Annals of Essentialism: sexual orientation and rhetorical asymmetry

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There's been a lot of discussion, both in the mainstream media and on the intertubes, of a study that came out a couple of days ago in the Proceedings of the National Academy of Sciences: Ivanka Savic and Per Lindström, "PET and MRI show differences in cerebral asymmetry and functional connectivity between homo- and heterosexual subjects", PNAS, 6/16/2008.

And in this case, the study's rhetorical reception is more interesting than the study itself.

Let's start with a minor point of interest: the way that MSM editors chose to spin their headlines. Like the study's title in PNAS, the headline of the PNAS press release treated the four categories in the study equivalently: "Symmetry of Homosexual Brain Resembles That Of Opposite Sex, Swedish Study Finds". And a few news outlets took this same path: "Gay Brain Structure Similar to Straight Opposite Sex", Bloomberg; "Homosexual brain resembles that of opposite sex", AFP; "Scientists Link Brain Symmetry, Sexual Orientation", Wired News; "Gay brains structured like those of the opposite sex", New Scientist.

However, the great majority of headline writers took another approach.

Some laid it out as a discovery about homosexuals: "What the Gay Brain Looks Like", Time; "Scans see 'gay brain differences'", The BBC; "Brains of homosexuals are different", Times of India.

Others — the largest group — laid it out in terms of the similarity of homosexual men and heterosexual women: "Gay men and heterosexual women have similarly shaped brains, research shows", The Guardian; "Gay men and straight women share brain detail", Reuters; "Study: Gay Men, Straight Women Share Brain Characteristics", Fox News; "Gay men and heterosexual women have similar brains, study finds", The Telegraph; "Gay Men, Straight Women Have Similar Brains", Washington Post; "Scans find gays' feminine side is in the brain", Times Online; "Gay Men, Straight Women Have Similar Brains", National Geographic; "Why straight women and gay men get along so well", 680 News; "Gay Men, Straight Women Share Same Brain", eCanada Now; "Women 'share same emotional brain traits' as homosexual men", Daily Mail; "Gay men and straight women have similar brains", Salon.

I found only one headline that highlighted the similarity of homosexual women and heterosexual men, and this was a painful pun in the satirical IT rag, The Register: "Lesbians like straight men, researchers find". (Well, there was a blog post "Straight men and gay women have similar brains" by Daniel Cressey at Nature, making this same meta-analytic point about the distribution of headlines.)

There were no headlines of the form "What the straight brain looks like", or "Brains of heterosexuals are different, study finds".

Scientific American's headline was ambiguous, and false on both readings: "Study Says Brains of Gay Men and Women Are Similar". This might attribute similarity to "gay [men and women]", i.e. to gay men and gay women; or it it might be parsed as "[gay men] and women", i.e. gay men and women of whatever kind. Either way, it's wrong.

But much more interesting than the headlines, in my opinion, was the uniformly essentialist language in which all sources describe the study's results. In this respect, the journalists all follow the PNAS press release:

Ivanka Savic and Per Lindström, of the Department of Clinical Neuroscience at the Karolinska Institute in Stockholm, Sweden, now report that the brains of heterosexual men and homosexual women are slightly asymmetric—the right hemisphere is larger than the left—and the brains of gay men and straight women are not. [emphasis added]

It's natural to read this as a prediction about the brains of individual men and women. If you're a heterosexual male or a homosexual female, then your cerebral hemispheres will be slightly asymmetric. If you're a homosexual male or a heterosexual female, then your cerebral hemisphere will not have this property. Right? Nope, sorry, not even close.

Let's ignore the problematic assumption that all humans divide neatly into these four categories of sexual orientation, and assume that we're talking about people at the extreme ends of the Kinsey scale (though I don't think this is actually true of the study in question). [Added later: yes it was -- the HeM and HeW were 0, the HoM 6, and the HoW 5.5 on the Kinsey scale -- sorry, I missed that earlier.] What did the study actually find about brain symmetry? Here's the crucial table (click on the image for a larger version):

Among the 25 heterosexual males in the study, the average size of the right cerebral hemisphere was 624 cc, and the average size of the left cerebral hemisphere was 612 cc, or about 1.9% smaller. Among the 20 homosexual women in the study, the right hemisphere averaged 548 cc, while the left hemisphere averaged 543 cc, or about 1.5% smaller.

