If you’ve been following the news, or twitter, you’ll have noticed that the current pope, Pope Benedict XVI (pronounces Kss-vee) has decided to retire at the end of the month, to spend more time with his twitter account. Anyway, the Grauniad had an interactive thingy up, which, they suggested, “illustrates the idea that a long-serving pope is often followed by one whose papacy is much shorter”. Well, possibly. But you really need to do a bit more than stare at a fancy graphic. You actually need to do some analysis of the data.
Of course, first one has to grab the data. Then we can plot it:
and we can see that there is a lot of variation, and possibly some long-term trends (e.g. recently popes seem to have survived longer). But is a long-lasting pope followed by one who keels over quickly? Well, in statistical terms that would mean that lengths of papal reigns would be negatively auto-correlated. And we have a nice tool to look at that sort of thing: it’s called the autocorrelation function, or ACF. Our hypothesis is, in technical language, that the lag one ACF is negative.
We can calculate that, and we find that it is 0.15. So, it is (a) small, and (b) in the wrong direction. No p-values needed. But this might be an effect of the longer-term trends in the data. We can remove this by fitting a suitable smooth curve (a spline, for those who want to know), and look at that:
The pink line is the fitted line, with the (approximate) 95% confidence interval.
We can see the long-term trends: from about 600AD to 1100AD was not a good period for popes. And, but for a blip around the 15th Century life seems to be improving. But what about the lag 1 acf? Well, that is 0.02, so basically zero, and also still in the wrong direction.
All in all, I think this disproves the notion that long reigns are followed by short ones. Except, it might be that this has changed over time. If we only look at the residuals for popes who started their papacy from after 1800 (i.e. the last 14 popes), we get an estimate of -0.09, which is at least in the right direction. Except that the approximate standard deviation is 0.29, so much larger. If we only look at the 9 popes who started poping after 1900, we get an acf of -0.62, with a standard error of 0.30. So we might just about have crept up to statistical significance (the z-statistic is -2.1, so less than -1.96 for a 5% significance), but (a) the sample size is small, (b) the significance is marginal, and the large-sample used may be way off, and (c) I’ve had to poke around a bit to get to something which might be marginally significant, so there is a certain amount of data dredging: looking for rubies in the rubbish and not stopping until I find one.
All in all, a pope will not spring eternal. Sorry.