X^2 ¼
ðbcÞ^2
bþcand the test is known asMcNemar’s chi-square. If the test is one-sided,zis used
and the null hypothesis is rejected at the 0.05 level when
zb 1 : 65If the test is two-sided,X^2 is used and the null hypothesis is rejected at the 0.05
level when
X^2 b 3 : 84[It should be noted that 3: 84 ¼ð 1 : 96 Þ^2 ,sothatX^2 b 3 :84 is equivalent to
za 1 :96 orzb 1 :96.]
Example 6.2 It has been noted that metal workers have an increased risk for
cancer of the internal nose and paranasal sinuses, perhaps as a result of expo-
sure to cutting oils. Therefore, a study was conducted to see whether this par-
ticular exposure also increases the risk for squamous cell carcinoma of the
scrotum.
Cases included all 45 squamous cell carcinomas of the scrotum diagnosed in
Connecticut residents from 1955 to 1973, as obtained from the Connecticut
Tumor Registry. Matched controls were selected for each case based on age at
death (within eight years), year of death (within three years), and number of
jobs as obtained from combined death certificate and directory sources. An
occupational indicator of metal worker (yes/no) was evaluated as the possible
risk factor in this study; results are shown in Table 6.2. We have, for a one-
tailed test,
z¼26 5
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
26 þ 5p¼ 3 : 77
indicating a very highly significant increase of risk associated with the exposure
(p< 0 :001).
TABLE 6.2
Controls
Cases Yes No
Yes 2 26
No 5 12212 COMPARISON OF POPULATION PROPORTIONS