Estimating the IQ of Chris Lagnan
Summary:
Perfect score on the SAT
scores of 42 and 47 on the mega test. The 1st corresponds to a z-score of 2.62 when compared to readers (M = 15, SD = 8.24) who submitted scores to the Omni magazine. Apparently the same magazine claims that the average IQ of the readers is 140 - as if I’m going to believe that. Given that there is going to be a non-zero amount of cheating/overreporting/nonrep sample issues, I think it’s fair to say that Chris would score above all of these test takers - corresponding to a z-score of 3.4.
hit the ceiling (I believe) on the WAIS-III
I’ll assume for now that the 1st corresponds to a z-score of above 4.24, the mega test corresponds to a z-score above 2.62, and the third corresponds to a z-score above 4. Normally I would just give the test taker a z-score of about 4 because I am skeptical of the reliability of ceilings on IQ tests besides the old SAT, but since Chris Lagnan has hit the ceiling on two different tests, that is much less of a concern to me.
Currently assuming the IQ test has a g-loading of 0.9, the SAT has a g-loading of 0.84, and the mega test has a g-loading of 0.58.
The simulation ended with an estimate of 168 and SE of 6.6 (53 individuals).
g <- rnorm(90000000)
iq <- 0.9*g + rnorm(90000000)*sqrt(1-0.9^2)
mega <- 0.58*g + rnorm(90000000)*sqrt(1-0.58^2)
sat <- 0.84*g + rnorm(90000000)*sqrt(1-0.84^2)
subby1 <- data.frame(iq, g)
subby1$mega = mega
subby1$sat = sat
subby2 <- subset(subby1, (subby1$iq > 4) & (subby1$sat > 4.24) & (subby1$mega > 3.4))
mean(subby2$g)
sd(subby2$g)