Gifted Issues Discussion homepage Forums General Discussion Innumeracy in Gifted Education Advocacy

99.9936 But I bet it's not exactly a normal distribution that far out on the tail, anyway.

Agreed, but people with IQs of 160 and 40 are almost certainly nowhere as common as the 99.7% number implies.

But intelligent people end up single parents, suffer I'll health and get made redundant just like anyone else. And rampant idealism, existential depression and having been damaged by not having your needs met all of your childhood can lead to low income too.

I would love to see the recent studies that support this. I do understand that America was once (1950-1970s) a more meritocratic society thanks to the GI bill but nowadays I get the sense that the access to high SES occupations is restricted to a few high achievers (on tests that have a strong correlation with intelligence/strong work ethic) and a lot of non high achieving members of select populations. I desperately want to be proved wrong here so some recent studies showing that things are still meritocratic in the USA would help.

But we're talking about the tail end of the bell curve, so "on average" is meaningless in this context. Optimal earnings generally coincides with optimal intelligence, in the 110-125 range.

This forum abounds with information about how top intelligence and top earnings don't go hand in hand (various studies, personal stories, etc.), so I can't help but wonder why you'd continue making this argument. In an environment filled with gifted parents who are trying to find low-cost testers and stuck arguing with public school systems, it's actually quite offensive.

It's not, because the number of children with IQ >= 130 from a certain group depends on the average IQ of children in the group. If the average IQ of children of college gradutes is 115, a much higher fraction of them will be gifted than the children of parents who did not go beyond high school. In other words, the entire distribution of IQ in some groups is shifted toward the right, and in other groups shifted toward the left, which has implications for the incidence of giftedness.

This argument is a solid demonstration of innumeracy. Whether the gifted population in your sample is 1 in 50 or, let's say, 1 in 10, the group still isn't large enough to significantly influence averages.

Also, you're now excluding gifted people who don't graduate college.

I think the argument is correct. If variables X and Y are drawn from normal distributions with SD = 15, but the E[X] = 115 and E[Y] = 100, there is a much higher probability that X >= 130 than that Y >= 130.

If you define "very tall" as a height of 6ft 6in or more, there are many more very tall men than women because men are taller and their distribution of heights is shifted to the right relative to the distribution of female heights. Do you think the children of parents who both dropped out of high school are as smart on average as the children of parents who both earned college degrees? Unless you do, you should not be surprised if a smaller fraction of the former group than the latter one have IQs >= 130.

Your argument relies on the following assumptions:

1) That averages have anything useful to say about statistical outliers.
2) That educational attainment is solely related to ability, and is therefore a useful proxy for intelligence.

As for the first assumption, 1 in 10 is still a "much higher proportion" than 1 in 50, but my argument still holds.

As for the second, high tuition, helicopter parenting, and a public school system designed to serve the bright-but-not-gifted population are all well-documented socioeconomic influences on educational attainment that have nothing whatsoever to do with ability.

The issue of socioeconomic status (and social mobility) in relation to IQ is an empirical issue, and it is investigated empirically from time to time. An old article that I somehow missed at the time of publication, but which I coincidentally saw while searching for something else a few days ago, mentions some of the other influences on socioeconomic status besides IQ (that is, "controlling for IQ") in one study sample.

http://www.newscientist.com/article/dn11711-smarter-people-are-no-better-off.html

What I find most innumerate about most popular literature on gifted education is the complete lack of discussion of error in IQ testing. On that issue, allow me to quote Lewis Terman, the developer of the Stanford-Binet IQ test.

"The reader should not lose sight of the fact that a test with even a high reliability yields scores which have an appreciable probable error. The probable error in terms of mental age is of course larger with older than with young children because of the increasing spread of mental age as we go from younger to older groups. For this reason it has been customary to express the P.E. [probable error] of a Binet score in terms of I.Q., since the spread of Binet I.Q.'s is fairly constant from age to age. However, when our correlation arrays [between Form L and Form M] were plotted for separate age groups they were all discovered to be distinctly fan-shaped. Figure 3 is typical of the arrays at every age level.

"From Figure 3 it becomes clear that the probable error of an I.Q. score is not a constant amount, but a variable which increases as I.Q. increases. It has frequently been noted in the literature that gifted subjects show greater I.Q. fluctuation than do clinical cases with low I.Q.'s . . . . we now see that this trend is inherent in the I.Q. technique itself, and might have been predicted on logical grounds." (Terman & Merrill, 1937, p. 44)

It's still true today that the error of IQ scoring is greatest in the range high above the median IQ. So particular test-takers will flip rank order with each other if each takes more than one IQ test. And that's why to talk about the "highly gifted" as a lifelong category one belongs to is just flat wrong from the get-go. But, yes, there is a whole lot of innumeracy in gifted education advocacy, which grates on my nerves, as I read John Paulos's book on that subject back when it was first published.