Wednesday, September 9, 2015

The Study of Mathematically Precocious Youth and The Inappropriately Excluded

Yesterday I found myself in a kerfuffle over 'The Inappropriately Excluded' on Twitter.  Wow, arguing subtle points of cognitive theory and statistics in 140 character bites - that is insanely frustrating.  So, I'm moving over here to my personal blog where I am not limited and I will link back to the other combatants.

The difference of opinion was over whether is a strong refutation to the inappropriately excluded.  Let me say at the outset that every single scientific conclusion is made in the face of some contradictory evidence.  No theory should explain all the evidence because some of the evidence is wrong.  The research into IQ and careers by Robert Hauser is not completely consistent with my conclusions and I do not dismiss that.  It is possible that the exclusion is less dramatic and those who would want to argue that would quite properly use Hauser as an argument.

However, from the perspective of one of the inappropriately excluded the paper under question is a very poor refutation.  In defense of the paper, it really wasn't trying to make a point about very high IQ and commensurate career success.  Still, it is being used as such in my current argument.

The paper states that the children selected are one in 10,000 which implies a D15IQ of 156 which on the surface, if we also accept that their career performance at 38 is commensurate with their intelligence would be a powerful refutation.  However, to begin with, the calculation is incorrect.  The mean SAT score was 1325, which at the time was about 99%'ile and implies, if, IQ equivalent is meaningful, a mental age of about 23.  At age 13, this implies an R16IQ of 23/13=177 which equals a D15IQ of 156.  So, while the calculation is incorrect, on the surface, the conclusion appears correct.

However, that is probably a substantial overstatement of the mean IQ.  Per the Spearman model differential performance is caused by specific factors and a general factor (g).  The general factor explains about 50% of performance differences when applied to a specific performance item.  Now, as we are all aware, some people have a talent that causes them to perform in a specific area much better than their general performance.  That is clear here where the median SAT-M was 690, a truly extraordinary score for a 13 year old, and the median SAT-V was a more ordinary 545.

Among high scorers as a whole, SAT-V tends to be slightly higher than SAT-M, however, generally very close to each other.  a 145 point difference strongly suggests that something in addition to general intelligence is at work.  If we were to estimate IQ from the SAT-V it would imply a mental age of about 20 and a R16IQ of 154 or a D15IQ of 143.  So, in the absence of other problems, which I will discuss later, a more defensible conclusion would be that these young people have a mean IQ of 143 and, additionally, possess a significant talent in mathematics.

However, there are other problems.  If you were to give IQ tests to 100,000 people and select the top 100, you would have selected people with D15IQs over 146.  However, not really.  The reason is that people have good days and bad days and their tested IQ will vary based upon which they were having when they took the test.  Test makers give a margin of error of 4 or 5 points.  Well, when you do the above process, you are selecting high IQ people to be sure.  But you also are introducing a selection bias toward people who were having a good day and would probably not score as well if they took an IQ test again.  It is generally not significant, but when you are selecting one in 10,000 it does become significant and means that the computed IQ of 143 is probably high by 2 or 3 points.

There is a second selection bias.  The SAT is not an IQ test, however, during the time the test was administered, it had a correlation of about 80% with IQ.  So, one can think of the SAT as .8IQ+.2?.  In normal situations, that would probably not be significant.  However, in situations where you are selecting high SAT performers, you are also selecting high ? performers and, therefore, a conversion will tend to overstate IQ, again probably by 2 or 3 points.

Lastly, as all girls do not reach menarche at precisely the same age, not all children reach intellectual maturity at the age 16 that is assumed in calculating IQ tests.  Consequently, when you select high IQ children, you are differentially selecting early maturers.  That is important because their apparent intellectual superiority disappears when they mature early and by age 16 or 17 the other kids have caught up.  Again, in most circumstances this is not very important, but when you choose the very highest performers at age 13, you are, again, introducing a 2 or 3 point selection bias.

So, in total, this group of high SAT performers, if they had their IQs measured at age 38 would probably average between about 134 and 137.  However, because their math talent would cause them to max out their quantitative part scores, they may score as high as 140.  This places them at an IQ range where we would expect the exclusion to be moderate and a significant percentage of them would be expected to have solid careers commensurate with their IQs.

Leta Hollingworth placed an upper limit on the range of success at 155 R16IQor 144 D15IQ.  While that is the point where the exclusion reaches a relative 50%, I would set it higher, since about half of Nobelists have IQs higher than that.  So, we see that based upon the 'one in 10,000' statement, this group would appear to be outside Hollingworth's 'success sweet spot' (and mine as well), but based upon the likely actual IQ, they are comfortably within it.  And, with a pronounced talent, high performance especially in STEM is to be expected.

However, in truth, the performance of the group is not particularly impressive.  They achieved 107 graduate degrees out of 320, which, while good, is not impressive.  11% or 35 became tenured professors, but between them, they only published 60 papers by age 38.  Many individual academics manage that by themselves.  Arthur Jensen published over 400 peer reviewed papers, for example.  They are responsible, as a group, for 49 patents.  There are 37 currently active inventors who have individually created more than 500 patent families (a patent family is all the patents registered with regard to one invention).

To reiterate, there are always research data that are at odds with a conclusion.   Robert Hauser's research, while not eliminating the exclusion, is the most contradictory.  I don't place as much weight on his work as I would if he reported IQs above 133.  A few STEM luminaries have taken a few high IQ tests, notably the LAIT and Mega, and have done very well on them.  This, in addition to some theoretical considerations, explains why I have a caveat about Math and Physics in the article.

We need a comprehensive 150+ IQ study similar to the Minnesota Twin Study on the heritability of intelligence.  Without it, my conclusions, while well supported and generally consistent with a preponderance of the evidence, are not as strongly supported as I would like.

Yesterday's kerfuffle is a good example of how confirmation bias interferes with the thought processes of the highly intelligent.  Those who argued with me don't want the inappropriate exclusion to be true and they went out to find evidence that it wasn't.

1 comment:

  1. A correction. The primary antagonist is an Economist, not a Physicist. I'm not sure it matters, but someone corrected me so I am acknowledging it.