No sex please, I'm a statistician

My 'garbage statistics' detector went onto high alert when I noticed the headline 'Don’t panic, but there’s a one in 30 chance you’ve had sex with your cousin' in that usually understated publication*, the Metro.

We'll come back to that specific statistic, but it was probably prompted by a press release from a company called AncestryDNA, which apparently has done a 'demographic analysis' to produce this shock result. I can't find any link to the actual research, which is a touch suspicious, but various other publications have produced information from the press release including:

  • 'For the average Brit' there's a one in 300 chance that a complete stranger is their cousin
  • The average British person has 193,000 living cousins within Britain
  • The 'typical Brit' has five first cousins, right up to 174,000 sixth cousins
  • Researchers used birth rates and census data to estimate how many close living relatives each of us has.
Okay, so now we're getting a little closer to the facts, although there's still a lot of room for baloney in what we've been given. That last piece of information does mean that in principle such calculations are possible, though I suspect it was sampled rather than using the full census data.

We can, first of all, totally dismiss the headline, even if the numbers are right, because no one considers sixth cousins to be 'cousins' - in fact 'cousin' on its own specifically means first cousin - so this is clearly a ridiculous exaggeration. But it would also be interesting to see if those two figures - there's a 1 in 300 chance that complete stranger is a [sixth cousin or closer] and 1 in 30 chance 'you've had sex' with them.

There are about 65 million people in the UK, so select one at random and to get that 1 in 300 chance having 193,000 relatives is the right order of magnitude. However, none of us has an equal chance of coming into contact with everyone in Britain. My suspicion is that because there often clusters of relatives near where we live, there may be a better than 1 in 300 chance that a stranger you meet at random is a sixth cousin or closer.

I struggle a lot more with the 'one in 30 chance you've had sex with your cousin.' Firstly, as a headline it's too specific. They didn't say 'the average Brit', they said 'you.' Hardly any individual is 'the average Brit', so immediately this falls down as a suggestion. But even if we rework the headline to 'there's a one in 30 chance the average Brit had sex with their cousin' there are big problems.

The majority of individuals will have had significantly fewer than the mean number of sexual partners. Why? In a 2010 survey, these were apparently 9.3 for men and 4.7 for women. This average comes from a very skewed distribution. Women, for instance, can only have had 5 fewer than the average (in round figures) number of partners but could have had many more than the average. So this makes the average unrepresentative.

My guess (I could be wrong, because I don't have any information on the 'research') is that all AncestryDNA did was to take than 1 in 300 chance of a stranger being a cousin and divide it by 10 as the average number of partners. If so, that is dire in so many ways. They seemed to have applied the male figure to the population as a whole. Then there are issues with the way the population is segmented. One is that we are even less likely to have sex with someone from anywhere in the country than we are to meet them. And the other problem is that we tend to have sex with people of relatively similar age. This cuts out a vast swathe of the population, and could have a significant impact in terms of chances of being related.

You could say I'm breaking a butterfly on the wheel here. It was just a 'fun bit of research' for marketing purposes. But once you claim you have done serious research and get the media to spread it around, I think there is a responsibility to be clear how the numbers are produced, and to make that research as high quality as possible.

*Irony alert