Andy Latto is of course right that the MEDIANS of the male and female distributions can be different. I came up with the same example as he did where the female population consists of v virgins and p prostitutes and v>p. Then the female median is 0 and the mail is p. So then I looked at the distributions given in top line of tables 10 and 11 and used them to estimate the total number of partners of males and females. It was an estimate because when they say 32 % 0f men reported between 3 and 6 partners I used 4.5 etc. Doing it this way I found men have about 50% more partners than women. Mike Greenwald asks, how a median can be 3.8. Good question! Maybe I'm revealing my own innumeracy but then please tell me what it means for an integer valued random variable to have a fractional median. I suppose if exactly half the values were greater than n then any number between n-1 and n could be a median, n+1/2 would be a natural candidate. Tables 10 and 11 have fractional medians everywhere. One funny datum is that the median number of life partners for women up to age 40 is 3.9 while for those up to 44 it goes down to 3.8. I suppose this could be sampling error, (unless it shows that women are getting more promiscuous over time). Anyhow, someone please help me out on those fractional medians David At 10:22 AM 9/28/2005, you wrote:
Date: Mon, 26 Sep 2005 03:55:11 -0700 From: David Gale <gale@math.berkeley.edu> For example, Tables 10 and 11 of the survey show that the median number of partners "in lifetime" for males over forty is 8 while that for females is 3.8. To immediately recognize the inconsistency imagine the same survey with but with the words sexual partners replaced by spouses.
It's entirely possible that this data contains reporting error, of course, but I don't think that it is inconsistent; it seems entirely possible to me that these statistics are both correct.
Suppose there were 20 men and 20 women in a population. Suppose that 15 of the women have no sexual partners, and the other 5 women each have sex with all 20 men. In that situation, the median number of partners for the men is 5, and the median number of partners for the women is 0.
Since men and women will of course have the same mean number of partners, the fact that the median for women is much smaller than it is for men suggests that the distribution of number-of-partners for women is more skewed than it is for men. This is confirmed by other studies I've seen that reported the full distribution, rather than just the mean or median. A few female prostitutes who have sex with a very large number of men, raising the female mean a lot with virtually no effect on the female median, is certainly part of the cause of such a skew.
For more of the same look at Figure 6 on page 6. More inconsistency: when men and women are asked for the number of partners over the past 12 months, Tables 1 and 2, the numbers come out the same, within epsilon.
Again, I see no inconsistency. I can certainly construct data where this would be true, but the long-term median number of partners for men is greater than for women.
Is this an example of innumeracy in high places?
I think that at least some of the innumeracy is here on the math-fun list, where no-one seems to have noticed that in expecting the median for men and women to be the same, you are attributing to the median a property that is held by the mean, but need not be held by the median.
Andy Latto andy.latto@pobox.com
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