lem, we have k independent samples of binary data ðn 1 ;x 1 Þ;ðn 2 ;x 2 Þ;...;
ðnk;xkÞ, where then’s are sample sizes and thex’s are the numbers of positive
outcomes in thek samples. For thesekindependent binomial samples, we
consider the null hypothesis
H 0 :p 1 ¼p 2 ¼¼pkexpressing the equality of thekpopulation proportions.]
Example 6.12 The case–control study of lung cancer among male residents of
coastal Georgia of Example 6.6 was referred to in an attempt to identify rea-
sons for the exceptionally high rate of lung cancer (Table 6.15). We have
e 11 ¼
ð 46 Þð 61 Þ
299
¼ 9 : 38
e 12 ¼ 46 9 : 38
¼ 36 : 62
e 21 ¼ 61 9 : 38
¼ 51 : 62
e 22 ¼ 253 51 : 62
¼ 201 : 38leading to
X^2 ¼
ð 11 9 : 38 Þ^2
9 : 38þð 35 36 : 62 Þ^2
36 : 62þð 50 51 : 62 Þ^2
51 : 62þð 203 201 : 38 Þ^2
201 : 38
¼ 0 : 42This result, a chi-square value, is identical to that from Example 6.6, where we
obtained azscore of 0.64 [note thatð 0 : 64 Þ^2 ¼ 0 :42].
Example 6.13 A study was undertaken to investigate the roles of bloodborne
environmental exposures on ovarian cancer from assessment of consumption of
TABLE 6.15
Shipbuilding Cases Controls Total
Yes 11 35 46
No 50 203 253
Total 61 238 299
INFERENCES FOR GENERAL TWO-WAY TABLES 227