Mathematics and Education

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The Solitary Statistic

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Note: This is part of a longer article published in the Journal of Humanistic Mathematics “Rumors of our rarity are greatly exaggerated: Bad statistics about women in science.”

In 1980, an article in Science reported large gender differences in scores on the quantitative section of the SAT (known as the SAT-M) taken by seventh and eighth graders.[i] There was no pretense that these occurred in a random sample. About 10,000 students had taken the test as part of a talent search for a program at Johns Hopkins University. The Science article resulted in headlines such as “Do Males Have a Math Gene?” (Newsweek) or “The Gender Factor in Math” (Time).[ii]

Three years later, talent search statistics were again featured in Science.[iii] Between 1980 and 1983, about 64,000 students had participated. Two hundred and eighty of them scored 700 or above on the SAT-M—about 13 boys to every 1 girl.

During the next two decades, the talent searches continued at Johns Hopkins and were initiated at other universities, but—vampire-like—the 13 to 1 statistic never aged. Until 2005, it was reported without later statistics in journal articles (Behavioral and Brain Science,[iv] 1988; Current Directions in Psychological Science,[v] 1992; Psychological Scientist,[vi] 2000), scholarly books (Male, Female: The Evolution of Human Sex Differences,[vii] 1998; International Handbook of Giftedness and Talent,[viii] 2000; The Blank Slate: The Modern Denial of Human Nature,[ix] 2002; Gender Differences in Mathematics,[x] 2004). In 1991, the statistic appeared in a popular book Brain Sex: The Real Difference Between Men and Women[xi]—still in print and referenced by a more recently published popular book (Boys and Girls Learn Differently!,[xii] 2001). In 2003, the statistic appeared—still unaccompanied—in The Essential Difference: Male and Female Brains and the Truth About Autism.[xiii]

So, what’s the problem with reporting, years later, a solitary statistic from 1983? Nothing—if you are interested in discussing only what was known in 1983. However, to report this statistic without related later statistics is to suggest that nothing has since changed or more recent information does not exist. But, in Johns Hopkins talent search statistics collected between 1984 and 1991, the average 700-or-above boy to girl ratio was 5.7. The sample size was 243,428, considerably larger than the earlier samples. Talent searches conducted by Duke University between 1981 and 1992 produced an average 700-and-over ratio of 5.6. The sample size was 308,397. These findings were reported in conference proceedings rather than a high-circulation science magazine. They did not make headlines. In 2005, Hopkins researchers reported in High Ability Studies, a journal on giftedness, that the 700-and-over ratio had dropped to 3. New ratios were also reported in a letter to the editor of the Johns Hopkins Magazine in 1997 and an interview in the Chronicle of Higher Education in 2005.[xiv]

Talent Search Sample Sizes With 700-and-Over Ratios

year N N scoring 700 or above M/F Ratio
Total M F M F Scores ≥ 700

Hopkins

1972–1979a 9,927 5,674 4,253
1980–1982b 39,820 19,883 19,937 113 9 12.6
1984–1991b 243,428 122,185 121,063 622 106 5.7
1997c 4
2005d 3

Nationwide

1980–1982a ~24,000e 147 11 13
1983f 121 12 10
1980–1983g 268 23 12

Duke

1981–1983h 39,754 19,157 20,597 32 3 10.7
1984–1986 73,278 35,424 37,854 54 6 9.0
1987–1989 92,268 44,642 47,626 94 6 15.7
1990–1992 103,097 50,231 52,866 91 33 2.8
1981–1992 308,397 149,454 158,943 271 48 5.6

See endnote for sources.[xv]

In 2006, these statistics were brought to more general attention in background material for a petition from the Association for Women in Mathematics. (Disclosure: I was then the president elect and helped to compile this material. For details, see my article in the Mathematical Association of America’s newsletter FOCUS.[xvi])

In 2007, old and new ratios were given in two publications addressed to a wide academic audience: a book called Why Aren’t More Women in Science? and an article in Psychological Science in the Public Interest.[xvii] However, a popular book published a year later (The Sexual Paradox: Men, Women, and the Real Gender Gap[xviii]) cited only the 13 to 1 ratio.

