The strongest evidence for our position consists of a meta-analysis3 derived from 57 general-population samples, many of which are normative or carefully constructed representative samples, with a total of 80,928 participants. This reveals no sex difference in general cognitive ability up to the age of 14 and a significant sex difference at 15, which then increases to its adult value of 5 IQ points in favour of males. There is further evidence for a mean male advantage of 4–6 IQ points in four independent adult samples5,6,7 (n = 11,896); Jackson and Rushton8, in a huge standardization sample (n = 102,515) that is much bigger than the Mexico study9, also reported a male advantage of 3.6 IQ points among 17-year-olds, which is somewhat greater than our estimates3,4 for this age group.

At two points in his critique1, Blinkhorn addresses the ‘file drawer’ problem, in which non-significant results fail to get published. Such a bias cannot be operating in this instance because, as Blinkhorn himself notes, almost none of the published literature on the Progressive Matrices has focused on sex differences. Furthermore, the idea that a null sex difference is unpublishable is belied by the huge number of books and articles, including Blinkhorn's, that claim exactly that. Therefore, the fact that 21 out of 22 student samples showed a male advantage suggests the phenomenon is robust.

Blinkhorn criticizes us for not adopting the principle of weighting results by sample size, and for excluding the very large study from Mexico9. This misses a central point of meta-analysis. We carried out a number of tests for moderator variables (factors that cause under- or overestimates of the sex difference) and found strong evidence for two: these were the type of test and the tendency of some universities selectively to recruit either brighter men or brighter women. In the presence of strong moderators, many of the studies in the sample provide biased estimates of the sex difference in IQ score.

It is clear from the box plot (Fig. 1) that the Mexico results conform to estimates from the most male-biased samples, which provide substantial underestimates of the sex difference in IQ. Given the strong probability of bias in this sample, to weight it by its sample size (9,048) would risk a serious underestimate of the population sex difference in IQ. For this reason, we followed the advice of a definitive article on meta-analysis10 and took the median of estimates, including Mexico9, which equated to 4.6 IQ points.

Figure 1: Selection biases in IQ measurements.
figure 1


A comparison of Mexico, on the d-score (male mean minus the female mean, divided by the within-group standard deviation) difference in IQ, with samples showing pro-female and pro-male selection biases among university students. Horizontal bars represent the median; red rectangles, the interquartile range; tails, outliers. Sample sizes: female-biased studies, number of samples k = 10, n = 6,812; male-biased studies, k = 10, n = 4,296; Mexico study, k = 1, n = 9,048.

Many of Blinkhorn's difficulties stem from his assumption that our focus was on university students. This makes little sense, because the IQ difference in students is dependent on which population is considered, whereas the sex difference in the general population, our actual focus of interest, is highly stable3. This also explains our choice of Cohen's d (Fig. 1), as this provides a standard metric that partly controls for range restriction. According to accepted meta-analytical procedures11, a difference of 0.31d translates into a 4.6-point IQ difference in the general population: this is an underestimate and not the overestimate suggested by Blinkhorn.

Blinkhorn also implies that the Progressive Matrices may be biased against women. This issue has been investigated12 by using the conservative procedure of eliminating possibly biased items, identified by methods of differential item functioning: that analysis showed negligible evidence of bias.

However, we agree with Blinkhorn on the need for large representative samples, which is why we continue3,4 to make use of these.