Friday Weird Science: Will this spoil the surprise?

Note: I am unabashedly ripping of the title of this thread from Scicurious, who normally ends the week with a “Weird science” post. She’s been on vacation, and so I thought I’d pick up the slack for this week only...

Have a look at this graph. tell me what the relationship between these two variable is. Not what you think the variables are, but how would you describe them?

I don’t want to spoil the surprise. More about this graph when you click here for more.


This graph was taken from research paper that has been making a lot of headlines. The headlines are unusual because it’s not Science or Nature, but is in a journal I suspect does not normally make science headlines: I never knew there was an Asian Journal of Andrology.

The headlines, while unusual, are not surprising in this case.

Because the graph is about predicting penis size.

And now, one half of my readership is giggling and the other half is nervous.

The design of this study by Choi and colleagues is simple. They measured the index and ring fingers of men who were going in for urological surgery. During the surgery, they measured the penis size of the patient.

“Wait, back up,” I hear you say. “What about fingers? Don’t tell me they were testing that old myth about guys with big hands.”

No, that’s not what they were doing. It’ been known for several years now that the relative lengths of your index and ring fingers is hypothesized to be influenced by the amount of testosterone (and perhaps other hormones) you received in your mother’s womb when you were but in an embryonic state. A ring finger that is longer than the index finger is correlated with high doses of testosterone, according to this hypothesis.

As far as I have been able to determine, the idea that finger ratio is due to pre-natal testosterone is still an hypothesis without definitive evidence supporting it. As you can imagine, it’s not an easy thing to test experimentally, since ethics review panels generally frown on fiddling with the hormone levels of the unborn. Manning and colleagues for some interesting evidence supporting this idea.

But I digress.

If the relative lengths of the two fingers is due to testosterone, testosterone is well known as a powerful hormone that has many different effects on the human body. In development, testosterone does have effects on sexual differentiation. So if testosterone is a common cause for both longer ring fingers than index fingers, and male sex organ development, it stands to reason those two features would be correlated.

And that’s the graph we started with.

When you looked at that graph a moment or two ago, what did you think about it? Probably you thought that it looked like it had about as much order as the buckshot marks on a highway sign in redneck country.

It’s been a few moments since you’ve seen that, so let’s look at that graph again, this time labelled and with the authors’ regression line.

I learned about this paper from a headline: “Digits reveal all about manhood size!” But to me the lesson from this paper is not how much finger length ratios reveal about penis size, but how little they reveal.

The way you measure the relationship between two variables is by a correlation coefficient, usually abbreviated r. r can go from 0 (no relationship) to 1 or -1 (perfect relationship). In this graph, the r value is -0.2.

If you think that sounds like a pretty low value, much closer to random than a perfect relationship, just wait! It’s even worse than you think.

The value of r squared is more informative than plain old r, because r² that tells you how much variation in the data is explained by the relationship between these two variables. Here, -0.2 times -0.2 is 0.04, or 4%.

Or, to put it another way, 96% of the variation in penis size is not predicted by knowing digit ratio.That is to say, almost all of it. Quite contrary to the way the story is being told in the headlines, which imply that you can pretty much tell everything at a glance.

This is interesting case of the difference between statistical significance and biological importance. While the effect is statistically significant, it doesn’t give you a lot of predictive power. If you want to guess penis size, you’re not much further ahead looking at the man’s two finger than if you just guess the average.

So I have no reservations about posting this:

Because you still know nothing ‘bout me.



Research

Choi I, Kim K, Jung H, Yoon S, Kim S, Kim T. (2011). Second to fourth digit ratio: a predictor of adult penile length Asian Journal of Andrology: In press. DOI: 10.1038/aja.2011.75

Manning J, Bundred PE, Newton DJ, & Flanagan BF (2003). The second to fourth digit ratio and variation in the androgen receptor gene Evolution and Human Behavior 24(6): 399-405. DOI: 10.1016/S1090-5138(03)00052-7