Wednesday 27 February 2013

The ordinal scale of IQ could be converted to an interval scale of 'rtIQ', using reaction time measurements


One of the major limitations of IQ as a measure of general intelligence is that it is an ordinal scale, not an interval scale.

As an ordinal scale IQ is based on rank order of magnitude, so that a person with more IQ points is higher ranked than someone with fewer IQ points. But the scale's interval of the 'IQ point' has no consistent value, and strictly speaking cannot be subjected to comparative mathematical calculations.

This is because the magnitude of difference between adjacent IQ points is not known and is presumably uneven - such that the difference in test performance of 15 IQ points between IQ 130 and 115 may be different in magnitude from the difference of 15 IQ points between IQ 70 and 85 (and also differences in IQ test perfomance are themselves not usually or necessarily measurable on a meaningful interval scale).


This is because IQ scores are constructed by doing an IQ test on a nationally representative group of people, putting the tested sample into rank order (hence ordinal scale) according to their score, then projecting the rank ordering onto a standard distribution curve with an average of 100 and a standard deviation of usually 15.


However, if IQ could be rooted in an objective value such as reaction time, then ratios of differences between IQs could be expressed; for example, the difference between Subject A and Subject B could be said to be half or double the difference between Subject A and Subject C.

For example, Silverman gives the modern average reaction time for men as 250 milliseconds with a standard deviation of 47 - which implies that the distribution of reaction times is sufficiently near-normal (at least near to the mean) to make this summary statistic valid.

If we assume that these reaction times sample were representative of the UK population (of course they are not!), this would mean that Silverman's data could be used to generate a new type of IQ - the reaction time IQ or rtIQ using the same method as current IQ (mean of 100 and SD of 15):

156ms = 130
203ms = 115
250ms = 100
297ms = 85
344ms = 70

And each rtIQ point corresponds to (47 / 15) approx 3 milliseconds difference in reaction time.


The rtIQ would be an interval scale - based on the real magnitude of reaction times but expressed in terms of percentages, which would preserve the mathematical differences between the original reaction times measures in milliseconds.

This means that rtIQ measurements cannot be used to say something like A is 'twice as intelligent' or 'half as intelligent' as B - in other words cannot be used to describe ratios - but could be used to say, for example, that the difference in rtIQ between 115 and 130 was half of the difference between rtIQ 70 and 100 - something which cannot be done using the current ordinal IQ measurements.


Speculative note: Ratios between numbers on an interval scale are not meaningful, so operations such as multiplication and division cannot be carried out directly.

However, the question arises whether rtIQ is not only an interval scale, but could be regarded as a ratio scale - since it is based upon a measure of time which is indeed a ratio scale such that four seconds is twice as long as two seconds.

If rtIQ is regarded as a ratio scale, then it would be true to say that a man with rtIQ would be somewhat more than twice as intelligent as another with rtIQ of 70, because a reaction time of 156ms is more than twice as quick as 344ms.

This would further imply that the range of human intelligence would be a little higher than twofold (as measured by rtIQ that includes approximately ninety-six percent of the population (plus and minus two standard deviations).


Furthermore, the use of rtIQ sets an absolute upper limit or cut-off to human intelligence - which is the physiologically-constrained minimum reaction time - representing the maximum speed of  processing of which the nervous system is capable.

And, in fact, this upper limit would probably not be much higher than represented by a reaction time of 150ms - somewhere between 100ms and 150ms but closer to 150 than 100; since this seems to be close to the minimum time required for the physiological processes of nerve transmission (and muscle response) to be accomplished.

This would mean that the distribution of reaction times at the high intelligence end would be non-normal, and rtIQ would have a plateau. If rtIQ points continued to imply 3ms differences in rt, then the maximum rtIQ would be reached somewhere between 130 and 145.


All this usage of reaction time as a ratio scale would make sense if, and only if, general intelligence was conceptualized in terms of something-like nervous system processing speed - akin to how 'fast' a computer is.

Clearly rtIQ is not exactly the same concept as general intelligence has been (rt is a smaller, sub-division of 'g' - although, presumably, significantly correlated with it) - and so would involve a re-definition and require replication of much of the predictive and discriminative research which has been done on g.