Sunday, August 30, 2009

Additional information on IQ of teachers

++Addition++I realize now that Inductivist, using the OCC80 variable, was only looking at high school teachers. The difference between our estimates for that level of teaching is negligible. Thus the post is a complement to, not a critique of, his.


The Inductivist recently used Wordsum scores from the GSS to estimate the average IQ of high school teachers by decade. Another one of the blogging world's best raised a few follow up questions and directed them to me in response, prompting a turn to the database.

Frustratingly, I wasn't able to find a variable identifying teachers (it would be optimal for all quant bloggers to adopt the practice Agnostic started and include those used at the end of a post), and lack the patience to wait for Inductivist to fill me in. The GSS does record occupational information based on the International Standard Classification of Occupations, however. ISCO has had two major revisions since its inception, the last in 1988, and varies slightly by country. After a lot of googling, I've identified codes for "teaching professionals" in the US for respondents participating from 1988 and after*.

Going this route allows for some additional insights to be gleaned. Converting Wordsum results to IQ scores under the assumption that the Wordsum mean for whites is equivalent to an IQ of 100 with a standard deviation of 15 yields an average IQ of 108.4 for all teaching professionals surveyed over the last two decades. For high school teachers, this gives an estimate about one point higher than Inductivist found. The small discrepancy is probably due in part to the inclusion of administrators among educational professionals by ISCO methodology. It is also marginally closer to what I would have guessed before having any data to go by.

The total sample size for teaching professionals is 742, allowing IQ estimates by educational level to be made. The following table shows the estimated average IQ for education professionals at the post-secondary (college and university), secondary (high school), primary and pre-primary (K-8th grade), special education (gifted and short bus), and "other teaching professionals not elsewere classified" (13% of the total, perhaps professional mentors and the like) levels:

High school107.4150
K-8th grade107.4369
Special ed.105.918

Treating Wordsum scores as proxies for IQ scores works quite well, but it's not perfect. For one thing, a perfect score of 10 equates to a maximum IQ of 127.8. As only 3% or so of the population has an IQ of 128 or higher, this artificial ceiling does not have much of an effect most of the time when Wordsum-to-IQ conversions are made for groups of GSS respondents. However, in the case of university and college educators, it does--36.9% of those surveyed scored a 10. If this contingent averaged an IQ 2.5 SDs above the white mean rather than the presumed 1.86--which is certainly plausible--the average IQ estimate for university and college educators would be slightly north of 120, with the professorial average higher still.

The 107.4 for high school and K-8th grade teachers is not a typo--they just happen to be the same, although the curve is noticeably wider for secondary educators, with a Wordsum standard deviation of 2.08 for those at the high school level to 1.78 for K-8. Perhaps math and science teachers pull the distribution to the right while PE, art, and other soft electives teachers push it to the left?

The following table shows the same for whites only:

Level (whites only)IQN
High school109.3133
K-8th grade109.0321
Special ed.109.415

As expected, the white distribution essentially parallels the distribution for all educational professionals, shifted to the right a couple of points.

The response pool is not large enough to break non-whites down by educational level. The table below shows the estimated average IQ of all educational professionals by race:


The black-white gap is almost exactly one standard deviation, adhering to the fundamental law of sociology described by La Griffe du Lion. Taking into account the fact that 18.2% of white educational professionals earned a Wordsum score of 10 compared to 6.7% of non-whites, the black-white difference appears to be right where the lion would predict for it to be, small non-white sample sizes notwithstanding.

GSS variables used: ISCO88(2300-2399)(2331-2332), RACE, WORDSUM

* The GSS does not offer much help in this regard, stating only that respondent occupations from 1988 onward use ISCO-88. This instructional guide on ISCO put out by Stanford shows professional educators to be represented by codes 2310-2390 (see pg 15). This more helpful listing from the University of North Carolina breaks educational categories down to the fourth digit, and the codes match up perfectly with what the GSS returns, with the exception of a discrepancy among secondary education professionals. The UNC source shows it to be represented by 2320, while the GSS returns data for 2321 but nothing for 2320 (the fourth digit is the most arbitrarily assigned--something the Stanford guide deals with in detail). Most of the possible four digit combinations from 110 to 9999 are not used, which is why I am confident I've identified the correct educational classifications--pegging four of the five in a 100 digit range with the one exception differing only by the fourth digit is almost certainly not due to chance. The Wikipedia entry agrees with both of these sources. Further, the results have face validity not only within the educational profession, but for various other occupational categorizations as well. Still, I must add a disclaimer to what is presented above--I am only 99.9% certain that I have identified the classifications correctly.