This is the case for some, but not all,[xix] chapters of The Science on Women and Science, “a collection of articles by distinguished scholars,” published in 2009. It was edited by Christina Hoff Sommers, whose claim begins this essay.

Talent Search Ratios Cited in The Science on Women and Science

Chapter author Ratio cited and description of population
Simon Baron-Cohen

p. 13

13 to 1 “among individuals who score above 700 (out of a possible 800) points, the sex ratio is thirteen to one (men to women).” Baron-Cohen cites Geary’s 1996 article in Behavioral and Brain Sciences which gives the source, “The ratio of boys to girls at the lower end of SAT-M scores is a rather modest 1.5:1, but increases to 13:1 for those scoring > 700 (Benbow & Stanley 1983).”
Jerre Levy &

Doreen Kimura

p. 214

11 to 1 “among those [children aged 12 or 13] who scored 700 or above on the math SAT.”
Amy Wax

p. 163, note 27

13 to 1 in “studies of profoundly gifted early adolescents.” New ratios are not given, Wax writes “that pronounced male advantage has strongly moderated recently” and cites sources that give the ratios.
Richard Haier

p. 192

3 to 1 down from 13 to 1 in Johns Hopkins studies of mathematically precocious youth.

In March 2010, Sommers wrote in Forbes Magazine that efforts to encourage women in science “should take into account the true state of the research on gender and science—not just the assertions of impassioned activists.”

It may be more difficult that Sommers thinks to agree on the “true state of the research on gender and science,” but researchers can, at least, endeavor to cite current statistics accurately and to interpret them with care.

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[i] C. Benbow & J. Stanley, “Sex Differences in Mathematical Ability: Fact or Artifact?,” Science, 210, no. 12 (1980): 1262–1264.

[ii] Facsimiles of these headlines are shown on p. 377 of Eccles & Jacobs, “Social Forces Shape Math Attitudes,” Signs, 11, no. 2 (1986): 367–380.

[iii] C. Benbow & J. Stanley, “Sex Differences in Mathematical Reasoning Ability: More Facts,” Science, 222, no. 4627 (1983): 1029–1031.

[iv] C. Benbow “Sex Differences in Mathematics,” Behavioral and Brain Sciences, 11 (1988): 169–183, see p. 172.

[v] D. Lubinski & C. Benbow, “Gender Differences in Abilities and Preferences Among the Gifted: Implications for the Math/science Pipeline,” Current Directions in Psychological Science, 1, no. 2 (1992): 61–66, see p. 62.

[vi] C. Benbow et al., “Sex Differences in Mathematical Reasoning Ability at Age 13: Their Status 20 Years Later,” Psychological Science, 11, no. 6 (2000): 474–480, see p. 474.

[vii] D. Geary, Male, Female: The Evolution of Human Sex Differences, American Psychological Association, 2002, see p. 315. A revision was published in 2009.

[viii] K. Heller et al. (Eds.), International Handbook of Giftedness and Talent (2nd Ed.), Elsevier, 2000, see p. 640.

[ix] Steven Pinker, The Blank Slate, Viking Penguin, 2002, see pp. 344–345.

[x] A. Gallagher & J. Kaufman (Eds.), Gender Differences in Mathematics: An Integrative Pyschological Approach, Cambridge University Press, 2004. Chapters 1 and 2 discuss the attention given to the statistic, e.g., pp. 14, 26. Other chapters cite it as evidence of the distribution of mathematical ability or performance, e.g., pp. 66, 189.

[xi] A. Moir & D. Jessel, Brain Sex: The Real Difference Between Men and Women, Carol Publishing Group, 1991, see p. 16.

