Repopulating Canterbury?

Stuff has a story about twins in Canterbury, which is driven by two general human tendencies shared even by statisticians: thinking babies are cute, and overestimating the strangeness of coincidences.  We hear that

Canterbury mums have given birth to 21 sets of twins in the past six weeks.

and

 10 years ago the average would have been about six to eight sets a month.

Using the StatsNZ Infoshare tool (go to Population | Births -VSB | Single and multiple confinements by DHB) we find about 100 sets of multiple births per year in Canterbury DHB and a further dozen or so in South Canterbury DHB, without much change for the past ten years.  That means about nine or so multiple births per month on average.  If you use the average twin rate for all of NZ  (2.7%) and the number of births in the Canterbury region, you get a slightly lower 7.7 sets of twins per month on average.

If there are, on average, 9 multiple births per month, how long would you have to wait for a six-week period with 21?  Because the possible six-week periods overlap, it’s hard to do this calculation analytically, but we can simulate it: 9 per month is 108 per year, which is 108/52 per week.  We simulate a long string of one-week counts from a Poisson distribution with mean 108/52, and see how long we have to  wait between six-week totals of at least 21.  The average waiting time is about two years.  (you have to be a bit careful: the proportion of six-week intervals over 21 is a lot more than one in two years, because of the overlap between six-week intervals)

So, this is a once in two years coincidence if we just look at Canterbury.  It’s much more likely if twin stories from other regions might also end up as news — the probability is hard to estimate, because twins in Canterbury really are more newsworthy than in, say, Waikato.