OK, "slightly asymmetric", we're with the program so far.

And the 25 heterosexual women averaged 581 cc on the right, and 581 on the left; while the 20 homosexual males averages 608 on the right and 609 on the left.

OK, check. Slight asymmetry for the straight males males and the lesbians, not for the gay guys and the straight women.

But wait a minute. There are those ± thingies, the "standard deviations". If the cerebral-hemisphere volumes are distributed "normally", as we would expect, and if the estimates of means and standard deviations in the table were actually the true population values values, then we can calculate what the expected distribution of hemispheric volumes (and the expected distribution of hemispheric asymmetries) will look like, for individuals within each sex-by-sexual orientation category. And when we do that, a completely different picture emerges.

For the heterosexual males in the study, the distribution of right and left hemispheric volumes is predicted to look like this:

And among the individuals in this group, the right hemisphere will be greater than the left hemisphere about 57.9% of the time, while the left hemisphere will be greater about 42.1% of the time. (Assuming independence — which is an inappropriate assumption, since the variables are probably correlated…) This predicts that among the 25 HeM subjects in the study, 14 should exhibit the "characteristic" right-greater-than left asymmetry, while 11 do not.

For the 25 HeW women, since their average values are equal, half will be predicted to be asymmetrical in one direction, and half in the other — this predicts that 12 or 13 should show the right-right-than-left asymmetry supposedly characteristic of heterosexual males, while 12 or 13 do not.

If we do the same calculations for the means and standard deviations reported for the other categories, we get predictions that might have been presented as follows:

Rightward hemispheric asymmetry was found in the brains of 14 of 25 heterosexual males and 11 of 20 homosexual females, but in only 13 of 25 heterosexual females and 10 of 20 homosexual males.

How much media play do you think the study would have gotten, if the results had been spun like that?

Or to put it another way, how many readers of the media descriptions do you think understood the story in those terms?

[added later: As Brett points out in a comment, the fact that the hemisphere sizes are correlated means that assuming independence decreases the effect. To allow for this, I should instead look at the by-category means and standard deviations of their "asymmetry index" AI = (R-L)/(R+L), and estimate how often this will be greater or less than 0. This predicts results like:

Rightward hemispheric asymmetry was found in the brains of 18 of 25 heterosexual males and 17 of 20 homosexual females, but in only 11 of 25 heterosexual females and 10 of 20 homosexual males.

If that's how it came out, it's a more striking result -- but still far from categorical...]

I'm not arguing that this paper's results are scientifically meaningless, just that they don't mean what nearly everyone reading the media coverage — and the PNAS press release — thinks they mean.

[While we're discussing the details of the study, I should point out one other possible issue. The authors tell us that "The inter-rater correlations was [sic] 0.85 … for cerebral hemispheres", which is not a wonderful number, given that we're looking for a one or two percent difference in samples of 20 or 25.]

The re-spun numbers I've just given are the likeliest outcomes given the cited means and standard deviations, but the actual counts were no doubt different, because with such small sample sizes, the outcomes for different samples are likely to vary quite a bit. The study's authors don't give us the actual numbers, but they do give some information to suggest that the situation is not quite as bad as my numbers suggest, though it is still a long way from the essentialist implications of their discussion:

A post hoc evaluation detected asymmetry exceeding two standard deviations of that in HeW (who were hypothesized to have symmetrical volumes) in 1 HeW, 4 HoM, 7 HoW, and 12 HeM.

I'm a bit puzzled about how 12 out of 25 HeM could wind up with asymmetries greater than 2 standard deviations, given a difference in means of 12 cc on standard deviations of 43 and 41, i.e. mean left and right hemispheres differing by about 0.28 standard deviations. Either there's something funny about the distribution, or I'm not understanding the statement correctly. But even on this way of presenting things, which I'm sure was selected to make the groups seem as different as possible, it's clear that we're looking at a graded set of differences, not a categorical distinction.

[added later: Oh, I think I see what they did. They're looking at the distributions of their "asymmetry index" (AI), (R-L)/(R+L), expressed in terms of the standard deviation of the AI for HeW, which was 0.005. Thus the average HeM AI of 0.012 ±0.02, which differs from 0 by 0.012/0.02 = 0.6 of a standard deviation in terms of its own standard deviation, differs from 0 by 0.012/0.005 = 2.4 if you measure it in terms of the variability in the HeW distribution. So if you look at the individual HeM AIs, it could well be true that almost half of them are more than two HeW standard deviations away from zero. If this is what they did, it's is tricky language at best, it seems to me...]

