Many people do not react particularly positively when you tell them what their IQ is, particularly when this information is unsolicited.
Not in the sense of 'I think you're an idiot', or 'you seem very clever'. Broad statements about intelligence, even uncomplimentary ones, are fairly easy to laugh off. If you think someone's a fool, that's just, like, your opinion, man.
What's harder to laugh off is when you put an actual number to their IQ.
Having done this a couple of times now, the first thing you realise is that people are usually surprised that you can do this at all. IQ is viewed as something mysterious, requiring an arcane set of particular tasks like pattern spotting in specially designed pictures, which only trained professionals can ascertain.
The reality is far simpler. Here's the basic cookbook:
1. Take a person's score on any sufficiently cognitively loaded task = X
2. Convert their score to normalised score in the population (i.e. calculate how many standard deviations above or below the mean they are, turning their score into a standard normal distribution). Subtract off the mean score on the test, and divide by the standard deviation of scores on the test. Y = [ X - E(X) ] / [ σ(X)]
3. Convert the standard normal to an IQ score by multiplying the standard normal by 15 and adding 100:
IQ = 100 + 15*Y
Because that's all IQ really is - a normal distribution of intelligence with a mean of 100 and a standard deviation of 15.
Okay, but how do you find out a person's score on a large-sample, sufficiently cognitively-loaded task?
Simple - ask them 'what did you get on the SAT?'. Most people will pretty happily tell you this, too.
The SAT pretty much fits all the criteria. It's cognitively demanding, participants were definitely trying their best, and we have tons of data on it. Distributional information is easy to come by - here, for instance.
You can take their score and convert it to a standard normal as above - for the composite score, the mean is 1497 and the standard deviation is 322. Alternatively you can use the percentile information they give you in the link above and convert that to a standard normal using the NORM.INV function in excel. At least for the people I looked at, the answers only differed by a few IQ points anyway. On the one hand, this takes into account the possibly fat-tailed nature of the distribution, which is good. On the other hand, you're only getting percentiles rounded to a whole number of percent, which is lame. So it's probably a wash.
And from there, you know someone's IQ.
Not only that, but this procedure can be used to answer a number of the classic objections to this kind of thing.
Q1: But I didn't study for it! If I studied, I'm sure I'd have done way better.
A1: Good point. Fortunately, we can estimate how big this effect might be. Researchers have formed estimates of how much test preparation boosts SAT scores after controlling for selection effects. For instance:
When researchers have estimated the effect of commercial test preparation programs on the SAT while taking the above factors into account, the effect of commercial test preparation has appeared relatively small. A comprehensive 1999 study by Don Powers and Don Rock published in the Journal of Educational Measurement estimated a coaching effect on the math section somewhere between 13 and 18 points, and an effect on the verbal section between 6 and 12 points. Powers and Rock concluded that the combined effect of coaching on the SAT I is between 21 and 34 points. Similarly, extensive metanalyses conducted by Betsy Jane Becker in 1990 and by Nan Laird in 1983 found that the typical effect of commercial preparatory courses on the SAT was in the range of 9-25 points on the verbal section, and 15-25 points on the math section.
So you can optimistically add 50 points onto your score and recalculate. I suspect it will make less difference than you think. If you want a back of the envelope calculation, 50 points is 50/322 = 0.16 standard deviations, or 2.3 IQ points.
Q2: Not everyone in the population takes the SAT, as it's mainly college-bound students, who are considerably smarter than the rest of the population. Your calculations don't take this into account, because they're percentile ranks of SAT takers, not the general population. Surely this fact alone makes me much smarter, right?
A2: Well, sort of. If you're smart enough to think of this objection, paradoxically it probably doesn't make much difference in your case - it has more of an effect for people at the lower IQ end of the scale. The bigger point though, is that this bias is fairly easy to roughly quantify. According to the BLS, 65.9% of high school graduates went on to college. To make things simple, let's add a few assumptions (feel free to complicate them later, I doubt it will change things very much). First, let's assume that everyone who went on to college took the SAT. Second, let's assume that there's a rank ordering of intelligence between college and non-college - the non-SAT cohort is assumed to be uniformly dumber than the SAT cohort, so the dumbest SAT test taker is one place ahead of the smartest non-SAT taker.
So let's say that I'm in the 95th percentile of the SAT distribution. We can use the above fact to work out my percentile in the total population, given I'm assumed to have beaten 100% of the non-SAT population and 95% of the SAT population
Pctile (true) = 0.341 + 0.95*0.659 = 0.967
And from there, we convert to standard normals and IQ. In this example, the 95th percentile is 1.645 standard deviations above the mean, giving an IQ of 125. The 96.7th percentile is 1.839 standard deviations above the mean, or an IQ of 128. A surprisingly small effect, no?
For someone who scored in the 40th percentile of the SAT, however, it moves them from 96 to 104. So still not huge. But the further you go down, the bigger it becomes. Effectively you're taking a weighted average of 100% and whatever your current percentile is, and that makes less difference when your current one is already close to 100.
Of course, the reality is that if someone is offering these objections after you've told them their IQ, chances are they're not really interested in finding out an unbiased estimate of their intelligence, they just want to feel smarter than the number you told them. Perhaps it's better to not offer the ripostes I describe.
Scratch that, perhaps it's better to not offer any unsolicited IQ estimates at all.
Scratch that, it's almost assuredly better to not offer them.
But it can be fun if you've judged your audience well and you, like me, occasionally enjoy poking people you know well, particularly if you're confident the person is smart enough that the number won't sound too insulting.
Of course, readers of this august periodical will be both a) entirely comfortable with seeing reality as it is, and thus would nearly all be pleased to get an unbiased estimate of their IQ, and b) are all whip-smart anyway, so the news could only be good regardless.
If that's not the case... well, let's just say that we can paraphrase Eliezer Yudkowsky's advice to 'shut up and multiply', in this context instead as rather 'multiply, but shut up about it'.
The strange thing is that even though people clearly are uncomfortable having their IQ thrown around, they're quite willing to tell you their SAT score, because everybody knows it's just a meaningless test that doesn't measure anything. Until you point out what you can measure with it.
I strongly suspect that if SAT scores were given as IQ points, people would demand that the whole thing be scrapped. On the other hand, the people liable to get furious were probably not that intelligent anyway, adding further weight to the idea that there might be something to all this after all.