D'oh!

Oops, wrong Simpson.  This paradox is also known as the reversal paradox.  From Esther Inglis-Arkell, writing in io-9.

Simpson's Paradox "proves" smoking is good for you
How do you prove that smoking is beneficial to your health? By employing Simpson's Paradox, of course. This paradox shows that a large grouping of data can be worth much less than the sum of its parts. 
If I were at a tobacco company, and I wanted to prove that smoking was good for you, I would only have to do two things. First, I would have to wrap my soul in a paper bag, throw it to the ground, and stomp on it. Next, I would have to look at a study done in the UK in the early 1970s. 
The study was meant to study how a number of different factors affected people's health. Among other things, it took a look at smoking, and whether it has any health affects. In particular, it looks at women and their survival rates over the next twenty years. Amazingly, forty-three percent of the nonsmokers died, whereas only thirty-eight percent of the smokers died. Clearly cigarettes saved their lives! 
Or perhaps it was Simpson's paradox. Simpsons paradox is named after Edward Simpson, but was noted by many people. Sometimes there are clear trends in individual groups of data that disappear when the groups are pooled together. In this case, when the women were broken down by decade, each single group shows smokers had a higher mortality rate than nonsmokers. However, many more of the young women smoked than the older women. Although cigarette smoking increased mortality across the board, more young smokers than significantly older nonsmokers will live for the next twenty years. Add all the groups together and, although tobacco is bad for people, it won't take forty years off their lives and so in the aggregate appears beneficial.

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