Did John Edwards have an advantage all along?

The advantage being that there are fewer sons of mill-workers – meaning he had a monopoly on the narrative (I don’t know if his father was a flour-mill-worker or not). From The American Journal of Industrial Medicine, via Reuters:

Using data from the Washington State health department, researchers found that the children of men who worked in flour mills were disproportionately female. Of 59 children born to these workers between 1980 and 2002, 37 — or roughly 63 percent — were girls.

In contrast, just over 51 percent of children born in Washington during that period were boys, according to the findings published in the American Journal of Industrial Medicine.

The current study found that, besides the low prevalence of male births, boys born to flour mill workers also weighed significantly less than average. Their average birthweight was 7 pounds, compared with nearly 8 pounds among girls born to flour mill workers, and about 7 pounds, 12 ounces among boys born statewide.

Unfortunately, and despite their false promises, my library either doesn’t have access, or won’t give it to me, off-campus, but from the paper’s abstract:

Background
The Washington State Department of Health has collected and coded parental occupation information on birth certificates since 1980. We used these data to search for possible effects of parental occupational exposures on birth outcomes.

Methods
We tabulated sex ratio, birth weight, and proportions of multiple births, still births, and malformations by mothers’ and fathers’ occupations.

Results
There were 59 births (22 boys and 37 girls) where the father’s occupation was specified as flour mill worker. The sex ratio of 0.373 (95% confidence interval [CI]: 0.261-0.500) was lower than the mean sex ratio of 0.512. The mean birth weight for flour mill workers’ boy babies was 3,180 g (95% CI: 2,971-3,389), compared to an overall mean of 3,511 g for all boy babies. The mean birth weight of flour mill workers’ girl babies was 3,602 (95% CI: 3,380-3,824), compared to an overall mean of 3,389 for all girl babies.

Conclusion
The low prevalence of male infants born to fathers of flour mill workers in Washington State suggests that fumigants that they are exposed to are causing testicular dysfunction. The very low birth weight seen in the male infants of flour mill fathers is unprecedented and may be another genotoxic endpoint.

This lack of access is annoying, because I really want to see the paper. Why, you ask? Well I can certainly understand that question, having just asked it myself (hat-tip to Colonel Blake).

This sort of analysis is prone to several statistical problems. The first is what we call “power”. “Power” is a function of sample size: small samples are under-powered. Why? Because a small sample has less information, possibly too little information, with which to establish properly the distribution of the data. Moreover, too-small samples are less and less likely to represent properly a population (meaning your results apply only to your sample – in this case Washington State, say – and not to the population at large). The authors are, above, using confidence intervals, meaning they’re relying upon the Central Limit Theorem. They certainly can do this, although their sample of 59, with p = .373, isn’t all that close to the criteria for textbook statistics (at nearly 50/50 probabilities, one is a lot more assured of underlying normality).

I’m just wary of small samples. I’d like to see what else they did. The proportion of males is statistically significantly less than the population proportion (we can see this because the 95% confidence interval of the proportion of males does not include 0.512), but I’m willing to bet the confidence intervals of each (p = .373 and p* = .512 overlap significantly, and I’d like to see by how much (meaning I’d like to see how the confidence intervals work using the “population” numbers, rather than the mill-worker numbers).

The other problem I’d like to see worked out is Simpson’s Paradox. Simpson’s paradox is an aggregation issue and the classic example of it, in fact, relates to low-birth-weight babies (of smokers). It basically says that, merely by dis-aggregating data, one can draw incorrect conclusions. In the case of this paper, the low-birth-weight problem, once children have been separated by gender, might not have been observed had they not been separated by gender.

Don’t get me wrong – I’m not suggesting that there’s nothing here worth responding to. At the very least it has picked up the workers of Washington State, and Washington State ought to respond – assuming the “population” numbers are also Washington State, rather than national, in which case another set of comparisons would be needed. This is more a stats-geek level of interest.

Oh, I think Edwards’ father worked at a textile mill.

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