On That Fluoride-IQ Study & Statistical Silliness

I am in the Northwoods at the water’s edge, far from the teeming masses, and I only had time to glance through this new study that claims that women who eat fluoride while pregnant have sons with lower IQs. And daughters with higher IQs.

The good news is nobody has an IQ. IQ is a test score, a score on a non-unique partly culturally dependent test, and therefore variable, despite what you might have heard claimed elsewhere.

Of course, there are dumber and smarter people and smarter people generally do better on IQ tests, even though IQ tests are imperfect measures of smartness—or dumbness. Please read the link before commenting about IQ tests.

Paper is “Association Between Maternal Fluoride Exposure During Pregnancy and IQ Scores in Offspring in Canada” in JAMA Pediatrics by Green, Lanphear, and Hornung. Author’s stated objective was to “To examine the association between fluoride exposure during pregnancy and IQ scores in a prospective birth cohort.”

If you’re in a hurry, skip the rant and go to the meat below.

Rant

Nobody—and that includes the authors—gives a damn about the “association” (or “link”) between test scores and fluoride. What every wants to know, and now some believe, and for all I know may be true or false, is whether fluoride causes dumbness or smartness.

Yet instead of a directly and manly statement about cause, we have these watery circumlocutions. The old way of doing statistics encourages this sleight-of-mind. Everybody says “link” or “association”, or even “correlation”, because people (falsely) believe “null hypotheses” can be disproved using wee p-values (or Bayes factors). And when “null hypotheses” have been disproved, everybody believes causes have been found.

It does no good, no good at all, to remind anybody that correlation is not causation, and that in no way are null hypotheses disproved by hypothesis testing. Not in the face of grand budgets and wee Ps and scary chemicals.

In any case, it’s worth asking why the correlation-is-causation fallacy is so compelling to scientists and researchers.

That wee Ps bless results is certainly one aspect. Everybody takes it that a wee P has proven an “effect” is present. After all, the parameters in probability models are called “effects”, and their value measures “effect size”, and speaking of effects is to use causal language.

This is all not so, and regular readers know all the reasons why. All uses of p-values are a mistake and result of flawed logic. There as no good uses of p-values. Get rid of them. And so on.

Now if you accept that fluoride is or could be a cause of dumbness is boys and smartness in girls, then you have no choice but to believe these causes have been proven if the P is wee. This is because the only other cause you allow yourself is “chance”, and even though people speak of “due to chance”, which means “caused by chance”, everybody knows chance can’t cause anything, because chance isn’t a thing. It has no causal powers.

This happened here. The only thing the authors allowed themselves to believe was fluoride was a cause, and nothing else, in the two groups pressed into service. Some 228 women living in “nonfluoridated areas” and 141 living in “fluoridated areas”. Any other difference responsible for the living quarters of these women was not considered as causal, even though the authors allow the possibility when they speak of limitations.

Yet everybody knows nobody believes limitations sections of papers; they’re just cover-your-ass boilerplate. If people really believed what they said in limitations, they’d never have released the study until they made sure they had isolated, to the best of anybody’s ability, the true cause. But papers must be published! Besides, everybody else makes the same mistakes, so it’s accepted practice.

Real Meat Is Here

Whatever. You can skip everything above and concentrate on their Figure 3 (in part duplicated above), which shows how the magic of regression as paper generator and hypothesis prover is done.

We see blue (male) and orange (female) dots plotted by fluoride level (said to be measured without error! and the error not accounted for in the regression!) by IQ test score. Dots look like the glitter on the floor after a photo shoot. Whatever level of fluoride you’re at, there is a huge spread for both boys and girls.

Right away we have proved if fluoride is a cause of smartness and dumbness, it’s not a very strong cause, because they’re no large systematic trend to the dots for either sex by fluoride level.

We do see more variability in boys. But as anybody who has ever worked with test data knows, boys are always more variable. In any big group there will be proportionally more boys at the top and bottom than girls. What’s the cause of this inequality? Hey, maybe it’s fluoride.

If fluoride were a cause of smartness and dumbness, why is it sex selective? Anybody?

Next we see two things that did not happen, and are not real. The blue and orange lines. The blue line slants down, the orange up. The implication is that increasing fluoride causes boys to become dumber, where dumbness is measured by IQ test. But also that increasing fluoride causes girls to become smarter.

Which immediately reveals this regression is asinine. Look at how few tots are after 1 mg/L. That smaller samples are more variable than larger is Stats 101. Boys are more variable than girls, as all experience shows. Therefore what is almost certainly happening is that this result is spurious.

Plus if the measurement error of fluoride intake were accounted for (which nobody does, since nobody understands the predictive way), the “effect” would vanish.

Update Those shades on the lines indicate parametric and not predictive uncertainty! Parameters don’t exist: test scores do. More over-certainty—spoken of well in the award-eligible international seller.

The second panel shows two shades of blue, the lighter dots being fluoridated women; or, rather, women who live in fluoridated areas. This is a horrible graph because non-fluoridated women are rare at high levels, allowing the light blue dots, and the regression, to focus on them. Maybe that’s not so big a trouble, except again we have the same small-sample-large-variability problem.

No, none of this can be believed. If fluoride is doing something, or did something, to these women and their offspring, it isn’t much.

If fluoride were a cause of smartness and dumbness, why is it sex selective?

Thanks to Al Perrella and Dan Hughes for tagging this paper. A bunch more criticism are here (I didn’t read any).

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