# Execution rests on IQ test

The BBC are reporting that convicted murderer Daryl Atkins may be executed by the state of Virginia, based on a recent IQ test where he scored 74, four points above the legal definition of retardation, which had previously excluded him from the death penalty.

When first tested in 1998, his IQ measured 59, well below the 70 points cut-off level. The cut-off of 70 is significant, owing to design of the IQ test.

Intelligence shows a specific sort of distribution in the population, and follows a common pattern, known as a normal distribution.

Rather than design a test with arbitrary figures, modern IQ tests have been created with specific statistical properties to make them easier to interpret: the average IQ is 100, and the standard deviation (the average variation from the average) is 15. Click here to see a graph of this in a pop-up window.

The cut-off of 70 is two standard-deviations below the average. It is known that 95% of the population will score within two standard deviations on either side of the average. This makes the legal definition of retardation, at least in Virginia, as having an IQ score in the bottom 2.5% of the population.

There is no easy explanation as to why someone’s IQ score might rise during a 7-year period. Prosecutors are arguing that he ‘pulled-punches’ on the original test, the defence argue that his interaction with lawyers has raised his IQ – although many factors, such as distraction, the skill and reliability of the tester, and familiarity with the tests can affect the score.

Interestingly, the prosecution are arguing that his IQ is actually 76, 2 points higher than the defence claim. Why quibble over two points?

Possibly because of another statistical property of IQ. It has a standard error of measurement (the average error in assessing the presumed true score) of 5 points.

Even taking into account a standard error of measurement of 5 points, a score of 76 would definitely be above the level of retardation – making Atkins eligible for the death penalty, whereas a score of 74 is still ambiguous.

Interestingly, it was a supreme court decision, based on Atkins case, that first made it illegal to execute convicts considered legally retarded.

Statistical properties aside, the whole concept of IQ itself is still controversial among some psychologists, and was most notably criticised in Stephen Jay Gould’s book The Mismeasure of Man.