2.170 More smokers live at least 20 more years! You can see the headlines: “More smokers than nonsmokers live at least 20 more years after being contacted for study!” A medical study contacted randomly chosen people in a district in England. Here are data on the 1314 women contacted who were either current smokers or who had never smoked. The tables classify these women by their smoking status and age at the time of the survey and whether they were still alive 20 years later.41
| Age 18 to 44 | Age 45 to 64 | Age 65+ | ||||
|---|---|---|---|---|---|---|
| Smoker | Not | Smoker | Not | Smoker | Not | |
| Dead | 19 | 13 | 78 | 52 | 42 | 165 |
| Alive | 269 | 327 | 167 | 147 | 7 | 28 |
(a) From these data, make a two-way table of smoking (yes or no) by dead or alive. What percent of the smokers stayed alive for 20 years? What percent of the nonsmokers survived? It seems surprising that a higher percent of smokers stayed alive.
(b) The age of the women at the time of the study is a lurking variable. Show that within each of the three age groups in the data, a higher percent of nonsmokers remained alive 20 years later. This is another example of Simpson’s paradox.
(c) The study authors give this explanation: “Few of the older women (over 65 at the original survey) were smokers, but many of them had died by the time of follow-up.” Compare the percent of smokers in the three age groups to verify the explanation.