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.


Monday 25 February 2013

Relationship between intelligence and life history speed: population and individual levels


The relationship between population and speed of life history is probably somewhat complex; but (as far as I understand the matter) I think it could be summarized by saying that:

1. At the population level, there is usually a correlation between higher intelligence and slower life history speed.

(This is presumably due to natural selection, historically, in situations where both higher intelligence and slower life history are, on average, adaptive.).


2. At the individual level, within a population, intelligence and life history speed are uncorrelated.

Or, more accurately, intelligence and life history speed are dissociated at the individual level; such that a highly intelligent person may have either slower or faster life history; and the same applies to low intelligence persons.


The dissociation can be seen in two stereotypical male high intelligence types: the sexually aggressive business executive or politician (fast life history - urgency of reproductive effort leading to early sex, multiple partners, more children with lower/ zero investment per offspring); versus the nerdy professor (slow life history - delayed reproductive effort, late marriage to single partner, few children with high investment per offspring).


The dissociation is, presumably, caused because while intelligence and personality are inherited, life history is triggered by the environment, by some experience (probably) early in life.

Or, an individual's specific life history trajectory is selected-from a certain range of possible life history speeds.

The range of possible life history speeds is innate and inherited, but the specific life history speed which is embarked upon is a consequence of environmental cues, triggers or stimuli.


This implies that fast life history parents often have slow life history children and vice versa.

And this means that life history is different from intelligence and personality, because childrens' intelligence and personality is, on average, similar to their parents'.

(Yet, at the same time, some populations will have different average life history speeds from others; and a different average range of life history speeds.)


Thursday 7 February 2013

What is the main selection mechanism causing the 'dysgenic' decline in intelligence over the past couple of centuries?


It seems very probable that general intelligence (or 'genotypic IQ') has declined by more than one standard deviation since late Victorian times, and presumably even more since about 1800 when the Industrial Revolution began to become obvious and these changes probably began.

But what was the cause?


Using reaction time data, the decline in genotypic IQ is of-the-order of 1.5 IQ points per decade - that is about 15 points in a century - or one standard deviation.

(This rough estimate of the size and rate of decline in 'g' has been replicated by a more sophisticated and completely different - as-yet unpublished - analysis of reaction time trends that I have seen.)

In other words, the average Englishman from about 1900 would be in roughly the top 15 percent of the population in 2000 - and the difference would be even larger if we went back further towards 1800.


These numbers are not intended to be precise - indeed real precision (in the sense of exact accuracy) is not available in IQ studies for many reasons to do with the difficulties of truly random and sufficiently large population sampling; and the fact the IQ points are not on a 'ratio scale' but are derived from putting a population sample into rank order on the basis of (usually) one-off testing.

But anyway, I think that a decline of 1.5 IQ points per decade is probably too fast to be due purely to the effect on gene frequencies of differential fertility between people of different intelligence levels.

No doubt the measured decline is substantially to do with the fact that higher intelligence is correlated with lower fertility; but within this, I think there must be at least two explanations operating at the same time.


Differential fertility would lead to a decline in intelligence - let's say - by a reduction in the proportion of high IQ genes in the population.

This happens mostly because since the Industrial Revolution almost-all children that are born will survive; so reproductive success becomes almost-purely a matter of fertility; and the most intelligent sectors of the population are the least fertile, and less fertile with each generation; until eventually (i.e. for the past several decades) the most intelligent people are sub-fertile, below two offspring per woman - so that the genes which make them most intelligent will decline with each generation - first declining as a proportion of the gene pool, and then declining in absolute prevalence. 


My suggestion is that the additional mechanism of decline in intelligence is the opposite of the above: an increase in the proportion of low IQ genes in the population.


There is, I suggest, a difference between high IQ and low IQ genes.

High IQ genes have (presumably) been selected for in the past because they increased intelligence, and thereby (under ancestral - especially medieval - conditions) increased reproductive success.


But low IQ genes are spontaneously occurring deleterious mutations. These were not 'selected for'; rather it was a matter that selection failed to eliminate them.

In technical terms, the mechanism for low IQ genes is mutation-selection balance.


The idea is that before the Industrial Revolution, individuals with a higher mutational load had lower-than-average reproductive success due to very high (near total) childhood mortality rates among those of lowest intelligence.

But after the Industrial Revolution got going, and mortality rates declined for the least intelligent so that even the poorest families usually raised several-to-many children, then there was a double-whammy dysgenic effect: a reduced proportion of high IQ genes with each generation (due to progressively lowering fertility among the higher IQ) and also an increasing accumulation of IQ-damaging deleterious mutations with each generation.

So that (roughly speaking) since the Industrial Revolution, individuals with the greatest mutational load (IQ-harmful genes) have been initially been above-replacement fertile (having on average more than 2 surviving children per woman, for the first time in history perhaps), and also differentially more fertile than those with the least mutational load.


So that compared with 150 years ago there are a lower proportion (and a lowering absolute amount) of IQ-enhancing genes in the gene pool of England, plus a higher proportion and accumulation of deleterious IQ-damaging mutations.


And this double-whammy effect is, I think, why the general intelligence has declined so rapidly and so much in England over the past couple of centuries. 


NOTE: The focus upon accumulation of deleterious genetic mutations due to relaxation of the selection effect of childhood and early adult disease and mortality (which had previously served as a sieve of strongly fitness-reducing mutations) was something I got from Narrow Roads of Gene Land: evolution of sex, Volume Two of WD Hamilton's collected papers. One aspect is that such relaxation of selection is probably unprecedented in human history - indeed, it is possible that recent post-Industrial Revolution conditions may have generated a positive selection in favour of deleterious mutations (amplifying their frequency, at least up to the point when they become fatal or induce sterility). At any rate, the quantitative effect of this process of accumulating deleterious mutations in a population is only imprecisely measurable (I believe); whereas the quantitative effect of differential fertility on differential IQ is pretty well understood, and fairly precise measurements of the effect size are possible.