July 30, 2013

Always ask for the margin of error

The Herald now has picked up this morning’s UK story from the London Fire Brigade, that calls from people handcuffed or otherwise stuck in embarassing circumstances are on the rise.  The Fire Brigade only said

“I don’t know whether it’s the Fifty Shades effect, but the number of incidents involving items like handcuffs seems to have gone up.

The Herald has the relatively sedate headline “‘Fifty Shades of Grey effect’ plagues London“, but the British papers go further (as usual).   For example, the Mirror’s headline was “Fifty Shades of Grey sex leads to soaring 999 calls“.  This is the sort of story that’s too good to check, so no-one seems to have asked how much evidence there is of an increase.

The actual numbers quoted by the fire brigade for calls to people stuck in what could loosely be called household items were: 416 in 2010/11, 441 in 2011/12, and 453in 2012/13. If you get out your Poisson distribution and do some computations, it turns out this is well within the expected random variation — for example the p-value for a test of trend is 0.22 (or for the Bayesians, the likelihood ratio is also very unimpressive). Much more shades of grey than black and white.

So, if you don’t have hot and cold running statisticians at your newspaper, how can you check this sort of thing?  There’s a simple trick for the margin of error for a count of things on a hand calculator: take the square root, add and subtract 1 to get upper and lower  limits, then square them again.  Conveniently, in this case, 441 is exactly 21 squared, so an uncertainty interval around the 441 value would go from 20 squared (400) to 22 squared (484).



Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »