This article summarizes the main statistical arguments and the one logical argument used for and against Goldberg’s ideas. To be clear: I am convinced by his arguments in the main and differ from him only at the edges, and trivially. If you have not read him, I urge you too. He writes beautifully and clearly and has given much thought to answering his critics, and has more room in his three books than we have here.
- Group A members are more variable than group B members : The usual implication of this is that, even if there are just as many group A and B members near the mean, more of group A members than group B members will be found at the extremes of behavior. This is only “usual” because it is possible for group A members to be more variable but for group B members to have a higher or lower average and so be found more often in the upper or lower extremes. Each trait has to be judged on its own empirical findings.
- Correlation is not causation: This is true. But it is also true that when there is causation, there is correlation. When causation is absent, correlation can be present spuriously or it may be absent. Too often, Goldberg’s critics acknowledge a correlation but then drag out the “correlation isn’t causation” card, as if by displaying it they have proved that causation is absent. The proof of causation is extra-statistical in the following sense: we have to look beyond the data presented and the model used and ask whether or not the causation is plausible, highly probable, and consonant with other information we possess. What makes a statistical argument worthy is if it can be used to make reliable predictions and not just that is explains previously observed data well.
- The SAT/IQ test isn’t correlated with success: This is false in general but potentially true when conditioning on a subgroup. Suppose you follow graduates of University A, the best in the country (in a particular subject) that accepts only the best according to the SAT/IQ test. All graduates will have an SAT/IQ test and all will go on to success and failure. In this group, any measure of success will not be correlated between the SAT/IQ score because all of these scores are high. Across the population in general, however, SAT/IQ tests are highly predictive of success (and should only be used in their predictive sense).
- Between-group differences are larger than within-group differences: So what? As Goldberg points out, the within-group difference of height in men or women is much larger than the between-men-women difference, but nobody is foolish enough to think this means that men and women are equally tall, or that the small between-group difference doesn’t lead to large differences both on average and at the extremes. Several very good statisticians have been caught making this error.
- The difference in number of genes is small: And so it is. But again, so what? The number of different genes between humans and higher primates is small but the phenotypical differences are enormous. It’s not the number of different genes that count but what those different genes do.
- After controlling for income, group A is the same as group B: This is true, but in using this argument, Goldberg’s opponent has agreed with him. We return to our initial question: if Sally is over six feet and so is Bill, are both Sally and Bill over six feet? And if people are paid by height—the taller receiving more—Sally will be paid as much as Bill, but on average women will receive less than men because, on average, women are shorter than men. Therefore, if you took a group of men and women (all remunerated by height) and statistically controlled for height you would find that tall women received as much as tall men. You will not have proven that men and women are equally tall. It is the tallness —the difference—that has caused the economic success.
- You cannot derive an ought from an is: David Hume first taught us this and it is true. It does not follow, and nobody believes it is true, that therefore there can be no oughts. It is only true that whatever oughts exist are believed without reference to external evidence or empirical findings. Thus, the oughts we believe are based on a priori evidence; that is, our intuitions. This type of evidence should not be castigated: all of mathematics, for example, is founded on the very same kind of beliefs (the axioms). Further, we might not be able to prove an ought is true but we might be able to infer it is with high probability. It is also true that all cultures hold many of the same oughts.
A corollary to the last, and what comprises Goldberg’s main uphill battle, is to convince detractors (usually on the Left) that their criticisms are founded on unspoken and unacknowledged oughts.
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