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Some more sociological platonism: Tamsin Osborne ("Are men happier than women?", New Scientist, 7/25/2008) explains that "I've just received the rather troubling news that I am doomed to be unhappy in later life". This turns out to mean that she will have a (very) slightly less than even chance of being in the happiest half of a gender-balanced sample of Americans older than 50 or so — and her way of expressing this is a typical (and thus interesting) example of the journalistic (and perhaps scientific?) tendency to turn small group differences into essential group characteristics.

The bad news came to Ms. Osborne from Anke C. Plagnol and Richard A. Easterlin, "Aspirations, Attainments, and Satisfaction: Life Cycle Differences Between American Women and Men", Journal of Happiness Studies, published online 7/11/2008, which takes its happiness data from the United States General Social Survey, "a nationally representative survey conducted annually from 1972 to 1993 (with a few exceptions) and biannually from 1994 on".

Plagnol and Easterlin fit an "ordered logit regression" model to GSS data, from which they generate and plot these happiness trajectories by age, where "mean happiness" is denominated on a scale from 1 to 3:

Note that this is fake data — the model represented by these lines explains a bit less than one percent of the variance in the survey answers of the 12,341 males of various ages who responded to the overall happiness question, and about 1.6% of the variance for the 15,926 women.

Plagnol and Easterlin don't plot the raw response distributions that they're fitting their model to, or give us a table of the numbers. But a rough way to evaluate Tamsin Osborne's fate, from the point of view of expected happiness over the life span, would be to compare the model's difference in mean responses by sex at ages 18 and at 80 — a bit more than 0.1 on a scale of 3 — to the overall standard deviation of responses for each sex, which is about 0.63. This would predict that at age 18, the happiest half of of a sex-balanced sample would be about 53% female and 47% male, while at age 80, the happiest half would be about 53% male vs. 47% female. (Again, this a worst-case scenario based on the end-points of a linear model fit.)

So Tamsin Osborne can relax: her unhappy fate is hardly sealed. In the first place, this is not a prediction about whether any individual will be happy or unhappy, it's a prediction about the relative degree of happiness of males and females at different ages. In that comparison, her odds as a woman of ending up in the happiest half of a sex-balanced sample of older people are slightly worse than even — if she cares about this rather artificial competition. And finally, the whole model explains about one percent of the variation in self-reported overall happiness, so her mileage is quite likely to vary.

Results like these are apparently a big deal to sociologists and economists. But they should mean next to nothing to ordinary people — even though apparently everyone loves to infuse them with their favorite hopes, fears and prejudices.

Osborne's description of these results is that "women start their adult lives happier than men, but from the age of 48 onwards are more glum".

This is true, in some sense, as a statement about the proportions predicted by the parameters of a statistical model . But I'm confident that nearly all readers of the New Scientist will misinterpret these generic plurals (as Ms. Osborne encouraged them to do by describing herself as "doomed to be unhappy in later life"), and read them as statements about (nearly) all men and women, and therefore about themselves.

So I wonder how journalists — and for that matter, social scientists — really see what they're doing when they write this way. Do they (a) misunderstand the math, and mislead their readers simply by expressing their own mistaken beliefs? or do they (b) understand the math, but believe that their readers are not capable of understanding it, and so mislead their readers by simplifying the results in a way that they think is inevitable? or do they (c) understand the math, and realize that if they mislead their readers by expressing the results as big truths about human subgroups rather than small changes in the odds, they're get a lot more links?

(For an earlier adventure in modeling GSS happiness numbers, see "The 'gender happiness gap': statistical, practical and rhetorical significance", 10/4/2007, and the list of links at the bottom of the post, especially "Gender-role resentment and Rorschach-blot news reports", 9/27/2007.)

July 26, 2008 @ 4:20 pm · Filed by Mark Liberman under Language and gender, The language of science

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