One-third of adult smokers have a mental illness.

We write in response to Simon Chapman who questioned the estimate of smoking prevalence among people with mental illness in Australia [1]. Unfortunately Chapman has made a basic statistical error that has caused him to substantially underestimate the prevalence of smoking in people with mental illness. Sourcing data from the 2004 National Health Survey conducted by the Australian Bureau of Statistics [2] he reports that 21% of Australian adults were daily smokers, with smoking prevalence of 17.7% among people with no long-term mental illness. He then subtracts these figures to estimate 3.3 % of the adult population as being daily smokers who have a mental illness. This is not correct. When two proportions are calculated from two disjoint populations (ie. people with no long-term mental illness, and people with a long-term mental illness) with separate denominators, the proportions do not add to a total. Indeed, if there were no relationship between smoking and mental illness, one would expect the same smoking rate (21% in this case) among those both with and without mental illness.