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IQ scales – how do they work (part II)

Binet's IQ scale was flawed
IQ scale problems

In my last posting here, I explained the origins of IQ testing and how Alfred Binet proposed a beautifully simplistic equation for the measurement of intelligence:

IQ = (MA/CA) x 100

Where MA = test taker’s mental age

CA = test taker’s chronological or calendar age

We then discussed how establishing CA is easy. However, in arriving at an IQ scale, you first need to construct an IQ scale for MA. The derivation of an MA scale would involve putting large groups of Parisian children, organised by age, through a series of mental tasks there were believed to be associated with cognitive ability and intelligence.

There would clearly be some subjectivity in establishing what the average performance was for each age group, but if the sample was large enough and the test questions well crafted, it would become reasonably easy to establish questions that all the six year olds would be able to answer, but that only some of the five year olds would be able to answer, and so on and so forth.

To make the IQ scale and the MA scale valid however, one would need to recruit five year old children from all part of the country (not just Paris) if one were really to create an IQ scale that would be applicable to the whole of France. So what is emerging here is that although Binet’s contributions to the art of IQ testing were significant, his methods were imperfect. The first imperfection would be that Binet’s IQ scale would only really be applicable to Parisian children (rather than the French as a whole – as we know now that average IQ scores are higher in urban areas than they are in rural areas) and that the establishment of an MA scale contained some degree of subjectivity in establishing the cut-off success rates for different questions that should be achieved  by children of a particular age group.

But the real fatal flaw in Binet’s simple IQ equation is that it would end up breaking down as the test takers grew older.

Let’s look at an example:

If Jean-Pierre, a 10 year-old, was established to have a mental age (MA) of an average 12-year old, then Jean-Pierre’s IQ score would be calculated as follows:

Jean-Pierre IQ = (12/10) x 100 = 120

So Jean-Pierre, with an IQ of 120, would be bright for this age. Jean-Pierre was an intelligent 10 year old boy.

Binet IQ Scales – the MA scale would become its own downfall

But what Binet and others would soon come to realize is that the MA ‘peaked’ at 15 or 16 years of age (although we now believe that fluid intelligence peaks closer to the age of 25), which creates a challenge in using the above-mentioned equation. This is a typical example of an IQ scale problem.

By the age of 20, Jean-Pierre may then have had the MA of a 16 year old (the peak MA). So his IQ would be calculated as follows:

= (16/20) x 100 = 80. So all of a sudden, Jean-Pierre’s IQ has dropped to 80 from 120. Did he really become less clever?

But even if you were to correct for this issue by assuming that Jean-Pierre had an MA corresponding to his own age, i.e. MA = CA = 20, then this implies that his IQ would still have decreased to 100. A drop of 20 points vis-a-vis his IQ result at the age of 10.

So what is going on? What is happening to the IQ scale?

Well the answer is simple. The Binet IQ equation and his scale seemed to apply relatively neatly for children, and perhaps even teenagers up until the ages 15 or 16. But the problem would be exacerbated as the test taker aged. And this IQ scale would totally break down for older test takers in their 20s and beyond.

If Jean-Pierre, by the age of 42, would have then seen his MA decline to match that of the average 14  year old, (as mental ability declines after our late 20s) then Jean-Pierre’s IQ would then be

IQ = (14/42) x 100 = 33, which most modern IQ scales would agree corresponds to severe mental retardation. In the absence of Jean-Pierre having acquired a illness of some description, this would clearly not make any sense.

I will continue explaining the move towards more modern standard scores in my next posting.

Meanwhile, you can try iq-brain.devv.website’s IQ tests here.