# IQ and age (part I) The relationship between IQ and age is a complex one. At its roots, IQ testing as we know it today was developed by Frenchman Alfred Binet in the late 1890s when he was asked by the Paris ministry of education to devise a test which would help weed out weaker children from the classroom so that ‘normal’ or ‘bright’ children wouldn’t be slowed down in their learning.

Binet would eventually come up with a concept of a quotient, which was represented as follows. The Intellectual Quotient (IQ) would be calculated as follows:

IQ = (MA / CA) x 100

where MA was the “Mental Age” of the test taker, while CA was the “Calendar Age” of the test taker. It can be clearly seen from the above equation that having an MA > CA would mean that the child’s IQ would have been greater than 100. If MA were  < CA on the other hand, that child’s IQ would have been less than 100. And if MA = CA, then that child’s IQ would have been exactly 100.

## IQ and age – Binet’s equation highlights some of the issues

So at its very historical root, IQ testing is all about age. And how mental age (effectively how advanced your thinking is) inter-plays with your actual age. To illustrate the point very simply, if a 10-year old would be able to think logically in the same way that a smart 20 year old man is able to do, that 10 year old child would clearly be considered a genius and would have an IQ which is off the charts.

Conversely, if a 20 year old man has the cognitive ability of an average 10-year old, this man would be considered to be intellectually challenged and may be suffering from borderline mental retardation.

So the interplay between age and IQ was clear from the smart. IQ and age: it’s all about age and cognitive ability for your age. However, this very example demonstrated the problem with the quotient method.

If a 12 year old girl (CA = 12), has the cognitive ability for an average 20 year old, then her IQ would be calculated as follows:

(20/12) x 100 = 166

But what about a 40 year old  (CA = 40) with a cognitive ability to match the average 20 year old (MA = 20), does this person really have an IQ of (20/40) x 100 = 50?

Clearly this does not make any sense. What critics of Binet’s method was that it did not apply to adults because of this type of conceptual and mathematical incongruency. It would later become assumed that brains reach an ‘adult’ state around the ages of 15/16. Which means that the peak MA would need to be capped at 15/16. Indeed, Mensa for instance assume that you have reached an adult IQ state by the age of 17 as the bar is lower for both 15 and 16 year olds. So in other words, a 16 year old needs to get less right answers to reach an IQ of 132 (top 2% if test has standard deviation of 16 points) than a 17 or an 18 year old.

But again, this is inconsistent with findings that fluid intelligence (Gf) peaks in our mid 20s. before declining thereafter.

So in fact, MA should really have peaked at a level of MA = 25. This probably means that under the old Binet IQ calculation method, the test might have worked for say 3 to 25 year olds. The old IQ calculation method provides a good conceptual basis for understanding IQ and age relationships, even though the quotient method has since been replaced by standard scores. In my next posting, I will elaborate on IQ and age effects as we age.