Wednesday, March 18: Fun with statistics

An article on the Herald front page today discusses the alleged links between working nights and breast cancer, on which basis the Danish government has paid compensation to "40 women who developed breast cancer after working night shifts in state sector jobs:

"One report on which the IARC [International Agency for Research on Cancer] based its findings showed a 36 per cent greater risk of breast cancer for women who had worked night shifts for more than 30 years, compared with women who had never worked nights."

Professor Neil Pearce of Massey University says that the 36 per cent increase, while not trivial, is "not huge". But it's not clear that reporter Martin Johnson picked up on that message when he put 36% in big red letters in a special side box. People in general don't understand statistics, and you can bet that there are a considerable number of people who have read that and immediately thought that this statistic means:

• 36 per cent of women who work nights will get breast cancer
• if you work a single night shift, you will be 36 per cent more likely to get breast cancer
• 36 per cent of women work night shifts
• 36 per cent of night shifts will give you breast cancer
• working night shifts will give 36 per cent of your breasts cancer
• reading about night shifts will give you 36 cancers

But seriously now, folks. The reason that 36 per cent is "not huge" is that the base rate (the percentage of women who get breast cancer normally) is relatively low - although obviously still far too high. Not much multiplied by 1.36 is still not that much. Worth looking into, both by scientists and policy makers? Definitely. Worth putting in big red letters under a scary headline on the front page? Probably not.

And let's remember - this 36 per cent figure comes from a single study. And the contrast in criteria used by the original study and the Herald article (via a Massey University study - *ahem*) is informative: in the original report, 'night workers' were women who had worked night shifts for more than 30 years; in the Massey study quoted by the Herald and then extrapolated to find how many 'night workers' there are, it was anyone who had worked a night shift in the last four weeks. But that didn't stop the Herald putting (imagine big, red letters here) "50,000 women and 120,000 men work night shifts [in New Zealand]".

36 percent of 50,000 is 18,000. Oh. My. God...