To estimate the health risks of obesity, we might compare how long obese and nonobese people live. Smoking is a lurking variable that may reduce the gap between the two groups, because smoking tends to both reduce weight and lead to earlier death. So if we ignore smoking, we may underestimate the health risks of obesity. Illustrate Simpson’s paradox by a simplified version of this situation: make up two–way tables of obese (Yes or No) by early death (Yes or No) separately for smokers and nonsmokers such that 1) Obese smokers and obese nonsmokers are both more likely to die earlier than those who are not obese. 2) But when smokers and nonsmokers are combined into a two–way table of obese by early death, persons who are not obese are more likely to die earlier because more of them are smokers.
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