Estimating the IQ of gwern
From here:
-135 on SB as a child
-mid scores on some rando tests
-1500 on 2004 SAT
-32 on 2004 ACT
-roughly same score on GRE
I don’t know good stats for natrep populations on the ACT, but I will use the same mean = 980 SD = 200 that I used for Scott to estimate his SAT z-score. This is a z-score of 2.6. I’m not sure about the others - from what I gather from here and here the GRE and ACT scores are roughly the same z-scores relative to the population. Like I did with Cochran, I’ll use a regression coefficient of 0.86 instead, as it is likely he will get the same score on retry if he gets similar ones so many times.
Assuming:
longitudinal regression to the mean of 0.6
correlation between achievement and IQ of 0.86
The simulations(tm) return an IQ of 136 and a standard error of 7.5.
set.seed(1)
g <- rnorm(60000000, mean=0)
iq <- 0.6*g + rnorm(60000000)*sqrt(1-0.6^2)
sc <- 0.84*g + rnorm(60000000)*sqrt(1-0.84^2)
subby1 <- data.frame(iq, sc)
subby1$g = g
subby2 <- subset(subby1, (subby1$iq > 2.2 & subby1$iq < 2.4) & (subby1$sc > 2.5 & subby1$sc < 2.7))
mean(subby2$g)
sd(subby2$g)