Where does this confusion come from? Well, there's statistical illiteracy on the part of flacks, journalists and the general public. And this ignorance is fertile ground for a certain kind of quasi-dishonest hucksterism on the part of the flacks (who are paid to make things seem more interesting), the journalists (who will get better placement for more interesting-seeming stories), and, alas, the scientists as well, who are also interested parties.

But from a more abstract perspective, perhaps the problem is a linguistic one. The modern English language lacks good resources for discussing sampled properties of groups, in the same way that the Pirahã language is inadequate for dealing with arithmetic (see "The Pirahã and us", 10/6/2007, for some additional discussion of this point).

You could argue that this is just a lexical and cultural problem. We already have words and phrases like "distribution" and "percentile" and "standard deviation" and "effect size"; maybe the problem is that most people don't understand these concepts, and even those that understand them don't bring them to mind when they should.

But I think it's not quite that simple. It's hard to banish plural nouns and other simple and natural ways of referring to groups, as in these quotations from the Savic and Lindström paper:

HeM and HoW showed a rightward cerebral asymmetry, whereas volumes of the cerebral hemispheres were symmetrical in HoM and HeW.

HeM and HoW had significantly asymmetrical hemispheric volumes … In contrast, no asymmetry was detected in HeW or in HoM.

And once statements of this kind are on the table, it's hard not to take them as shorthand for universally-quantified generalizations, or (more likely) assertions about group archetypes or prototypes.

I don't have a solution to propose. But it's clear to me that we have a problem.

[I should mention in passing that Savic and Lindström's results about PET-derived amygdala connectivity can't be evaluated in the way that I've evaluated their hemispheric asymmetry data, because they only present pooled group data, in which

Functional connectivity was defined as the extent to which normalized rCBF in seed VOIs covaried with pixel-based rCBF values across the investigated subjects. The normalized rCBF was extracted from circular (5-mm) VOIs covering the right and left amygdala ... Significant covariations ... were calculated by using the entire brain as search space (multisubject condition and covariate analysis within SPM2).

That is, they looked for covarying brain regions within all of the pooled data for heterosexual males, all of the pooled data for homosexual females, etc. As a result, I don't see any way to characterize the amount of individual variation within each sexual-orientation group, or to compare it to the differences between groups. Based on the nature of their experiments, and what I know about the amount of individual variation in such experiments, I suspect that if you tried classify individuals' sex and sexual orientation on the basis of this data, the results would not show any sort of crisp or categorical differentiation.

One other aspect of their study puzzled me. The most striking fact about the measured hemispheric volumes, it seems to me, were the differences between groups in overall brain size. Thus the total cerebral volumes were these:

HeM 1236
HeW 1162
HoM 1217
HoW 1091

The fact that the heterosexual men's brains (well, the cerebral cortex parts) were about 6.4% larger than the heterosexual women's brains is as expected. But the fact that the heterosexual women's brains were on average about 6.5% larger than the homosexual women's brains was not something that I expected. (And the effect size in this comparison is apparently about 1.7-1.9, guessing from the standard deviations of the hemispheric measurements, which is a pretty big effect.) The heterosexual men's brains were about 1.6% larger on average than the homosexual men's brains. (Here the effect size is probably only about 0.4 to 0.5.)

The authors don't comment on this -- maybe it's a well-known effect that I've missed, though I can't find it in a quick glance at the literature on the neurology of sexual orientation -- but I wonder about it. If it's real, it's a much larger effect than the differences in asymmetry, and it presumably means something important. If it's an artefact of some sort that doesn't replicate, then it calls other aspects of the study into question.]

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25 Comments »

  1. Pekka K. said,

    June 18, 2008 @ 8:36 am

    I appreciate it very much when someone takes the time to explain things the way they should be explained in proper journalism. What can I say: I wish more people understood and respected the field of statistics. I wish I understood it better. However, there is one minor typo (I presume) I can't resist pointing out.

    "satistical IT rag, The Register"

    Would that mean being satirical about statistics?

  2. Brett said,

    June 18, 2008 @ 8:47 am

    "The re-spun numbers I've just given are the likeliest outcomes given the cited means and standard deviations…."

