24. de Vries (2004): 1064.
25. de Vries and Forger (2015).
26. Murray (2003).
27. A good one-source summary of the evidence is Lehre, Lehre, Laake et al. (2009).
28. Darwin (1900).
29. Remarkably, eight Nobel Prizes had been won using research on fruit flies through 2017: Thomas Hunt Morgan, 1933; Hermann Muller, 1946; George W. Beadle and Edward L. Tatum, 1958; Max Delbrück, Alfred D. Hershey, and Salvador E. Luria, 1969; Edward B. Lewis, Christiane Nüsslein-Volhard, and Eric F. Wieschaus, 1995; Richard Axel and Linda Buck, 2004; Jules Hoffmann, Bruce Beutler, and Ralph Steinman, 2011; Jeffrey Hall, Michael Rosbash, and Michael Young, 2017.
30. Bateman (1948). My summary is drawn from Trivers (1972): 53–54.
31. Trivers (1972): 56, 55. See also Williams (1966).
32. Geary (2017): 357.
33. Clutten-Brock (1989).
34. For the most comprehensive literature review of sexual selection in humans and across species, see Geary (2010): chapters 2–8. Archer and Mehdikhani (2003) has a concise review of the major theoretical approaches. See also Pomiankowski and Møller (1995).
35. Del Giudice, Barrett, Belsky et al. (2018).
36. Stewart-Williams and Thomas (2013).
37. The quotation from Reinhold and Engqvist continues:
Theoretical considerations reveal a slightly more complicated picture. Under the simplest genetic assumptions—alleles contribute additively to trait expression (heterozygotes are intermediate to homozygotes), and they have equal hemizygous and homozygous effects on trait expression (e.g., due to dosage compensation)—a polymorphic sex chromosome-linked locus will contribute twice as much to trait variance in the heterogametic sex, as it will to variance in the homogametic sex. Quantitative traits are of course polygenic and are likely influenced by genes spread across the sex chromosome and the autosomes. The contribution of the sex chromosome to trait variance should therefore depend on its relative size within the genome (i.e., the proportion of genes that it carries), with trait variance differences between the sexes being less pronounced in species with small sex chromosomes, and more pronounced in species with large sex chromosomes. In addition, differences will be dampened by environmental effects (i.e., will be lower for traits with low heritability). Even so, qualitative predictions of the model remain valid for any trait that is to some extent heritable irrespective of sex chromosome sizes. (Reinhold and Engqvist (2013): 3662–63).
38. Ritchie, Cox, Shen et al. (2018): 8.
39. Author’s analysis, National Health and Nutrition Examination Survey, 2015–2016 (www.cdc.gov). The sagittal abdominal diameter represents the mean of four measures. The blood pressure results represent the mean of the first three readings.
40. The greater female variability in BMI must be assessed in light of the much larger effect size for height (–1.91) than for weight (–0.62), which are the two components used to calculate BMI. The equation for computing BMI is w/h2, where w is weight in kilograms and h is height in meters.
41. Following Katzman and Alliger (1992), all mean VRs reported in this appendix use the mean of log-transformed values of the VRs. To see why using logged values is necessary when calculating means, recall that a ratio is the arbitrary choice of a numerator and denominator. Consider two tests in which the male variance is divided by the female variance. In the first test, the male variance is 100 and the female variance is 80, giving a VR of 1.25. In the second test, the male variance is 80 and the female variance is 100, giving a VR of 0.80. The simple mean of 1.25 and 0.80 is 1.025, falsely indicating that average male variance is slightly higher than female variance. The logged values of 1.25 and 0.80 are +0.223 and –0.223, leading to a mean of zero, which correctly transforms to a VR of 1.00.
42. Author’s analysis, Gordon, Churchill, Clauser et al. (1989).
43. Author’s analysis, Dodds, Syddall, Cooper et al. (2014): Table 2.
44. Author’s analysis, Janssen, Heymsfield, Wang et al. (2000): Table 1.
45. It is not clear how much the adjustment for BMI was affected by sample selection. The authors specify that they built variability in adiposity into the sample. One indication that this significantly affected the male-female distribution of BMI is that the variance ratio for weight was higher for women than for men (VR = 0.79). This is in striking contrast with the results from the NHANES nationally representative sample (VR = 1.25), the Nordic Reference Interval Project used in the Norwegian study (VR = 1.13), and the Army’s anthropometric study (VR = 1.77), which was representative of active-duty uniformed Army personnel.
