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IQ scales – how do they work? (part IV)

IQ Scales modernized by Weschler
IQ scales were modernized by Weschler

This is part IV in a series of posting about IQ scales.

In my last posting here, I explained how Binet’s IQ scale and equation of IQ = (MA/CA) x 100 would eventually come to be replaced by standard scores, introduced by Lewis Terman in the 1920s.

The beauty of standard scores is that they represented a great way of establishing the distribution of scores of test takers with only two variables: mean (or average) and standard deviation (SD). The introduction of standard scores eliminated the bizarre volatility that was associated with the Binet scale as test takers aged beyond adolescence.

But despite this clear advance in statistics, test publishers including Binet were averse to change. It was Weschler who in 1939 decided to change the IQ scale on his test and to adopt the upgrade of standard scoring methodology. Not only did the Binet tests keep the old quotients, but it was not until the 1960s that Binet would end up caving and adopting the much more reliable standard scores.

IQ scales – statistical properties introduced

The properties of a standard deviation are very neat:

  • We know that roughly 68% of all observations fall within 1 SD of the mean. In plain English, this means that 68% of the population will have a score of 100 + or 1 the SD of the mean (assumed to be equal to 100). So if the test in question has an SD of 15, this means that 68% of the population will have a score between 85 and 115
  • About 95% of the population will have a IQ score which is two standard deviations away from the mean of 100. And so¬†95% of test scores fall between 70 and 130
  • About 99.7% of the population will have an IQ score which is three standard deviations from the mean, translating into an IQ range of 55 to 145

No matter what the mean and the standard deviation change to, the IQ scale distribution should be the same, provided of course that the results on the test are normally distributed across the entire population.

So IQ scales are relatively simple, although the norming part of the test is significantly more challenging.

At iq-brain.devv.website, we compute distribution statistics which will let you know how your score stacks up relative to the population as a whole. A IQ score of 132 or more places you in the top 2% of the population.

Try out tests here.