    I do not believe that this is the case. You seem to have omitted one crucial factor–that there is a strong correlation between the volumes of the left and right hemispheres, which are each in turn correlated with overall head size. By treating the hemisphere sizes as independent, you have probably suppressed the measured effect, although I don't know the correlation between hemisphere sizes, so I can't evaluate the question quantitatively.

  3. Mark Liberman said,

    June 18, 2008 @ 8:58 am

    @Brett: I should have said "are the likeliest outcomes given the cited means and standard deviations, assuming independence. And you're right, the variables are surely correlated. Just one more reason why reviewers should insist, in studies like this, that the tables of raw measurements should be given.

  4. Mark P said,

    June 18, 2008 @ 9:17 am

    I appreciate this kind of analysis and hope you continue to do it. I fear that some researchers (although not necessarily these) are not familiar enough with statistics to do this themselves. I don't know how we could expect mainstream media to have even a glimmer.

    Also, given the small sample size, it wouldn't have been asking much for all the data to be shown.

  5. Leon said,

    June 18, 2008 @ 9:52 am

    I agree with your observations about the skewed presentation of the findings in terms of homosexual men and heterosexual women in MSM. However, I think you're being a little too premature in presuming "essentialism" — a term which could mean one of two things to me:

    1. The view that differences between e.g. people of different genders and sexual orientations are rigidly categorical rather than statistical.
    2. The view that biological phenomena determine gender or sexual orientation, rather that social/cultural factors or individuals' choices.

    Re 1:

    It's clear that we're looking at a graded set of differences, not a categorical distinction."

    Although our language may lack the means to describe it, I doubt many people understand these kinds of findings categorically, even if they're presented with a snappy, black-and-white headline. That said, there's a sense in which our precognitive faculties only work through broad generalizations. Most people would evaluate the statement "humans have two legs" as true, even though on further reflection, they may realize that they've ignored amputees, for example. Equally, "smoking causes cancer" seems to be a true statement, though of course it's also a "merely" statistical result — like all empirical knowledge.
    You suggest that the assertions in question are "shorthand for universally-quantified generalizations, or (more likely) assertions about group archtypes or prototypes". I think you're missing the fact that "universally-quantified generalizations" and "archetypes or prototypes" are equally just cognitive shorthand for strong statistical correlations. As in the smoking example, we use them all the time for economy of expression and ease of comprehension.

    In other words, I think almost nobody — at the "most conscious" level — reads the findings of these studies as ironclad categorical distinctions. But equally, we ignore outliers all the time in everyday communication and decision-making to save cognitive time.

    Let's ignore the problematic assumption that all humans divide neatly into these four categories of sexual orientation.

    I couldn't find that assumption in any of the headlines you selected, except by omission. Those who participated in the study presumably identified as "heterosexual" or "homosexual"; to include a Kinsey scale, or less common gender/sexual preference identifications (bisexual, transgender, third gender, etc.) would have made it considerably harder to find volunteers, statistically process results, etc.

    With respect to definition 2, although I only read the Guardian article, it did acknowledge that the direction of causality in this case isn't yet understood:

    Savic's team has yet to confirm whether the differences in brain shape are responsible for sexual orientation, or are a consequence of it. To find out, they have begun another study …

  6. Mark Liberman said,

    June 18, 2008 @ 10:08 am

    @Leon: My point about the headlines was that they mostly focus on the similarities between homosexual men and straight women, or on the brain characteristics of homosexuals, rather than on the similarities between homosexual women and straight men, or on the brain characteristics of heterosexuals.

    What I meant by "essentialism" is just that the articles — including the original PNAS report — talk about fairly small differences between overlapping group distributions as if they were categorical properties of all group members. Or at least all normal members of each group.

    And if you think that most people who read these articles understand this point, then you live in a world where people are more insightful than they seem to be in the world that I see.

  7. Matt said,

    June 18, 2008 @ 10:25 am

    I would suggest that a reason there's often confusion about these kinds of results is that the math neccessary to analyse them properly is, frankly, terrifying. And I've done at least some first-year statistics – if I'm in the ballpark but intimidated, I'd hate to think how people who have no experience at all feel.

    (That being said, I really think as many people should be forced to do statistics as possible, even though it's usually reviled, for this exact reason.)

  8. Mike Anderson said,

    June 18, 2008 @ 10:29 am

    Nice elaboration of the statistics. I'm using this post as an outside reading for my statistics students. Thanks.

