Gifted Issues Discussion homepage Forums Identification, Testing & Assessment Fractals and Bell Curves

I saw this NOVA show the other night and thought it was fascinating.
http://www.pbs.org/wgbh/nova/fractals/set.html
I've also been reading "Developing Math Talent" by Susan Assouline and Ann Lupkowski-Shoplik. The book discusses Above-Level Testing for Gifted Math students. In it there is a bell curve showing percentile rank of grade-level achievement test (page 151 Figure 5.1, Section A). The tail end (95% +) is expanded in Section B and shows another bell curve. I keep thinking about how that tail end (95%) could be expanded to yet another bell curve and it reminds me of this "strange attractor."
Does anyone have any insight about the relationship between Fractals and test score statistics?

Well... I think the second bell curve in the >95th%ile tail isn't really there in the first testing. It only comes about from retesting that population again with another (more suitable) measure. That is, on a single grade-level test with a normal distribution of results, the tail is just a tail. It's only on retesting with a different measure that you get a different distribution.

So consider it this way. If IQ (or giftedness, or whatever) really is normally distributed and accurately testable, the bell curve is just a bell curve. It has a mean and a standard deviation and a predictable shape based on those two statistics including the characteristic slope away from the mean in both directions (fewer and fewer people farther and farther away).

The problem is that with grade level testing, even if the results fall in a nice pretty bell, you're not accurately measuring that right hand tail. Probably not the left hand tail either, but I've not really looked into that. So when you retest those inaccurately-measured tail-end kids, you get them redistributed by whether they're just "high for their grade" or "high for even a higher grade."

If the original test were really valid at the tail end, and the second test measured the same thing as the first, you should have a tail-shaped distribution for that >95th population on both.

The example you mentioned shows a distribution for one test and then shows that an above level test yields a similar distribution among students at the tail. So it's not really a distribution with another hump at the tail, although I remember reading that someone else proposed a curve like that to explain the prevalence of high IQ individuals. In fact, I was thinking about this just the other day.

What if there were a gene that some small portion of the population had, and the expression of this gene were not on/off but governed by some complex interaction with other factors. Then the individuals who had the gene would express that gene along some continuum.

Here's an example: pretend the gene is for "extra long legs" (ELL). If we just take a random sample of the population we will include some individuals with ELL. We then measure everyone's legs and the results look like a bell curve with the ELL people at the far right end. If we then just take the ELL people and measure their legs, those measurements will fall on a bell curve, too. Their legs are all extra long, but they are not all the same length.

Intelligence is probably governed by a complex combination of genes whose expression is influenced by other genes and by environmental factors. So I wouldn't be surprised if the tails of the tails of the tails have humps. But the farther out you go, the smaller your humps will be relative to all the noise factors. So you really can't see what's going on. The test just can't focus on details that fine.

Thanks for the replies. On the show there were a group of scientists measuring branches from a tree in the forest. They used the measurements and distribution of the branches from a single tree and related via fractals the size and distribution of the trees in the forest. I am interested in looking at the distribution of IQ and levels of giftedness in some similar way. Thanks for pondering with me the fractal nature of Nature and how it relates to IQ.