[xii] M. Gurian, P. Henley, & T. Trueman, Boys and Girls Learn Differently!, Jossey-Bass, 2001, cites Moir & Jessel’s book, see also pp. 16–17.

[xiii] S. Baron-Cohen, The Essential Difference: Male and Female Brains and the Truth about Autism, Basic Books, 2003, p. 74. Although Benbow & Stanley, 1983 is cited on p. 72, the 13 to 1 ratio makes its appearance on p. 74 with no mention of the talent search and no footnote: “if you look at those people scoring above 700, the sex ratio is 13:1 (men to women).”

[xiv] J. Stanley, Letter to the editor, Johns Hopkins Magazine, September, 1997; R. Monastersky, “Primed for Numbers?,” Chronicle of Higher Education, 51, no. 26 (2005): A1.

[xv] Table sources.

a Calculated from C. Benbow & R. Benbow, “Biological Correlates of High Mathematical Reasoning Ability,” in Progress in Brain Research (Vol. 61), G. De Vries et al. (Eds.), Elsevier, 1984, p. 472.

b L. E. Brody, L. B. Barnett, & C. J. Mills, “Gender Differences Among Talented Adolescents: Research Studies by SMPY and CTY at Johns Hopkins,” in Competence and Responsibility: The Third European Conference of the European Council for High Ability, K. A. Heller & E. A. Hany (Eds.), Hogrefe & Huber, 1994, p. 206.

c J. Stanley, Letter to the editor, Johns Hopkins Magazine, September, 1997, http://www.jhu.edu/~jhumag/0997web/letters.html

d L. E. Brody & C. J. Mills, “Talent Search Research: What Have We Learned?,” High Ability Studies, 16, No. 1 (2005): 97–111.

e C. Benbow and J. Stanley, “15:1 Certainly Isn’t ‘Catching Up’!,” Psychological Reports (1983), p. 656 report a different ratio and an overall sample size of 23,736.

f Calculated from Benbow & Benbow, 1984 and C. Benbow “Sex Differences in Mathematics,” Behavioral and Brain Sciences, 11 (1988): p. 172.

g C. Benbow, “Sex Differences in Mathematics,” Behavioral and Brain Sciences, 11 (1988), p. 172.

h All Duke statistics from D. Goldstein & V. Stocking, “TIP Studies of Gender Differences in Talented Adolescents,” in Competence and Responsibility: The Third European Conference of the European Council for High Ability, K. A. Heller & E. A. Hany (Eds.), Hogrefe & Huber, 1994.

[xvi] C. Kessel, “Perceptions and Research: Mathematics, Gender, and the SAT,” Focus, 26, no. 9 (2006): 14–15.

[xvii] S. Ceci & W. Williams (Eds.), Why Aren’t More Women in Science?, American Psychological Association, 2007; D. Halpern et al., “The Science of Sex Differences in Science and Mathematics,” Psychological Science in the Public Interest, 8, no. 1 (2007): 1–51.

[xviii] Susan Pinker, The Sexual Paradox: Men, Women, and the Real Gender Gap, Scribner, 2008, p. 25. Interestingly, Why Aren’t More Women in Science?, which mentions later talent search ratios, is cited in The Sexual Paradox, but the later talent search ratios are not. The author did not reply to my query about this matter.

[xix] C. H. Sommers, Ed., The Science on Women and Science, American Enterprise Institute, 2009. The 13 to 1 ratio is cited by Baron-Cohen on p. 13; Levy & Kimura give the ratio as 11 to 1 on p. 214. In note 27 on p. 163, Wax gives the 13 to 1 ratio, says that “it has strongly moderated recently,” and cites Halpern et al., 2007 and Ceci & Williams, 2006 without giving later ratios. On p. 192, Haier says “three to one in recent data, down from thirteen to one in the early 1970s [sic] data.”

Written by CK

March 9, 2010 at 4:16 pm

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