OneSTDV said...

Good post.

Billare said...

I don't know much higher-level statistics. Not yet. Can someone who does answer me this -- is the neatness of the "fundamental constant", being nearly one standard deviation, supposed to suggest something about the physical cognitive apparatus that causes the IQ differentials, or perhaps something about the divergent evolutionary histories of SSAs and "Whites"? Basically, is the exactness of the constant significant or mere coincidence?

OneSTDV said...

"supposed to suggest something about the physical cognitive apparatus that causes the IQ differentials, or perhaps something about the divergent evolutionary histories of SSAs and "Whites"?"

Both probably. I'd say the latter caused the former.

Stopped Clock said...

Minor quibble (just trying to keep you on your toes): you can only treat 1 STDV as equivalent to 15 IQ points when you're centered at 100, right? 15 points would be more than 1 STDV here (but probably not by much).

Audacious Epigone said...


La Griffe law doesn't attribute a reason for the gap, only that it repeatedly and reliably shows up across a host of cognitive measures. OneSTDV's explanation seems reasonable to me.


I'm taking the SD for Wordsum scores and converting it to 15 IQ points. To place 100, I use the white mean Wordsum. So 15 points represents one SD wherever you are on the scale, I think (but when it comes to statistics, I only know how to drive the car, not why it works). It would be incorrect to say that 15 points, or 1 SD, represents an equally sized shift in terms of percentiles, of course.

Alkibiades said...

Good Post. The data does seem to fit my anecdotal experience. Granted my sample size n~20, is relatively small. Vox Day had a article where he posited that the average teacher IQ was 91 based on pre-recentering SAT scores.

Anonymous said...

Teaching is a weird profession. But, what do I know of other professions, I only worked in teaching. Anyway, when people asked me about public school and teachers, I always told them the same thing. About half the people in teaching are truly fine people who know their stuff and care about kids. The other half are derelicts who should not even be allowed to be around kids.

Anonymous said...

"Basically, is the exactness of the constant significant or mere coincidence?"

I would guess that, sans AA and quotas, it wouldn't be nearly as consistently observed. Because our government forces proportional representation of blacks in every field, the gap remains constant. If employers were allowed to hire on merit, without taking race into consideration, I'd expect the gaps to shrink and perhaps become negligible. For example, if blacks and whites needed the same GPA and SAT to get into a given college, you'd expect their average IQ scores at that college to be nearly the same.

Audacious Epigone said...


VD posited an average IQ of 91 for teachers? Do you have a link to that post by chance? It seems impossibly low.

In doing something similar with SAT scores by declared area of study, I estimated those going into education as having an average IQ of 99.3--right in the middle of the road. But roughly half of those kids won't make it through to graduation. One-quarter of the US adult population has a BA or higher, while virtually all "educational professionals" do. Even though the correlation between post-secondary education and intelligence has steadily declined over the last several decades, for the average teacher to be around 30th percentile of all adults strains credulity.


There are a high number of really sharp teachers (not that raw intelligence necessarily means great pedagogical skills, nor does low intelligence preclude it, especially at the pre-college level), with nearly one-fifth of white educational professionals scoring a perfect 10 on the Wordsum test, compared to only 5.5% of the population at large.


Right, we can either have blacks and Hispanics underrepresented but relatively indistinguishable from whites and Asians in cognitively demanding positions or blacks and Hispanics equally (or even overrepresented) but of noticeably lower quality than whites and Asians in the similar positions, but we cannot have both.

David said...

Fascinating post.

Anonymous said...

Doctors aren't that smart.