  9. Mark Liberman said,

    June 18, 2008 @ 10:42 am

    Matt: …reason there's often confusion about these kinds of results is that the math neccessary to analyse them properly is, frankly, terrifying.

    With respect, I disagree. Often, the best route to clarity is not an elaborate statistical model, but rather a more direct presentation of the facts. (Not that I'm in any way opposed to modeling…)

    In most of the arguments of this sort that I've made (e.g. here), simple tables of counts or proportions, or simple plots such as histograms or scatter plots, provide most of what's needed for people to understand the situation. To the extent that I've brought in more elaborate statistics, it's usually because the basic data necessary to reconstruct the counts or proportions or histograms hasn't been published, and I have to work backwards from the model parameters that the authors do provide.

    And a small number of very basic statistical ideas, like "percentile" and "effect size", adds a lot to these simpler modes of data presentation.

    it's certainly true that there are often reasons to make use of conceptually more difficult things like multilevel regression, generalized linear models, and so on. But we'd be a lot better off, I think, if both scientists and journalists tried to make the basic pattern of facts clear. Unfortunately, the basic facts are often unable to support the superstructure of speculative interpretation that various parties would like to add on top. And the apparent interest of this superstructure is often inversely proportional to the strength of its empirical foundation.

  10. Dan4th @ Difference Blog said,

    June 18, 2008 @ 10:43 am

    Thanks for this. I had some real concerns about Savic and Lindstrom's findings, let alone the reportage (which I usually assume to be completely weird). You've addressed them really well.

    One of my biggest concerns with the study was the way the male-asymmetry was presented as an assumption, as something "we already know." I could find no backup in other literature for what seemed to be the baseline assumption of their study, and their citation for the source was Cahill's 2006 review.

    http://www.differenceblog.com/2008/06/hemispheric-asymmetry.html

  11. John Cowan said,

    June 18, 2008 @ 10:54 am

    What pitiable creatures we anglophones are: victims of an insidious Whorfian mind-lock. (Unfortunately, in this case I don't think learning Lojban will help.)

  12. Nick Z said,

    June 18, 2008 @ 11:04 am

    Shouldn't Nature's "Straight men and gay women have similar brains" come under your "similarity of homosexual women and heterosexual men" heading?

    But I don't think it really counts, since it's really a blog post pointing out that no-one has reported the study in that way.

    [myl: Oops -- you're absolutely right, I was asleep at the switch on that one. I've fixed it in the body of the post.]

  13. Orbis P. said,

    June 18, 2008 @ 11:10 am

    Toronto Star science journalism reaches a new low: http://www.thestar.com/article/444461

    The headline itself isn't a big problem — "Gayness linked to brain", meh; but here's the startling opening paragraph: "A new Swedish study showing important similarities between the brains of homosexual men and straight women provides important new proof that people are born gay".

    Eh? It does what? How? Where? Can we stress how important it is a few more times?

    I would say that people do understand these kinds of findings categorically, when they are so presented; Leon's proposition that there's tacit conscious knowledge that these prototypes are merely approximations sounds like something that'd be testable in an experiment — has this been done before? Anyone with a better grasp of social science care to comment?

  14. Leon said,

    June 18, 2008 @ 11:24 am

    What I meant by "essentialism" is just that the articles — including the original PNAS report — talk about fairly small differences between overlapping group distributions as if they were categorical properties of all group members. Or at least all normal members of each group.

    "Fairly small" being the operative phrase — in other words, the problem isn't essentialism per se, but the fact that these particular essentialist generalizations weren't justified by the strength of the data. The journos could have just misunderstood how significant the result was, without possessing especially "essentialist" attitudes towards gender/sexuality.

    I'm quibbling because articles like this one seem fairly common, which argue that it is not possible to establish biology as a determining factor in gender/sexuality, generally using terms like "essentialism", etc.

  15. Mark Liberman said,

    June 18, 2008 @ 11:26 am

    @ Orbis P.: …"provides important new proof that people are born gay".
    Eh? It does what? How? Where?

    I believe that a second interpretive tendency may be coming into play here: if something's shown to have correlates in brain anatomy and physiology, then it must be innate.

