It started off with me estimating the vocal tract lengths of the speakers in the Philadelphia Neighborhood Corpus. Given sufficient acoustic data from a speaker, and making some simplifying assumptions, and taking into account the acoustic theory of speech, you can roughly estimate how long a person's vocal tract (meaning distance from vocal cords to lips) is. I went ahead and did this for the speakers in the PNC, and plotted the results over age.
Pretty cool, right? There's nothing especially earth shattering here. It's known that men, on average, have longer vocal tracts than women. I was a little bit surprised by how late in age the bend in the growth of vocal tracts were.
Here's the density distribution of vocal tract lengths for everyone over 25 in the corpus.
That's a pretty big effect size. Mark Liberman has recently posted about the importance of reporting effect sizes. He was focusing on how even though people are really obsessed with cognitive differences between men and women, the distributions of men and women are almost always highly overlapping.
Following Mark on this, I went ahead and calculated Cohen's-d for these VTL estimates.
So, 1.71 is a fairly large Cohen's-d effect size. I had heard that the difference in vocal tract length between men and women was disproportionately large given just body size differences. I managed to find some data on American male/female height differences, but the effect size is not impressively smaller than the VTL effect size (1.64, about 95% the VTL effect size).
Compared to the effect that Mark was looking at (science test scores), these effect sizes are enormous. The effect size of height between men and women is about 23 times larger than the science test score differences which warranted a writeup in the New York Times.
Yet, still not big enough.As I was thinking about how height difference is perhaps one of the largest statistical differences between men and women, it also struck me how often it is still not big enough for social purposes. Sociological Images has a good blog post about how even though Prince Charles was about the same height, if not shorter than Princess Diana, in posed pictures he was posed to look much taller than her. Here's an example of them on a postage stamp:
And in another post, they provide this picture of a reporter being comically boosted to appear taller than the woman he's interviewing.
My take away point is that when it comes to socially constructing large and inherent differences between men and women, even the largest statistical difference there is out there is still not good enough for people, and needs to be augmented and supported. Then take into account that most other psychological and cognitive differences have drastically smaller effect sizes, and it really brings into focus how the emphasis on gender differences must draw almost all of its energy from social motivations, rather than from evidence or data or facts.