Familiality estimates from restricted samples

In a recent paper here, Benbow, Zonderman, and Stanley (1983) report that the coefficient of regression of offspring IQ on parental IQ is much lower among the gifted than in the population at large. Thus, Benbow, Stanley, Kirk, and Zonderman conclude in a second paper, the gifted resemble their parents less than do people in general. In this paper, I show that this result is an artifact of the particular estimator of the regression coefficient employed by Bendoq, Zonderman, and Stanley. The leastsquares estimator, which they employ, is severely biased downward, if the sample on the dependent variable is restricted to the upper tail of the distribution, and this is precisely the nature of Benbow et al.'s sample. That is to say, in a bivariate normal distribution with constant regression coefficient, samples restricted to values of the dependent variable (here, child's IQ) above a certain value will always produce a lower regression coefficient than unrestricted samples drawn from the entire but same distribution. I introduce an unbiased estimator that can be calculated from the sample statistics reported in the Benbow, Zonderman, and Stanley article and find that the coefficient of regression of gifted child's IQ on parental IQ is, in fact, higher than the regression coefficients reported in the literature for unrestricted samples. That is, Benbow et al.'s data suggest that the gifted in fact resemble their parents more than do persons in general.