    I teased David Brooks for this in a post a couple of years ago:

    [Brooks] writes as if demonstrated group differences in brain activity, being "biological", must therefore be innate and essential characteristics of the groups, and not "socially constructed". But how else would socially constructed cognitive differences manifest themselves? In flows of pure spiritual energy, with no effect on neuronal activity, cerebral blood flow, and functional brain imaging techniques?

    The reporting on the Savic and Lindström article is a bit different, since the authors do go out of their way to argue that the differences they identify are innate. Their argument is not the strongest one ever seen, consisting basically in the assertion that the characteristics they examined are "unlikely to be directly affected by learned patterns and behavior". But the journalists are not inventing the innateness connection, they're just echoing what the scientists said, perhaps with a bit of amplification.

  16. Mark Liberman said,

    June 18, 2008 @ 12:12 pm

    Leon: I'm quibbling because articles like this one seem fairly common, which argue that it is not possible to establish biology as a determining factor in gender/sexuality, generally using terms like "essentialism", etc.

    I entirely agree. I once had a difficult argument with a colleague, in the context of a course we were co-teaching, about whether human sex is basically a binary category or not.

    My argument was that 99.X of the human population is either XY or XX, and so this is about as close to a categorical distinction as we're likely to find. The opposing view was that there are several other configurations such as XXY and XYY, as well as androgen receptor abnormalities and so on, so that the whole idea of "male" vs. "female" as biological categories is a social construct that should be avoided.

    There ensued some investigations of the population rates of various sorts of genetic and anatomical mixed states, which didn't converge — I came out with the impression that these are a few tenths of a percent of births at most, whereas my colleague pushed for much higher rates.

    So I'm sympathetic to your concern that anti-essentialism can be sometimes be used as a way to argue against making any distinctions at all.

    But frankly, I think that the bad effects of thinking in terms of group stereotypes — even those that are statistically supported to one extent or another — are more widespread and more generally pernicious. And a large proportion of commonly-accepted group stereotypes are not even true on average.

  17. Sridhar said,

    June 18, 2008 @ 4:10 pm

    If Scientific American's headline, parsed as saying that "[gay men] and women" have similar brains, is wrong on the grounds that it speaks of "women of whatever kind" rather than merely straight women, then does not the press release title "Symmetry Of Homosexual Brain Resembles That Of Opposite Sex, Swedish Study Finds" suffer the same problem, mentioning the opposite sex without explicitly restricting to its straight subset?

  18. Journo said,

    June 18, 2008 @ 7:21 pm

    Interesting, Mark, that you fault scientists as well. As a journalist and avid Language Log reader, I take special note of science reports when editing (my job) or consuming news. Here are my impressions. Often, in what seem like uncut radio interviews, such as on NPR's Science Friday, scientists usually repeat themselves in very specific and accurate language and seem exasperated yet polite trying to explain over and over and over that the findings are subtler than the conclusions the reporter is jumping to (no offense to Ira Flatow). In printed reports, unfortunately and in many cases, not even careful readers will be able to pick up the usually obvious clues present on radio that something in the reporting is amiss.

  19. Steve Harris said,

    June 18, 2008 @ 8:29 pm

    Probably the best way to understand the situation at a glance is with the graphs, as Mark infers them for us. But here's another way:

    How does your ability to predict the sexuality of a man (or of a woman) increase, by examining MRI scans of the brain?

    Let's assume a 10% incidence of gay men among the general population of men. Taking Mark's retrospectively estimated figures of 18/25 het men show assymetry and 10/20 gay men show assymetry, here's how the figures stand after we do the brain scans for an individual man:

    If we find no asymetry, we predict "gay"; and our chance of being right goes from 10% (without benefit of brain evidence) to 13%. (So brain-scan evidence is a very bad basis upon which to predict a man's being gay.)

    If we find asymetry, we predict "het"; and our chance of being right goes from 90% (without benefit of brain evidence) to 93%.

    (Want to put in your own favored gay incidence figure? Say that p fraction of men are gay. Without brain-scan evidence, your probability of being right when saying "this man is gay" is p. With brain-scan evidence showing no asymetry, your probability of being right when saying "this man is gay" is .5p/(.5p + .342). Brain-scan evidence of asymetry changes the probability of being right for "this man is het" from 1-p to .72(1-p)/(.72 – .22p).)

    It's slightly different for the women, where Mark's figures are 11/25 het women show assymetry and 17/20 gay women. Assume, again, a 10% incidence of gay women.

