT scores (or 1 in 4,000) in the nation, so the rank was probably just on the instance of the test.
I scored the equivalent of a perfect 1600 in today's SAT, which bests Bill Gates's own 1590. Before the 1995 recentering of the test from an average score of about 900 to 1000, the SAT was scored more stringently with an average of seven 1600s out of over a million in the nation per year (getting a perfect score then made the news); nowadays, it is closer to 700. I also scored a 790 out of 800 in the GMAT, which was the single highest score of my MBA program in my year and subsequent years (except for the most recent year in which an 800 was recorded).
My high school maintained anonymous scores for the past four years, and my score was the highest among a total of 1,600 student's across all those years--an outlier among outlier scores-- despite my school admitting the top third based on a competitive examination. It also was substantially above my Harvard class average.
With a 99+ percentile ranking for both sections of the test, it was clear to me that I made a triple nine (99.9% or 1 in 1000 in my composite score and probably in my individual ones as well). A triple nine is equivalent to a IQ of 149 (std 16); a double nine, 137.
I had taken a college statistics course at Columbia University during my last year of high school, and attempted to see if I made a quadruple nine (99.99% or 1 in 10,000; corresponding to 160 IQ) by computing a percentile from my composite score by assuming a normal distribution and estimating the variance and correlation of math and verbal scores. A normal distribution was a fair assumption because of how questions are "normed" from similarly distributed populations from past tests. I learned that was right on the threshold of a quad, but that the result was extremely sensitive to my estimates.
I decided after the interview to use the web to conduct my research, which was not at my disposal in 1990. Unfortunately, the recentered perfect score tops out at 99.98% or 2 in 10,000 (the original SAT topped out at 99.9995%), so I have to use my original scores.
I decided to look up the qualifying scores for various intelligence societies for the elusive 1 in 10,000 indicator. I was never really impressed with Mensa, because it used scores at the 98th percentile, which are below the average scores of the top public and private schools in the nation, but there are several intelligence societies with more stringent limits.
The intelligence society, Mega Society, which takes one in a million, obtained from an ETS statistician an actual histogram of SAT scores from the five year period between 1984-1988, of which one of the scores is my own, from which I can calculate my actual exact percentile. The process unfortunately is a bit tedious and not worth that much to my ego.
Fortunately, I can let others do the work for me. The Triple Nine Society publishes qualifying scores for various tests. I meet the bar for triple nines for both the SAT and GMAT, each by a wide margin. There is no society which admit members exactly at the quadruple-nine level. The Prometheus Society admits those who meet 1 in 30,000 or roughly 4 sigmas. I am lower than their cutoff but still within the range of statistical insignificance. (Fig 8.3.3)
It doesn't matter that my scores are high, since people still assume I am an idiot. It's also not really satisfying knowing that the tests are inherently flawed and not just for the limited material tested. For instance, I know many non-native English speakers, generally intelligent and gifted in math, feeding the bottom with dismal verbal scores.