Estimating the IQ of George Bush

Based on a message from Linda Gottfredson, Bush’s SAT percentile was 95. He also scored in the 85th percentile in verbal aptitude and the 65th in quantitative aptitude relative to applicants on a military test, who had an average recentered SAT score of 1051 - about the 85th percentile. Assuming a subsample standard deviation of 14 (which isn’t particularly important given his scores aren’t that extreme), these would be z-scores of 2 for verbal ability and 1.45 for quant.

assuming correlation of 0.84 for SAT, 0.79 for verbal, and 0.77 for quant

Simulations generate an estimate of 127 with a standard error of 6

set.seed(1)
g <- rnorm(60000000, mean=0)
iq <- 0.84*g + rnorm(60000000)*sqrt(1-0.84^2)
sc <- 0.79*g + rnorm(60000000)*sqrt(1-0.79^2)
sc2 <- 0.77*g + rnorm(60000000)*sqrt(1-0.77^2)

subby1 <- data.frame(iq, sc)
subby1$g = g
subby1$sc2 = sc2
subby2 <- subset(subby1, (subby1$iq > 1.5 & subby1$iq < 1.85) & (subby1$sc > 1.8 & subby1$sc < 2.2) & (subby1$sc2 > 1.25 & subby1$sc2 < 1.65))
mean(subby2$g)
sd(subby2$g)