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
9 comments:
I hear what your saying. I do. And I'm all for scientific integrity. It's one of the most important things in the world. But I just looked at my fingers..... and so I'm sorry but I'm totally telling EVERYONE that there is peer reviewed science telling them I have a huge shlong!
Wouldn't "stretched penile length" depend on how much they stretch it?
Did the people having the surgery know this was going on??
The study referred to must have been accepted purely on its gossip value! When there is only such a small correlation between just one variable and penis size, what sort of mess would they get in a multivariate study? The first graph looked like an r= 0 to me because of the huge spread of values. Imagine the size of the squared residuals in a multivariate version if all the other variables were as divergent as the 2-finger ratio? I would predict that the overall regression wouldn't be significant at all, swamping the finger ratio contribution into insignificance. Perhaps someone could suggest they do that study next. Truth may be stranger than fiction!
Not too long ago, someone in my division gave a talk that was largely clinical research. The group was comparing 2 measurments (total vs. 'free' or active analyte) and made the argument that the former provide no correlation to outcome whereas the latter did. Yet regression and spread of points for the latter looked very similar to the one pictured here. I recognize that clinical trials can rarely be as precise as model system research, but the point you make here is important: Fitting the data to a linear regression doesn't make the observation significant.
Namnezia: The whole reason I tracked down the paper was because I was interested in the issue of whether the patients knew. The methods say, "all patients gave informed consent." That's all they say, leaving me to wonder how... specific the consent form was.
Because one would think that, "We're going to be stretching your penis while you're under" would not get a lot of volunteers.
As for degree of stretching, they say that they were "fully stretched," which makes me glad the men were completely anaesthetized. There are some limits I'd prefer not be tested, myself.
Murfomurf: I don't think the study made it into the journal on gossip value. It's scientifically interesting, even given the caveats I mentioned in the main post.
I believe Matthew McIntyre has a paper or two on finger length and prenatal hormone exposure that deals with whether it is a robust indicator of androgen (I believe he is able to indicate that it is).
Of course, that doesn't make any conclusions drawn from that graph any better. May make it worse.
did the Koreans stretch the penis to the max ? 'Cuz that HURTS haha !
Mark: I suspect that's why this did the study under general anaesthesia.
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