Estimating the IQ of Marilyn vos Savant
summary:
score of 132 (not 228!) on an IQ test
score of 46 out of 48 on the mega test
Giving him the exact same treatment as Lagnan, I will assume she scored above a z-score of 4 on the IQ test and a z-score of 3.4 on the mega test.
The simulation ended with an IQ estimate of 135 and an SE of 6.5.
set.seed(34)
g <- rnorm(70000000)
iq <- 0.9*g + rnorm(70000000)*sqrt(1-0.9^2)
mega <- 0.58*g + rnorm(70000000)*sqrt(1-0.58^2)
sat <- 0.84*g + rnorm(70000000)*sqrt(1-0.84^2)
subby1 <- data.frame(iq, g)
subby1$mega = mega
subby1$sat = sat
subby2 <- subset(subby1, (subby1$iq > 2 & subby1$iq < 2.3) & (subby1$mega > 3.4))
mean(subby2$g)*15
sd(subby2$g)*15