Jeromy Anglim's Blog: Psychology and Statistics


Friday, October 2, 2009

Newspaper Reports IQ to be 180 | Is it True?

I was reading TheAge. Google is bringing out Google Wave. As part of the story they interview an Australian engineer on the project:
"Nigel, who has an IQ of 180, is also a maths whiz.." - The Age
This got me thinking. What does it mean to have a 180 IQ. IQ is a norm score. IQ typically has a mean of 100 and a standard deviation of 15. Thus, I asked the following questions:

  • What's the probability of having an IQ of 180 or higher?
  • One in how many people would have an IQ 180 or higher?
  • What's is the probability that someone who a newspaper reports as having a 180 IQ or higher, actually has an IQ of 180 or higher?



I decided to do some armchair stats in R:
iqValues = seq(100, 180, 5);
pThisIqOrHigher = 1 - pnorm(iqValues, mean = 100, sd = 15);
oneInThisMany = 1 / pThisIqOrHigher;
pThisIqOrHigherFormatted = formatC(pThisIqOrHigher, 
  digits = 8, format = "f");
oneInThisManyFormatted = formatC(oneInThisMany, 
  digits = 0, width = 10, format = "f");
cbind(IQ=iqValues, p=pThisIqOrHigherFormatted, 
OneIn=oneInThisManyFormatted)  
#       IQ    p            OneIn       
#  [1,] "100" "0.50000000" "         2"
#  [2,] "105" "0.36944134" "         3"
#  [3,] "110" "0.25249254" "         4"
#  [4,] "115" "0.15865525" "         6"
#  [5,] "120" "0.09121122" "        11"
#  [6,] "125" "0.04779035" "        21"
#  [7,] "130" "0.02275013" "        44"
#  [8,] "135" "0.00981533" "       102"
#  [9,] "140" "0.00383038" "       261"
# [10,] "145" "0.00134990" "       741"
# [11,] "150" "0.00042906" "      2331"
# [12,] "155" "0.00012287" "      8139"
# [13,] "160" "0.00003167" "     31574"
# [14,] "165" "0.00000734" "    136176"
# [15,] "170" "0.00000153" "    653327"
# [16,] "175" "0.00000029" "   3488556"
# [17,] "180" "0.00000005" "  20741279"

  • The probability of having an IQ of 180 or higher is 0.00000005.
  • That's one in about 20 million. I.e., if the norm sample was Australia, he's either the smartest or one of the top few smartest people in Australia
  • As for my thoughts on the final question: I think it's pretty low.

1 comment:

  1. I find it funny when people report IQ in the news as though something quoted from someone with a high IQ must be correct as though maybe IQ is inversely proportional to being wrong. My IQ is supposedly higher than my mum's (informally tested), but more often than not, in non-technological arguments, she'll be correct.

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