Question

David S. Moore and age at the time of the survey and whether they were still alive 20 years later. III. SMOKERS 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 smok- ing (yes or no) by dead or alive. What percent of the smokers stayed alive for 20 years? What per- cent of the nonsmokers survived? It seems sur- prising 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.

Answer 1

			Age 18 to 44		Age 45 to 64		Age 65+
			Smoker	Not	Smoker	Not	Smoker	Not	Total
	Dead	Observed	19	13	78	52	42	165	369
		% of row	5.1%	3.5%	21.1%	14.1%	11.4%	44.7%	100.0%
		% of column	6.6%	3.8%	31.8%	26.1%	85.7%	85.5%	28.1%
		% of total	1.4%	1.0%	5.9%	4.0%	3.2%	12.6%	28.1%
	Alive	Observed	269	327	167	147	7	28	945
		% of row	28.5%	34.6%	17.7%	15.6%	0.7%	3.0%	100.0%
		% of column	93.4%	96.2%	68.2%	73.9%	14.3%	14.5%	71.9%
		% of total	20.5%	24.9%	12.7%	11.2%	0.5%	2.1%	71.9%
	Total	Observed	288	340	245	199	49	193	1314
		% of row	21.9%	25.9%	18.6%	15.1%	3.7%	14.7%	100.0%
		% of column	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%
		% of total	21.9%	25.9%	18.6%	15.1%	3.7%	14.7%	100.0%

(a) 14.8% of smokers survived.

18.6% of non-smokers survived.

(b) Shown in the table above.

(c) 7.9% died.