In March 2009, the Spanish Directorate General of Traffic made the following announcement in the media: 22% of those who died in traffic accidents were not wearing seat belts. To save lives, everyone is recommended to use them.
Expressed in this way, the data are ambiguous. One might argue in this way: if just 22% of the victims were not wearing the seat belt, then a number over three times larger (78%) were in fact wearing seat belts when they died in an accident. Therefore it looks like it would better not to use the seat belt at all.
I’ll explain why this conclusion is fallacious. In order to draw the correct conclusion out of the data, one fact is missing: with or without accidents, how many people do use the seat belt and how many don’t? This piece of data can be found, although it took me some time and effort: 95% drivers do wear the seat belt, just 5% don’t. Combining this with the original data, we can compute the probability of dying in an accident with and without the seat belts: it is over 4 times higher among those who do not wear it than among those who do. If everybody used it, the number of deaths could decrease by 18%. Therefore the advice given was sound, although the data were incomplete.
Given how this news was presented, I feel moved to complain about the way in which politicians and the media use statistics and incorrectly report scientific data. If I do that, am I doing politics? Or am I defending science?