Fat lesbians and Bayes theorem

One of the most moronic cliches of management speak - and there's fierce competition - is that we should think outside of the box.
Nonsense. We must always think inside the box. I was reminded of this by this story from Tim, that lesbians are more likely to be obese than straight women. A commenter added that  "fat women are more likely to be lesbians."
This is very wrong. And our Bayesian boxes show us why.
Sadly, the paper Tim cites isn't webbed, but this paper (pdf) by Christopher Carpenter is. It estimates that lesbians are half  as likely again to be obese as straight women.  We can use these data to fill in our boxes, thusly.
It's clear from this that although lesbians are more likely to be obese than straight women, the vast majority of obese women - 98% - are straight.
This is simply because the proportion of lesbians in the population is small.
Indeed, even if every single lesbian were obese, it'd still be the case that if you were to see an obese woman, there'd be a greater than 90% chance that she was straight.
Not that this fact would be any use to you.

Comments

[Neal Hockley]

Disagree with you there.

"fat women are more likely to be lesbians" than thin women are

But of course "fat women are NOT more likely to be lesbians" than they are to be straight.

But i would have interpreted the commentator as saying the former, and I think that's the natural way to interpret them, because we instinctively know that the latter is false. (though I agree its ambiguous)

Anyway, they aren't wrong, at worst they are ambiguous

[Mark Wadsworth]

The tongue-in-cheek remark "fat women are more likely to be lesbians" clearly implied "than are non-obese women" and not "than to be straight".

The table you have produced clearly backs this up. 2.3% of obese women are lesbians as against only 1.3% of non-obese.

[chris]

Now you mention it, it is ambiguous. I assumed, of course, that he meant the latter.
Whilst I'm here, I'll point out another common ambiguity.
The chances of a fat woman being a lesbian in our table are 2.2%, whilst the chances of a thin one being a lesbian are 1.3%.
It's common for journalists to interpret statistics like this as meaning that the risk of a fat woman being a lesbian is 70% greater than the risk of a thin one. But it's only a 0.9 percentage point higher risk.
Lots of health scares arise from this reading.

[sanbikinoraion]

Doesn't anyone else find the total number of lesbians to be startlingly low in these numbers? I thought that somewhere between 5-10% of the population are gay.

[Mark Wadsworth]

Sanbik, puzzles me as well, but I believe (from experience as well as from published stat's) that many more men are gay than women are lesbian, I mean like 5% of men (at least) as against 2% - 3% of women.

It's got to do with evolution, all a bit complicated to explain.

[jameshigham]

Excellent economic theory, Chris. Now I'd like to see the actual stats.

[dearieme]

Not even 5-10% is cheerful, sanbi, never mind gay.

[james c]

''fat women are more likely to be lesbians"

than are thin womem, as your table shows.

[Rajeev]

Aye. Chris is usually so sharp. And this is a very non-PC comment: "the risk of a fat woman being a lesbian". No?

Pissing off both fat people and gay people in the same phrase.

[chris]

Rajeev - you raise a nice ambiguity about the word "risk." Most people think it's a bad thing - they speak of the risk of cancer rather than the risk of winning the lottery.
I was using it in the sense of "probability" with no such colour. This reflects my financial economics background; risk can often be a good thing.

[Karthic]

Thanks Chris.

[ejaz]

Applying Chi-square test of independence will result in either acceptence or rejection of the hypothesis that whether or not obesity is dependent on a woman being lesbian or straight.

Expected frequencies corresponding to observed frequencies can be obtained by multiplying the marginal sum of freuncies corresponding to each cell and dividing by the total number of frequencies.