This is the Base Rate Fallacy, which also crops up as the Prosecutor's Fallacy and False

Positive Paradox. A distinctive example was committed by the journalist Woodrow Wyatt, later Lord Wyatt of Weeford. He claimed that the statistics demonstrate that smoking is good for you. He put this argument in his misnamed column "The Voice of Reason" in the News of the World, and dared to write this in the late '80s, when there was no doubt that smoking was bad for you. But Wyatt observed that smokers had lower death rates from nearly all causes of death, including road accidents, and so smoking must be good for you. But we can see that these low death rates result from smokers having high rates of death from smoking-related diseases, which means that fewer of them survive to die from the causes that kill most of the rest of us. Since he worked in gambling, as chairman of the Tote, I do often wonder whether he was providing deliberate misinformation rather than falling into error.

Posted By: Tombs, Nov 15, 13:45:17