Estimating Eliezer Yudkowsky's IQ

From his old website: "I was eleven, in 7th grade, when I took the SAT. I got 670 Verbal, 740 Math. I placed - out of the entire 7th grade of the Midwest - 2nd place Combined, 2nd place Verbal, and 3rd place Math. There is a certificate on my wall from Northwestern University. It says: "Eliezer S. Yudkowsky has acheived the highest level of distinction as a top scorer in the 1991 Midwest Talent Search in competition with over 28,000 of the most able 6th, 7th, and 8th grade students in the eight state Midwest region."

I forgot to note he scored the 2nd highest of all of the most talented midwesterners - so I will assume he is the most talented child in the midwest that actually entered into this talent search. According to this data, about 700000 babies were born in the midwest. If we take that times 3 as a crude estimate for the total amount of 6th/7th/8th graders in the midwest at that time, we are left with about 2 million children. I don’t believe for a second they actually tested all of these children, and even if they did, regression to the mean is a terrible bitch, especially to gifted children.

I can’t exactly ignore the fact they sampled gifted children though - so I’ll just average the unreasonable bear case (28000) and the unreasonable bull case (2000000), which yields a z-score of 4.3.

Yudkowsky also commented on twitter he achieved a perfect score on the SAT in 1995 and has a tested IQ of 143. Unfortunately, he took the SAT right at the year it was recentered, so it is difficult to find accurate information regarding how that ranks relative to the whole population. Apparently, pumpkinperson claims that in the old SAT, only 1282 of 5.000.000 scored above a 1540, and according to this table a 1540 on the old SAT corresponds pretty closely to a 1600 on the new one. That perfect SAT score also corresponds to a z-score of about 3.5.

Combining these 3 scores produces an estimate of 151 with a standard error of 5.1. Longitudinal regression to the mean was considered for the score calculated at 11 years of age.

set.seed(10) #change this every time you iterate the code
g <- rnorm(60000000, mean=0)
iq <- 0.84*g + rnorm(60000000)*sqrt(1-0.84^2)
cs <- 0.83*0.84*g + rnorm(60000000)*sqrt(1-(0.83*0.84)^2)
gr <- 0.9*g + rnorm(60000000)*sqrt(1-0.9^2)

subby1 <- data.frame(iq, cs)
subby1$g = g
subby1$gr = gr
subby2 <- subset(subby1, (subby1$iq > 3.2 & subby1$iq < 3.8) & (subby1$cs > 4 & subby1$cs < 4.5) & (subby1$gr > 2.75 & subby1$gr < 2.95))
mean(subby2$g)*15
sd(subby2$g)*15

#appy <- c() #comment out after iterating once
appy <- append(appy, subby2$g)