Introductory Biostatistics

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 ފ^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