Counts and proportions
Phil Price writes (at Andrew Gelman’s blog) on the impact of bike-share programs:
So the number of head injuries declined by 14 percent, and the Washington Post reporter — Lenny Bernstein, for those of you keeping score at home — says they went up 7.8%. That’s a pretty big mistake! How did it happen? Well, the number of head injuries went down, but the number of injuries that were not head injuries went down even more, so the proportion of injuries that were head injuries went up.
To be precise, the research paper found 638 hospitalised head injuries in 24 months before the bike share program, and 273 in the 12 months afterwards. In a set of control cities that didn’t start a bike-share program there were 712 head injuries in the 24 months before the matching date and 342 in the 12 months afterwards. That is, a 14.4% decrease in the cities that added bike-share programs and a 4% decrease in those that didn’t.
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 »