12 August 2007

Appendix to Ennumeration Problem: Sexual Orientation Statistics

(Main article)

Folk traditions on sexual orientation are difficult to generalize, but according to official Canadian statistics on the matter, 1.3% of men and 0.7% of women self-identified as homosexual; 0.9% of women and 0.6% of men self-identified as bisexual. The US Center for Disease Control (CDC) has conducted studies of sexual orientation (the Bureau of the Census has not); according to this 2005 report (PDF),
Approximately 1 percent of men and 3 percent of women 15–44 years of age have had both male and female sexual partners in the last 12 months (table B). Among females, 5.8 percent of teens and 4.8 percent of females 20–24 years of age had had both male and female partners in the last 12 months; percentages were lower at ages 25–44.

The percentages of men and women who reported that they think of themselves as homosexual or bisexual are roughly equal at 4.1 percent. This represents about 2.27 million men and 2.29 million women 18–44 years of age
[4c; stats for sexual attraction suggested nearly identical ratios of sexual orientation, etc. between men and women]
It's interesting to note the CDC statistics tend to rely less on survey techniques ("self-reporting") and more on construction from medical records. It's also interesting to note that CDC research assumes much greater ambiguity in sexual orientation, but also differs from nearly all systems of self-reporting in (a) higher incidence of homosexual orientation than other official surveys, and (b) a higher incidence of homosexuality among women than men.

The well-known Kinsey Report is usually taken to mean that "10% of the population are gay," which is based on the Kinsey rating system (1 = exclusively hetero, 7 = exclusively gay, 2-6 are gradients in between); this refers to findings that 11.6% of white males (ages 20-35) were given a rating of 3 (about equal heterosexual and homosexual experience/response) throughout their adult lives. Even accepting the Kinsey Report findings as accurate, that would still be using a "one-drop" rule for homosexuality. In fact, the Kinsey Reports have serious problems as statistical references on sexuality, including very high proportions of prison inmates, male prostitutes, and (naturally) people willing to discuss the topics.

Mathematics of Sexual Partners
In assessing the explanation of sexual partner estimates, one possible explanation is that the immense disparity in reports by men and women reflects a greater number of same-sex relationships among men. Using a recent study by the National Center for Health Statistics (NCHS), men reported an average of seven partners, while women reported an average of four. Now, an obvious point to acknowledge is that the men reported an average of 7 women, while the women reported an average of four men. However, let's pretend that objection doesn't exist and plow ahead, since I'm merely illustrating a mathematical point.

The total number of relationships between men and women must be equal, since each female relationship with a man corresponds to precisely one male relationship with a woman. So the difference is RM - RF = 3. This is average number of same-sex relationships that men have in excess of the number experienced by women over the course of their lifetime.
2Rmm + Rmf = 7
2Rff + Rmf = 3
The pair of linear equations above features 3 unknowns; setting Rff = 0, Rmf = 3 and 2Rmm = 4, so Rmm = 2, or 28% of all male relationships. That is, to put it mildly, a bit high, especially since the disparity for the USA is rather low. Other international comparisons report ratios of >3:1, mostly in Latin countries. For the UK, it's 2. But based on the information above, it's reasonable to suspect at least some of the women's relationships are lesbian (Rff). How many? According to my calculations, the mean probable interval between lesbian partners is 4.14 years (with some possible overlap). According to the same reporting, the MPI between gay partners is 0.84 years (again, with some possible overlap). Thus, we can gather that the somewhat-smaller "pure lesbian" community reports about one-fifth the number of lesbian relationships, but I have no way of estimating the number of lesbian relationships among bisexual women, or gay relationships among bisexual men. So, while I'm already taking this exercise much too seriously, let's just assume 5Rff = Rmm:
10Rff + Rmf = 7
2Rff + Rmf = 3
Therefore Rff = 0.5, Rmf = 2, and Rmm = 2.5, which means 35% of male relationships are gay.

All this is totally silly, of course, since I'm already ignoring the fact that we have much more detailed self-reporting in the much-cited CDC study. For example, based on prior experience with sex surveys, and the well-known "pairwise paradox," the 2005 CDC study mainly focused on sexual activity in the last 12 months. While it's worth pointing out that the 12-month study period has a much closer mutual correspondence (e.g., 14.8% of men had no sexual partner vs. 13.9% of women; 62.2% of men had exactly one, vs. 66.8% of women; 17.6% of men had >1 partner, vs. 12.7% of women), there are still a few curious disparities: of those reporting two or more partners—which, incidentally, includes those who transitioned from one relationship to another in the last 12 months—3.1% of women reported having partners of both sexes, vs. 1% of men.
ADDITIONAL SOURCES & READING: William D. Mosher, Anjani Chandra, & Jo Jones , "Sexual Behavior and Selected Health Measures: Men and Women 15–44 Years of Age, United States" (PDF), Division of Vital Statistics, CDC (2002); Statistics Canada, "Canadian Community Health Survey" (2004);

A search of Kinsey Institute publications suggests that the word "homosexual" was last used in 1990.

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