    Brain-scan of woman shows asymetry: Predict gay; likelihood of being right goes from 10% to 18%. (So brain-scan evidence is not much better for predicting a woman is gay than for predicting a man is.)

    Brain-scan of woman shows asymetry: Predict het; likelihood of being right goes from 90% to 97%.

    (Do-it-yourself: With p fraction of woman being gay, brain-scan showing asymetry means likelihood of being gay is .85p/(.44 + .41p), while brain-scan showing no asymetry means likliehood of being het is .56(1-p)/(.56 – .41p).)

    I note that Mark's calculations require some basic knowledge of statistics; this here is elementary probability theory (Bayes' Theorem). I have found it much easier to teach this level of probability to vaguely interested science majors, than it is to teach the corresonding level of statistitcs (though possibly that reflects my own level of understanding of the respective subjects).

  20. Leon said,

    June 19, 2008 @ 9:43 am

    But frankly, I think that the bad effects of thinking in terms of group stereotypes — even those that are statistically supported to one extent or another — are more widespread and more generally pernicious.

    Hmmm — I think you're underestimating the extent to which we think in terms of group stereotypes, and the extent to which it's pernicious. Or to put it another way, I think you're overestimating the extent to which we "think" at all in everyday life, and the extent to which thinking more would necessarily improve what we've inherited through habit without compromising other things, such as time.

    I again give the example that "smoking kills" is far more of a generalization than than the statement "people are male xor female". Or take another, "eating a lot without exercise makes one fat" — this statement and its converse are both more or less true. And though we should avoid saying statements like this because they can be so offensive, equally, we "reason" along those lines all the time without thinking about it.

  21. Leon said,

    June 19, 2008 @ 9:44 am

    *In the second line, I meant "overestimating the extent to which it's pernicious"

  22. Ewan said,

    June 19, 2008 @ 9:47 am

    You write: "Scientific American's headline was ambiguous, and false on both readings: "Study Says Brains of Gay Men and Women Are Similar". This might attribute similarity to "gay [men and women]", i.e. to gay men and gay women." – I don't see why this would be so wrong, although it's surely somewhat misleading: gay men are similar to gay women, inasmuch as their cerebral asymmetries tend to match those of the straight opposite sex, rather than the straight same sex, a point which is underscored in various other headlines, including the press release headline, "Symmetry of Homosexual Brain Resembles That Of Opposite Sex, Swedish Study Finds." Their cerebral asymmetries are not similar, but the pattern in their cerebral asymmetries is, which would be an interesting point if, for example, you held that gay women were somehow fundamentally different from gay men.

  23. Mark Liberman said,

    June 19, 2008 @ 9:23 pm

    Leon: I think you're underestimating the extent to which we think in terms of group stereotypes, and overestimating the extent to which it's pernicious.

    I think that we agree about how common this form of thinking is, but disagree about how often it leads to false conclusions.

  24. claire said,

    March 12, 2009 @ 8:36 am

    Have i understood correctly that the researchers calculated the averages of left and right brains separately? If you must work in averages, wouldn't it have made more sense to take the ratio of left-right for EACH person, then find an average from there?

  25. Emilie said,

    May 6, 2009 @ 11:59 am

    I was reading,(tongue in cheek) this dialogue, noting no female names (until Claire's) responding. wondering about the size shape volume and symmetry of my heterosexual female brain. As a mother of six children, three boys and three girls, twins included, and also having been told that I appear "too masculine" both physically and mentally, I have reason to be curious about this conversation and how it unfolds.
    My understanding is that the size of the brain as a measurement of differences between the sexes is related to the typical size difference in human male and female bodies.
    I understand, correct me if I'm wrong, if anyone is still following this, that it is really not about how big the brain is or isn't, but about the centers of the brain associated in expressions of "female" behavior (centers that are normally stimulated in the process of responses like nurturing, empathy, verbal negotiation) and how it appears from the PETs that there is more neuronal growth and more neuronal connections available in those areas in heterosexual women and homosexual men.
    Lastly, I noted the overall negative and challenging tone of this conversation, and wondered…what makes us humans so unlikely to give a cheer when we see such a great accomplishment in our lifetime? Finally we are using our brains to study our brains! and personally, I really appreciate the work of the people who are brave enough to challenge "group think". This study is breakthrough, at least in the direction of getting past the obvious stereotypes due to ignorance , and everyone who was involved in this study, or who responded deserves a warm applause!

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