Alcohol Stats - the bitchslap
Transposed statistics -Times Online
Sir, Professor Ian Gilmore (letter, April 27) tells us that all but one liver-ward patients with alcohol-related liver problems were daily or very frequent drinkers, and deduces that “Middle England” drinkers are ending up on liver wards by regularly consuming what some might consider to be moderate levels of alcohol. Unfortunately, the deduction is misleading.
The premise shows that if one is a liver-ward patient then the probability of being a daily or frequent drinker is very high. But it says little directly about the probability of being on a liver ward, if one is a daily or frequent drinker — which is surely what one is interested in. This mistake has arisen sufficiently often for it to be given a name: the error of the transposed conditional.
Professor David J. Hand
President, Royal Statistical Society