For Better Sex, You Probably Need More Than Correlation

I finally got around to viewing the PETA (People for the Ethical Treatment of Animals) ad that NBC decided to ban from its Super Bowl coverage. I had imagined a rather sordid broccoli-loaded affair. But it turns out it was just like a Victoria’s Secret spot, only a bit more nutritious.
The point of the ad was that “Vegetarians have better sex.” Now that’s provocative — provocative enough to stimulate this confirmed omnivore to further research. Here’s what I learned.
PETA does not actually have direct evidence that vegetarians have better sex. Instead, it argues that:

Research has shown that vegetarians enjoy greater amounts of the nutrients that help boost sexual health and performance — such as vitamins A, C, and E and potassium — than meat-eaters do.

There’s a logical gap between PETA’s evidence and its conclusions. Any student of statistics knows the perils of mislabeling correlation as causation. But that’s not the problem here, as PETA is simply claiming a correlation between vegetarianism and better sex. But even if X (being vegetarian) is positively correlated with Y (ingesting vitamins A, C, and E), and Y (more vitamins) causes Z (better sex), we still don’t have enough information to conclude that X (being vegetarian) is positively correlated with Z (better sex).
Here’s a simple counter-example: when I get a cold, I take a multi-vitamin and I eat a few more veggies; you probably do something similar. But even as we both “enjoy greater amounts of the nutrients that help boost sexual health and performance,” I’m pretty sure you wouldn’t conclude that people with colds have better sex.
Interestingly, this is a case where a causal claim (become a vegetarian and you’ll have better sex) may be warranted, even if the asserted correlation (vegetarians have better sex) is wrong. That is, if vegetables are more loaded with the relevant nutrients than the alternative (which seems likely), and if those nutrients do improve sexual performance (as PETA asserts), then PETA would be on firm ground concluding that “vegetarianism causes better sex.” But causation isn’t correlation.
We can investigate the asserted correlation directly. Is vegetarianism correlated with better sex? The General Social Survey asks: “How often do you refuse to eat meat for moral and environmental reasons?” That sounds like it will isolate the folks PETA is talking about.
While there’s no data on the quality of sex, the frequency with which people had sex over the past year is measured, and so we can investigate the related question of whether vegetarians have more sex. It’s not quite the same as PETA’s claim, but if you believe that quality shifts demand curve up, then folks having better sex will also want more of it.
In the following chart, I divide the population according to their degrees of ethical vegetarianism. For each group (shown in each panel), the bars show a simple histogram — the proportions of that group reporting various degrees of sexual activity. Adding up the right-most three bars tells us the proportion of each group having sex at least weekly. Around 40 percent to 45 percent of people report having sex at least once per week, and there’s no real difference between ethical vegetarians and carnivores — a fact confirmed by a formal chi-squared test.

Unfortunately, it looks like there’s nothing here to support PETA’s purported vegetarian-sex link. I’m from a mixed household, and so my vegetarian partner is keen to remind me that quality and quantity are very different things. In fact, she finds my quantity evidence too weak to shift her beliefs, which remain firmly in the PETA camp.