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Errors of Omission?

To the Editors:

In “Of Beauty, Sex, and Power” (July–August 2009) Andrew Gelman and David Weakliem gave us insight into how purists consider statistics, yet they ignore the elephant in the room. Discarding differences a statistician scorns for strictly purist reasons can do harm. It would be a major contribution if someone were to employ statistics more fully.

The problem I often see is strict adherence to significance at the 99 or 95 percent confidence intervals without regard to the conditions being tested. If the analysis falls below one of those arbitrary levels, it is dismissed as being insignificant. Nonsense. If a test between choices A and B finds A to be the better, but if the difference does not satisfy the 95-percent mantra, the difference is deemed “not significant” and the possible better choice is discarded out-of-hand.

A pragmatic statistician would identify what level of significance the difference supports and report that statistic, then let economics decide what is significant and what is not. For example, if A and B cost the same and A were significantly different at the, say, 55 percent level, that is a significant difference. Las Vegas thrives on lower odds than 55 percent.

Purists have a role, a supporting role.

Robert Cowan
Gonzales, TX

To the Editors:

Gelman and Weakliem address some of the problems related to a group of papers related to sex ratios. The problems in this area of study are, however, much more difficult to address than their discussion suggests. For instance: The studies of completed birth cohorts that argue that the sex ratio is not a characteristic determined by the couple assume that couples have their last child without regard to the number of male and female offspring. If we instead postulate a preference for children of mixed gender, we find that the same data leads to the conclusion that the distribution of sexes among children born to a couple has a “significant” family component.

Also, demographic data from many countries suggest a positive correlation between the frequency of the O blood group in the population and the fraction of live male births. The fraction of boys born in a given year negatively correlates with the fraction of stillbirths in that year. Some studies suggest that a baby’s gender is related to the blood groups of the mother and child, with males being considerably more common when the mother’s and fetus’s blood group are both O and females being more common when mothers are O and their fetuses are A.

The issue may be even more complex. Maybe the gestation period for beautiful and not so beautiful people differs. It would be interesting to explore which parent’s beauty is the putative determinant of a child’s and whether the sex and ethnic origin biases influence notions of beauty. If the rating cadre is randomized in the United States, most couples of African or South American origin would likely be rated by people of European descent. And relatively few people of European descent would be rated by people of different ethnic origin. The authors, unfortunately, paid no attention to such alternative hypotheses.

Emilio Venezian
Banqiao, Taiwan

Prof. Gelman responds:

Cowan points out that, even if a pattern seen in data is not statistically significant at the 95 percent level, it might still be important. We agree. In fact, this was our motivation for writing this article in the first place: Satoshi Kanazawa found a pattern which was not statistically significant at the conventional level (when analyzed correctly) but still was interesting. As we discussed, one way to handle the problem of “suggestive but not significant” findings is to use external information to get a handle on how large underlying effects might be. In the example of attractiveness and sex ratio, plausible effect sizes were on the order of 0.1 to 1 percentage point, and our mathematics showed that a study of the size used by Kanazawa would not have a serious hope of finding effects so small. In other settings—for example, using large census databases—it might be possible to sift out such tiny effects. I’ll leave it to researchers in the applied field of biology to decide whether sex ratio differences of less than 1 percentage point have practical importance.

Venezian points out that various biological and sociological factors can affect the sex ratio and criticizes us for ignoring such factors. I would first like to distinguish ourselves from the writers whom we cited (Kanazawa and his collaborators); it is they, not we, who penned questionable claims such as “Engineers have more sons.” To return to the substance of the question: We suspect that, from the biological direction, many of these patterns are best studied with animals, where there is the possibility of direct experimentation. When studying sex ratios in humans, very large sample sizes are needed to find small differences. And, as Venezian notes, interpretation can be difficult. Unfortunately, this does not always deter busy journal editors from publishing the results of underpowered but attention-grabbing studies. And it does not always deter news editors from broadcasting questionable findings.

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