This is the third posting that investigates the question of IQ scales and their associated problems.

In my first posting here, I provide background on Binet’s invention of IQ scales and his proposed quotient for the measurement of intelligence: IQ = (MA/CA) x 100, where MA is the mental age of the test taker and CA is the calendar age of the test taker. The CA is easy to establish while the MA requires a scale of its own and a robust norming exercise to establish what the MA of different children pertaining to particular age groups should be.

I also provided an example here, of how Binet’s equation breaks down as the test taker gets older. And the very simple reason why this happens is that MA scale was built for children and might have been valid for teenagers up to 15/16 years in age (although the modern academic literature suggests that fluid intelligence peaks at the age of 25). Under Binet’s IQ calculation method, MA would be capped at 15/16 while CA would increase linearly with the age of the test taker. This ultimately means that the old quotient method was totally useless for calculating the IQ of adults.

So I ended up describing an example about a fictitious test taker name Jean-Pierre, who for argument’s sake, begins to experience a normal cognitive decline by the time he reaches 42 years of age. Binet’s IQ scale and equation would predict that Jean-Pierre, with an MA of 14, would have an IQ of 33 points, which is a level associated with mental retardation. In the absence of some serious illness, this score clearly does not make any sense.

The simple MA/CA formula ends up breaking down in late adolescence. It was Lewis Terman who recognized the problem of variability of IQ scores and in response proposed the use of standard scores in the 1920s. But as most industries and sectors, test publishers were averse to change which meant that several publishers including offspring of the Binet test continued employing the MA/CA equation for quite some time despite the mounting body of criticism associated with this equation and IQ scale methodology.

### IQ scales revolutionized by standard scores

The introduction of standard scores changed everything and for the better. The standard scores would mean that the IQ scale would change from an MA-centric one to the establishment of a distribution (i.e. mean or average and standard deviation) of the performance of people of a given age on the test. This is another way of stating that the MA calculation was expanded to reflect the IQ test performance of a particular cohort of test takers organised by age.

More importantly however, this resulted in much less variable IQ scores for the same person over time. Also, the properties of the normal distribution are such that if the mean and standard deviation are known, then one can extrapolate what the distribution of IQ scores might look like across a population, without needing to rely on CA and MA estimates for each test taker.

The norming process for such a test is quite different for the Binet IQ scales. The test publishers needs to find a representative sample of test takers withing their home country. Once the test is administered across the representative sample, the mean performance and standard deviation is established on the test. With these two variables, we can extrapolate distribution of results which are assumed to be centered on a mean of 100.

I will explain more about this in my next posting.

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