Due to anatomical constraints, humans (and mammals generally) can really only have sex with one partner at a time. And if two people are having sex, then the fact that person A is having sex necessarily means person B is too.

We know all this.

So how is it that we’re so ready to believe research which says men have more sex partners than women? How could the scientists who did the research not notice that little flaw in their project?

Gina Kolata highlighted the issue with respect to heterosexuals in a recent NY Times article. She cites David Gale, an emeritus mathematician from UC-Berkeley, who pointed out the logical impossibility.

Although she doesn’t state it explicitly, note that a few promiscuous women can’t explain the survey results. In one study, for instance, men claim 12.7 heterosexual partners, on average, and women 6.4. That’s about a hundred percent difference. At least a few of these highly promiscuous women would be in the sample, and you’d see a skewed bimodal distribution. There’d be a large number of women with numbers of partners in the low single digits, a trough with very few having, say six to twenty partners, and then a spike showing that a few women had dozens or hundreds of partners. The overall average would still have to be the same for both sexes.

Nor can the results be explained by assuming men are having all that sex when traveling to places outside the survey population. Some men would be traveling to the survey population, and the women who are having sex with them should show up as more promiscuous than the men in the population.

But the surveys don’t show any group of women, however small, who are more promiscuous. If you want to believe the surveys, then somehow men are having sex with phantoms.

The consensus among the experts seems to be that the likeliest explanation is that these are indeed phantoms. Men over-report the number of women they have sex with, and women under-report them.

Dr. Gale added that he is not just being querulous when he raises the question of logical impossibility. The problem, he said, is that when such data are published, with no asterisk next to them saying they can’t be true, they just “reinforce the stereotypes of promiscuous males and chaste females.”

The even more interesting point, to my mind, is how ready we are to believe stereotypes. Stereotypes shape thinking to such an extent that obvious nonsense does not register.

There’s an important take-home message in that. Anything that seems to support a stereotype should be examined with more skepticism, about ten times more, than “counterintuitive” results. Charles Darwin had an inkling of this, great thinker that he was. The story is that he had a booklet in which he wrote down observations that seemed to contradict his ideas. Otherwise, he said, he knew he’d forget those facts if he could.

The pitfalls of stereotypes are worse than other kinds of ignorance because they affect our assumptions, and assumptions are extraordinarily powerful things. Start from the wrong ones, and no amount of reasoning, statistics, flawless scientific methodology, or articulate verbiage in the conclusions can rescue anyone from producing nonsense. In other words: GIGO. Garbage in, garbage out.

There are thousands of examples, stretching out into all of time and space. It’s really quite sad. To avoid massive depression, I’ll go over just two recent examples. Add your favorites in comments.

Two Norwegian scientists analysed a huge number of records (250,000) on young men inducted into the Norwegian military. They found that the boy who occupied the role of oldest sibling, whether he was born the oldest or not, had a slightly higher IQ, on average, than younger siblings. (Science article) The difference? Three points.

The sample size is huge, so the results are statistically significant. Nothing wrong with the methodology. Nothing wrong with the conclusion, either. That’s what the results say.

But do they mean anything out in the real world?

Leaving aside the issue whether IQ tests measure anything except the ability to take IQ tests, there is generally more than three points difference in IQ tests taken by the same person at different times. Three points difference has zero predictive value for anyone’s success in life, even in intelligence-heavy fields like science or teaching. The results may be true, but it’s also true that I ate spaghetti three times last month. Just because it’s true, doesn’t make it interesting.

What made it interesting enough to publish in Science was the bias toward believing that there’s something special about oldest male heirs. What the scientists really proved is that there’s nothing special about their IQ tests. But there was a fever of media interest (eg BBC) because it could be used to confirm biases. A cold bath of skepticism would have landed closer to the truth.

A different sort of GIGO occurred recently with research on something called “social obesity.” (New England Journal of Medicine article) It sent Kate Harding into a well-deserved rant. Very briefly, the authors re-analyzed data from the huge, long term Framingham heart study, and found that some friends are likelier to have friends who gain weight. Obvious conclusion? Fat friends cause weight gain! … Not.

You would think some of the findings would have raised red flags. Geographic proximity had no effect on weight gain among friends. Surely, if the fatness of friends is important, interacting with them more often ought to increase the effect. Even more telling was that the weight gain among spouses was among the weakest correlations. If phone calls a few times a year from a distant friend are enough to validate weight gain, surely a spouse saying, “This way there’s more of you to love” would cause even more weight gain. Apparently not. That by itself tells you that all the statistics in the world are not finding a social effect.

What they are finding, who knows. The sample size is huge, the statistics are fine, but the meaning will have to wait until someone can apply some actual intelligence to the data, instead of just basking in bias confirmation about the obesity epidemic.

It all goes to confirm the same take-home message. Never, ever put your brain on the shelf. Even when something is published in Science, or the New England Journal of Medicine, or Shakesville for that matter. Always examine the assumptions. If the conclusion is something you like, examine the assumptions all over again. Even the best science will never change the fact that asking the right question is way more important than finding an answer.