Correlation does not imply Causation

The first time I heard the phrase “correlation does not imply causation”, I thought, well ok, but what’s a good real world example of this? I think the example given in the textbook I was reading was something to do with ice cream consumption and swimming pool use… fine but contrived. Here’s are more eye catching one that I saw in a post over at dynomight. The following two statements are true: If you measure a bunch of people’s blood levels of Vitamin D and also check to see how many of them die in a multiyear period you find that low vitamin D levels are highly correlated with higher mortality. Specifically, people in the 25th percentile are 30% more likely to die than those in the 75% percentile. Giving people vitamin D supplements has little to no effect on their health. The 25th and 75th percentiles are not that far from the mean! As a point of comparison, those percentiles for UK men’s height are about 174cm and 181cm1. Not particularly high or low values! How can this be? As…