suggesting that they are not the same and that a child seems more prone to
taking drug B than drug A. However, the chi-square statistic
X^2 ¼
ð 39 þ 31 Þ½ð 8 Þð 19 Þð 31 Þð 12 Þ^2
ð 39 Þð 31 Þð 20 Þð 50 Þ
¼ 2 : 80 ð< 3 : 84 ;a¼ 0 : 05 Þ
shows that the di¤erence is not statistically significant at the 0.05 level.
Example 6.6 In Example 1.2, a case–control study was conducted to identify
reasons for the exceptionally high rate of lung cancer among male residents of
coastal Georgia. The primary risk factor under investigation was employment
in shipyards during World War II, and Table 6.6 provides data for non-
smokers. We have for the cases,
p 2 ¼
11
61
¼ 0 : 180
and for the controls,
p 1 ¼
35
238
¼ 0 : 147
An application of the procedure yields a pooled proportion of
p¼
11 þ 35
61 þ 238
¼ 0 : 154
leading to
z¼
0 : 180 0 : 147
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð 0 : 154 Þð 0 : 846 Þ 611 þ 2381
q
¼ 0 : 64
TABLE 6.6
Shipbuilding Cases Controls
Yes 11 35
No 50 203
216 COMPARISON OF POPULATION PROPORTIONS