Report your rank, not your score.

by Andreas Baumann

I’m generally not a fan of the model of intelligence employed by mainstream psychometrics (for an excellent criticism by the excellent Cosma Shalizi, see here). That doesn’t mean that I avoid intelligence tests: I quite enjoy them as riddles or problems. However, when discussing intelligence, I’d much rather point to something substantial like a job well done or educational achievement than to success in a test measuring how great you are at taking this test.

However, one thing annoys me more than anything else in terms of intelligence testing: the way that the IQ is reported. An IQ score of, say, 105 is not a test score in the sense that getting 99 problems out of a 100 right; rather, it is a transpose of observed ability (as measured by ability to answer the test) to a theoretical distribution of ability in the population, which is normally distributed with mean 100 and standard deviation 15. So a score of 105 translates to being one-third standard deviation right of the mean. Not very intuitive, right?

What I suggest instead is reporting the cumulative function, ranging from 0 to 1. With this, an IQ of 105 would yield 0.63 – because your measured ability puts you ahead of 63 percent of the theoretical population. An IQ of 85 corresponds to 0.159, and an IQ of 125 would yield 0.952. Why is this a better way of stating the measured ability?
It has an intuitive appeal, since it states how large a chunk of the theoretical population you’ve fared better than.
People tend to interpret the IQ as an interval-scaled variable rather than an ordinal variable. While this way of stating it does not ameliorate this idiocy, I hope that the intuitive interpretation will remind people of what they’re actually looking at.
– This way of stating the it leads to more discrimination at the middle of the ability curve, where most of the population resides.

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