46. Buss (1989).
47. The authors also used meta-analyses of two traits that are not believed to be involved in sexual selection: anger as a personality trait (“touchiness”) and self-esteem. Neither showed a significant sex difference in either effect size or variance ratio. Archer and Mehdikhani (2003): Table 4.
48. Archer and Mehdikhani (2003): Table 4. The reported means were expressed in log-transformed variance ratios. I converted them back to the standard metric.
49. The huge effect size of 2.00 for preferred age difference is explained by the way the question was asked, which resulted in men in all cultures universally giving a negative number of years and women giving a positive number of years. The actual means across the 37 cultures were –2.66 years for men and +3.42 for women. That’s appropriately seen as a big sex difference in preferred age, but it’s a small one—just 0.76 years—if instead the respondents had been asked to give the preferred age difference between the man and the woman (men and women alike agree that it’s better if the man is older, and by a similar age difference).
50. This and the rest of the statistics are based on Borkenau, McCrae, and Terracciano (2013): Table 1.
51. There was a tendency for male variability to be greater in the more gender-egalitarian countries. The mean VR for the 10 most gender-equal countries on the Gender Inequality Index (GII) was 1.10; for the ten most gender-unequal countries, it was 1.03. But the relationship was not strong or consistent.
52. The six studies were Project Talent, with a sample of 73,425 15-year-olds (1960); the National Longitudinal Study of the High School Class of 1972 (1972), with a sample of 16,860 12th-grade students; the National Longitudinal Study of Youth (1980), with a sample of 11,914 noninstitutionalized 15-to 22-year-olds; the High School and Beyond Study (1980) with a sample of 25,069 12th-grade students; the National Educational Longitudinal Study (1992) with a sample of 24,599 8th-grade students as of 1988; and the National Assessments of Educational Progress from 1971 to 1992, with varying but extremely large samples of 17-year-olds enrolled in school. Hedges and Nowell (1995).
53. Hedges and Nowell (1995): Table 2.
54. Hedges and Nowell (1995): 44.
55. Hedges and Nowell (1995): 44.
56. Data for 1971–92 from Hedges and Nowell (1995): Table 3. Data from 2002 to 2015 from the Department of Education Statistics Data Explorer.
57. Arden and Plomin (2006).
58. Feingold (1994).
59. The “other political entities” were Macau and Hong Kong.
60. Machin and Pekkarinen (2008): Supplemental Tables 1 and 2. The authors also analyzed TIMSS and PIRLS scores, reporting that both showed significantly higher male variance in most (though not all) countries. Table S4.
61. Author’s analysis, PISA-2015 data. Variance ratios were averaged using logged values, and the result converted back to the ratio metric.
62. Feingold (1994): 83. He had also taken that position in earlier articles.
63. Warne, Godwin, and Smith (2013).
64. The figure shows the predicted and actual values calculated using the observed male and female means. A parallel plot that assumed equal means showed the same pattern with only mild attenuation. For values based on sex-specific means, 83 percent of the actual ratios were higher than predicted; for values based on the assumption of equal means, the corresponding figure was 73 percent.
The minority of cases that were below the diagonal (the actual values were smaller than the predicted values) were even closer to the diagonal in the case of the equal-means calculation than in the sex-specific calculation. Russell Warne also provided breakdowns by sex for subtests in the Armed Services Vocational Aptitude Battery (ASVAB) administered to the 1979 cohort of the National Longitudinal Survey of Youth. But the sample size was 11,914, meaning that only the 95th percentile and 98th percentile categories could be expected to have interpretably large samples. A further problem was that the VRs and effect sizes for three of the subtests (on auto shop info, mechanical comprehension, and electronics information) were so large that hardly any females got scores in the top percentiles. That said, the results were consistent with those from the Early Childhood Longitudinal Study. For the 95th percentile, the most interpretable category, the median predicted male-female ratio was 2.16 compared to 2.11 for the actual male-female ratio (the median is given rather than the mean because of the extremely large VRs for auto shop info, mechanical comprehension, and electronics information).
65. Johnson, Carothers, and Deary (2008): 526.
66. Author’s calculations of the predicted values based on Johnson, Carothers, and Deary (2008): Table 1. Actual values were given in Johnson, Carothers, and Deary (2008): 526.
67. Johnson, Carothers, and Deary (2008): Table 1.
68. Johnson, Carothers, and Deary (2008): 529.
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