In the previous installment, we saw that a study published in Science was poorly reported in the mass media. One of the most egregious errors was the attempt to make a small IQ difference look big. In this case, the source of the error was not just mass media reporters but Science itself, or to be more specific, its commentary by Frank Sulloway arguing that:

Critics might still argue that the mean IQ difference documented between a Norwegian firstborn and a secondborn is only 2.3 points. Such a modest difference, however, can have far greater consequences than most people realize. For example, if Norway’s educational system had only two colleges—a more prestigious institution for students with IQs above the mean, and a less desirable institution for all other students—an eldest child would be about 13% more likely than a secondborn to be admitted to the better institution (the relative risk ratio), and the odds of a firstborn being admitted would be 1.3 times as great. In medicine, new therapeutic benefits of this magnitude often make front-page headlines. In addition, such differences in opportunities gained or lost inevitably accumulate over one’s lifetime.

I think we can all agree with one of Sulloway’s statements: that new therapeutic benefits of this magnitude often make front-page headlines. But the reason is that many press releases use the same dubious statistical manipulations to make their findings look a lot more impressive than they really are. I could rebut the statistical reasoning behind Sulloway’s rhetoric here, and I could explain why it is that public health specialists grumble about odds ratios and relative risks for exactly this reason: they exaggerate the size of effects sometimes to the point of absurdity. I could criticise Sulloway’s rather odd assumptions about the number of colleges in Norway and his perfect correlation between IQ and college entrance score. But I won’t. One doesn’t need painstaking statistical arguments. All one needs is this graph:

The black line on the left is the IQ scores of those children who were second-ranked among their siblings. The green line on the right is the IQ scores of the first-ranked. (I am deliberately avoiding the terms “firstborn” and “secondborn” for reasons I made clear in the previous blog entry.)

When statisticians look at a collection of data, they are interested not just in the average but also in the distribution of that data. One of the common measures of distribution is the standard deviation. In IQ scores, the average is 100 and the standard deviation is 15. To give you some scale for that, the average height of American males is 69.3 inches with a standard deviation of 2.92 inches.¹

What this means is that an IQ difference of 2.3 is the equivalent of a height difference of 0.45 inches (1.14 cm), which is to say that the difference is not very large at all.

Also, it seems that nobody has considered the very simple hypothesis that first-ranked children are more likely to be given greater educational opportunities — an effect particularly pronounced in low-income families — and that this has raised their IQ by the very simple process of training them to answer academic questions. I can’t tell if this potential confounder was excluded or analysed in the paper because the paper is far too truncated to know (the entire paper takes up just one page of Science; Sulloway’s commentary takes up nearly two pages).

As for Sulloway’s statement that lost opportunities accumulate over a lifetime, I couldn’t disagree more. History is sprinkled with examples of people who missed opportunity after opportunity before finally achieving greatness. This is, I believe, what is really at the heart of all this guff about IQ and birth order, and why so many commentators keep describing this new finding in terms of birth order instead of social rank order. Even Sulloway, commenting in the same journal that published the original paper, continually uses the terms “firstborn” and “secondborn” when he really shouldn’t. I think this is a telling sign. Lurking beneath these conflations and exaggerations of effect lies a deep yearning for fatalistic explanations of a person’s character and life success. It’s in their birth order. It’s in their genes. It’s in their star signs.

Reference:
1. Block HW, Li Y, Savits TH. Mixtures of normal distributions: modality and failure rate. Statistics and Probability Letters: 74(3); 253-264, 2005