Statistical Tests Shows Greater Male Variance
The table above is from the new study in Science Magazine "Gender Similarities Characterize Math Performance" (abstract free, $10 for full study) recently discussed here on CD, in the WSJ, and on Marginal Revolution.
From p. 494-495 of the study: "The hypothesis that the variability of intellectual abilities is greater among males than among females and produces a preponderance of males at the highest levels of performance was originally proposed over 100 years ago. The variance ratio (VR), the ratio of the male variance to the female variance, assesses these differences. Greater male variance is indicated by VR > 1.0. All VRs, by state and grade, are >1.0 (see table above). Thus, our analyses show greater male variability, although the discrepancy in variances is not large (bold italics added)."
Actually, I don't think that is true, I think the difference in male-female variances IS very large, and is stastistically significant at the highest possible level of significance (.001 level). Here's why:
The statistical test for differences in variance is conducted by comparing the variance ratio to the critical values in an F-test table (test explained here and here), adjusted for sample sizes. Comparing the Variance Ratios in the table above (from 1.11 to 1.21) to the critical F-value of 1.06 for the .001 level of significance with large sample sizes > 1000 (F-table here), suggests that ALL of the variance ratios in the table above are statistically significant at the .001 level of significance.
In other words, the variance of male intelligence (based on standardized math tests) is significantly greater than the variance of female intelligence at even an early age (second grade), at the highest possible level of statistical significance (.001), and the statistically significant difference in male-female variance actually gets greater over time.
Bottom Line: The authors of the study apparently made a conclusion based on "eyeballing the data" ("the discrepancy of variance is not large"), when a statistical F-test of differences in variance shows that the discrepancy of variance is actually VERY LARGE, and is statistically significant at the .001 level (meaning that there is only a 1-in-a-1000 chance that we would find these results purely by chance, and a 99.9% chance that we have established a statistical difference in variances).