Having had even a rudimentary course in Statistics, I totally know what's going on in the equation below! That's exciting. (The copied post is from Andrew Sullivan:
Stats and Willies
15 Dec 2006 10:51 am
A reader answers my earlier reader's worry about the statistical validity of the large study that found that gay men have bigger willies than straight men:
As a stats nerd myself, I had to comment on your reader's concerns about the differential sample size regarding the penis size. His concern is very likely unfounded. The differential sample size, per se, would have no effect on the relative differences between the two groups or on interpretation of the differences. Indeed, both of these samples are very large sample sizes and so sample size should not affect the characteristics of distributions. Generally, you only worry about it when you have sample sizes below 30 and that is not the case here. If there were differences in the shape of the distributions, your reader would be right and it would confound interpretation. However, it does not appear as though that is the case (see attached article).
Even if the distributions were skewed with a small proportion having very large penises (and more so than the proportion of those having very small penises), it would not really be a problem unless they were skewed in different directions. Because of the large sample sizes, the outliers (either very large or very small) would not have substantial effect in affecting the interpretation of the differences (or the mean in this case). Unfortunately, as a straight guy, I’d like to believe it’s not true!, however I don't believe that there are statistical reasons to doubt the analyses ...
I've had several expert emails on this and they all agree. Here's the math:
According to Wikipedia, the population standard deviation in penis sizes is .8 inches. Other surveys had a smaller SD, but for argument's sake, we'll use the larger one. If we assume that gay and straight men have different average penis lengths but the same variance in lengths (i.e. Same standard deviation - this property is called homoscedasticty - no joke) we can use this .8 figure for our SD without issue. Our calculation is straight-forward:
Mean Difference in Penis Size: .33 inches
Gay Sample Size: 935
Standard Error (Gay Average): SD*Sqrt[N]/N = (.8)(Sqrt(935))/935 = .0262
Standard Error (Straight Average): (.8)(Sqrt(4187))/4187 = .0124
Standard Error (difference) = Sqrt(.0262^2 + .0124^2) = .028986
Z statistics = .33 / .028986 = 11.3847
With this very high z-statistic, the probability of Kinsey's results happening by pure chance are extremely, extremely low - way less than .0001. Of course, this result depends upon accurate self-reporting and our assumption about having the same variance. If this result is not true, it is not because of the sample sizes.
Alas, stats was not my strong suit in grad school - but I did pass! The issue of self-reporting would only be salient if gay men were more boastful than straight men, but I don't immediately see why this should be so. They're probably all exaggerating a little.
Of course, if we are to agree that gay men have slightly bigger peepees than straight guys, the question is: why? Maybe hormone levels in the womb are a factor. I've long thought that the theory that homosexality is partly a function of abnormally high levels of testosterone n the womb was worth looking into. The stereotype is that gay men are somehow more feminine than straight men. But it could be that they are actually more masculine in the sense of having higher testosterone levels in fetal development. That might also shed light on the black-white-Asian penis differential. Are there any solid studies on that? (Apparently not.)
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