Thursday, February 21, 2013

The Distribution of Penis Length

How long is the average penis?  This is a question that has plagued mankind since time immemorial.  In this blog entry, I will tackle the question head on.  To begin, it is useful to know a little history about the penis of the modern man.

In proportion to body size, Homo sapiens have one of the largest penises in the animal kingdom.  Anthropologists contend that the penises of our ancestors were proportionally smaller.  The most common theories suggest that penis length began to increase when our ancestors began walking upright, on two legs.  Animals must exert force on the ground to propel themselves forward.  Since the center of mass for quadrupeds is in front of their hind limbs, their hips are positioned to allow backward movement of the limbs, which produces an equal and opposite, and largely horizontal, force.  Bipeds, on the other hand, have their center of mass directly over their feet.  When our ancestors began walking upright, they still had to exert force through their legs, but now they had to use one leg to do it, while extending the other leg forward to prevent themselves from falling on their faces.  This required a re-positioning of the hips.  Our pelvises gradually shifted so that our legs were directly below our centers of mass, and grew smaller to allow greater efficiency in locomotion.  As a repercussion of these changes, the female’s uterus was pushed further up into the body, making it more difficult to access, and vaginal length increased.  Consequently, only the males whose penises were long enough to reach the closest to the uterus were able to successfully reproduce.  It was a selected trait.

Fast forward to the present day and our culture reveres long penises, as if we inherently know their reproductive value.  I think it is ironic that we see large penises as symbols of masculinity, when we owe credit for their size to women.  Penis length is directly dependent on the length of the vagina.  That is useful to keep in mind when reading studies about penis size.  Some have shown that there are differences between ethnicities, but that could only be because of ethnic differences in vaginal size, and there are far fewer studies measuring that.

LifeStyles, the condom manufacturer, carried out a survey of erect male penis size in Cancun, Mexico, consisting of 300 subjects (source:  http://abcnews.go.com/Entertainment/WolfFiles/story?id=90588&page=1).  The participants were mostly American college students on spring break, so the sample may not have been entirely random.  Here is the distribution of the data:


The probability distribution for this data is positively skewed, and resembles a chi-square distribution.  The skew causes the median to be the best measure of central tendency (think of measuring household income; the high earners/outliers pull the mean up, so the median is a better measure).  The median of this data set is 5.65 inches.  However, the skew is slight enough that it can be said to be approximately normal.  Statistical methods for testing hypotheses that are based on the normal distribution are usually robust enough to give accurate results for distributions that are approximately normal.

A more recent study by Richard Lynn of the University of Ulster in the UK collected data on a large sample of men from 123 different countries (source: http://xa.yimg.com/kq/groups/1292538/662920758/name/Examination+of+Penis+size+and+r-K+selection.pdf).  Here is a summary of the data:

Note about data:  The number of observations on the y-axis measures the number of countries whose mean length matches the value on that axis.  It is not the number of individuals with a certain length, but rather an average of a large number of individuals. 

This data set has a negative skew, so the median is once again the better measure, although in this case it is because the mean is pulled too low.  The median for this data set is 5.8 inches.  The Jarque-Bera stat is large, suggesting the distribution is not normal.  In this case, this statistic appears to be right, but the Shapiro-Wilk test would have been more appropriate due to the small sample size.  (The Jarque-Bera was just the default normality test statistic with the software package I used, so I kept it there).

The two aforementioned data sets are based on completely different sampling methods, so comparing the distributions would be unsound.  But if it would satisfy your curiosity (as it does mine) the medians, 5.65 and 5.8, average to 5.73 inches.  So you could say that 5.73 inches is the approximated global average penis length.  But wait a second; I mentioned that size varies by ethnicity and geographic location.  You can view an interactive map of global penis sizes here:  http://www.targetmap.com/viewer.aspx?reportId=3073 or a static version that is easier to make comparisons with here:  http://www.everyoneweb.com/worldpenissize/   The maps show that Asians typically have the shortest penises (3.5-4.25 inches), while Africans and South Americans typically have the longest (6-7 inches).  

Penis size does not seem to correlate with stature; otherwise the Nordic countries would dominate, and the African countries would be among the smallest.  A former professor of mine, Richard Steckel, wrote a paper called Biological Measures of the Standard of Living (source:  http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.22.1.129).  In his paper, he described how stature correlates with a higher standard of living, because people need to be properly nourished in order to grow tall.  Comparing the maps linked to above with maps of stature and standard of living across the globe, it appears that penis size is unrelated to both height and standard of living.  That is an interesting observation. 

Further Reading:  Evolution of Human Walking, by C. Owen Lovejoy, http://www.clas.ufl.edu/users/krigbaum/proseminar/lovejoy_1988_sa.pdf

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