Tuesday 18 February 2014

A nice bunch of flowers


Grasp a bunch of flowers in your hand, making sure you hold them towards the bottom of the bunch so that it splays out in a pleasing fashion, and you are well on your way to winning a lady’s heart, and to understanding Spearman’s law of diminishing returns.

The general factor of intelligence is strongest at lower levels of intelligence. It may be a case of “All neurones to the pump”. When abilities are low, most problems are difficult. In such cases, all resources have to be thrown at the problem. When abilities are higher there is more spare capacity for differentiation of abilities. Brighter persons have a lower proportion of their abilities accounted for by a common factor, even though the have higher absolute abilities.

So, if we stick to the flowers analogy in this post-Valentine’s day phase, the flowers of intellect of less able persons are tightly held together. The vector of “flowerness in common” runs from the bottom of the bunch of flowers to about two thirds up the bunch. In bright persons “flowerness in common” runs from the bottom to about one third up the bunch.

So, if you confine your studies of human beings to university students, not only will you misrepresent average mental abilities, but you will also diminish your measures of g, and be ever more likely to find apparently new, disparate mental abilities.

So, psychologists should study people who are not at university. I suppose that, more self-servingly, they might argue that everyone must go to university, simply to provide them with more representative study samples. However, the main effect of being at university is inebriation and delusions of adequacy, so it would probably be better to avoid university students altogether.

Flowers generally work, though.


  1. James Thompson said:
    The general factor of intelligence is strongest at lower levels of intelligence.

    Have you read Aja L. Murray, et al's article disputing the statistical validity of Spearman's Law of Diminishing Returns? If so, any opinions on it?


  2. Had not seen it (or more correctly probably saw but did not properly notice it) and will read and comment later, though it looks intrinsically plausible that skewness could have this effect. Then need an explanation for skew, I suppose.

  3. wonderful flower metaphor! g may be a weaker determinant at higher ability levels because higher g increases variability, which factor analysis takes advantage of…

    I’m writing the following to remind myself of these things - back when I was a cowboy, factor analyzing achievement tests for rural majority group 3rd graders, we’d get 2 factors (math & reading - some kids differentiated enough by then to be really good at one & not so good at the other) but the amerindian population of 3rd graders (same school district) yielded only one general factor. why? because the test measured something different for them? nahh, b/c they were still all pretty low (no one had differentiated enough to be good at one thing & not so good at the other). Some thought it meant the test had differential internal validity – heck no, it's the same dang reading & silly math items for all. Some thought g was less a determinant for the high group – no, they get more factors precisely because they have more g (& therefore more variability). Lower their g & you lower their # of factors.

    one needs a lot of g in order to be able to differentiate into being very good at one thing & average at another - folks with more g will have more variability & therefore more [correlated] factors. groups with lower ability will have less variability & therefore yield fewer factors.

    as ability/age goes up, more (separate but related) factors emerge. honest IQ tests should yield 1 general factor from say infant to age 2-ish, 2 factors (a verbal/crystal & a nonverbal/fluid) from 2-ish to 5 or 6-ish, 3 from age 6 to… but a very bright 5 year old may have differentiated ability enough for 3 highly g-loaded factors & a few less g-loaded ones to stand for him. at age 1 pretty much it's all a glob of undifferentiated g… & those honest IQ tests with say 3 or 4 high g measures for adults + additional low g (relatively independent) measures, should probably experience the power of g by combining those high g measures into oh say an overall composite:) or throw the low g subtests in too (tho spearman’s indifference of the indicator method kind of screws over the bright learning disordered kids who are high on high g-loaded stuff & low on low g-loaded stuff (“processing” in my vernacular) & incorrectly calls them "average."

  4. Major Hochstädter24 February 2014 at 01:24

    …the flowers of intellect of less able persons are tightly held together. The vector of “flowerness in common” runs from the bottom of the bunch of flowers to about two thirds up the bunch. In bright persons “flowerness in common” runs from the bottom to about one third up the bunch.

    You do realize this is gibberish, don't you?

    The whole point of an analogy is to make a complicated concept easier to understand. Not only do I get no better understanding of whatever it is you're trying to clear up from this analogy, but I don't even understand what the analogy is supposed to mean in its own right. What the hell does "flowerness" going two-thirds of the way up the bunch have to do with how tightly you hold the flowers? For that matter, what the hell is "flowerness" anyway?

    As Lyndon Johnson might say, if you've lost me, you've lost pretty much any normal person who could be expected to follow an analogy.

    1. g is the common vector that runs through the correlated vectors of groups of abilities. The vector analogy comes from Dennis Child's "The Essentials of Factor Analysis" 1971 which I always found a very useful primer. If the analogy of a bunch of flowers does not work for you (the more the stalks line up the closer they approximate to the essence of all flowers, in the way that g stands for the essence of problem solving ability) then the vector analogy will make more sense, though it is a somewhat less striking image. So, sorry to have lost you, but hope this suggestion helps.

  5. I'm afraid I agree--- the flower metaphor doesn't work. Go back to the lab and try again--- getting a good metaphor is important.

    You make a highly important point. Suppose we think about using IQ tests to hire firemen and physicists. Where is the test more useful? It's for the firemen. 10 points of IQ---- which is tough to measure from a chatty interview---- matters a lot for being a fireman. It doesn't matter much for a physicist. Of course, having a high IQ is absolutely essential for being a physicist, but we *can* tell the difference between 85 and 145 by chatting with someone, and the difference between 145 and 155 is unimportant.

    1. Sorry to disagree, but the difference between 145 and 155 is important, and makes a measurable difference to intellectual achievements, and even to wealth among entrepreneurs. David Lubinsky very good on the relevant research findings. I have done several posts on this result.

    2. You'd know better than I. I was being hyperbolic, though--- a little extra brains can never hurt (unless accompanied by even more extra pride). I should look at the earlier posts, but is the 10 points as important in 145-155 as in 95-105?

    3. Much more important in terms of the outcome for society, though 10 points in the middle of the average range makes a lot of difference to the individual. IQ 155 appears to be very much faster and brighter than IQ 145, though at those elevated levels one is probably using the rankings physicists assign to each other.

  6. Here's something I've wondered about: are IQ tests less accurate at measuring g for high-IQ people? If you're designing an IQ test, I would think you are most concerned about distinguishing 100 from 105, since there are lots of people in that range, and not so concerned about 140 vs. 145. If there indeed exists a second consideration--- that g matters less to performance for high IQ people--- that adds even more reason to not bother to measure it precisely.
    Thus, it might be possible to design an IQ test especially for high-IQ people that would measure tehir IQ better. It would measure low IQ worse, since maybe nobody under 130 could answer a single question, though.
    All this holds true for inaccuracy with low-IQ people too. I know there are IQ tests for very young children, which is to say, for very unintelligent people. Are there IQ tests for very smart people?

  7. For high intelligence, special tests are preferable. The redoubtable Alice Heim created the AH5 for this purpose, and it was given to virtually all university psychology students from the mid 60s onwards. Equally, for precise assessments of low intelligence other approaches and tests are required. That is the main finding: there are 7 tribes of intelligence (see post).