C¼ð 15 Þð 100 þ 30 þ 44 þ 23 Þþð 40 Þð 30 þ 23 Þþð 100 Þð 23 Þ
¼ 8380
D¼ð 5 Þð 100 þ 30 þ 40 þ 10 Þþð 44 Þð 30 þ 10 Þþð 100 Þð 10 Þ
¼ 4410
leading to generalized odds of
y¼
C
D
¼
8380
4410
¼ 1 : 90
This means that the odds that the more educated person favors more restriction
for smoking in public places is 1.90. In other words, people with more educa-
tion would prefer more restriction on smoking in public places.
1.3.4 Mantel–Haenszel Method
In most investigations we are concerned with one primary outcome, such as a
disease, and are focusing on one primary (risk) factor, such as an exposure with
a possible harmful e¤ect. There are situations, however, where an investigator
may want to adjust for a confounder that could influence the outcome of a
statistical analysis. Aconfounder,orconfounding variable, is a variable that
may be associated with either the disease or exposure or both. For example, in
Example 1.2, a case–control study was undertaken to investigate the relation-
ship between lung cancer and employment in shipyards during World War II
among male residents of coastal Georgia. In this case, smoking is a possible
counfounder; it has been found to be associated with lung cancer and it may
be associated with employment because construction workers are likely to be
smokers. Specifically, we want to know:
TABLE 1.16
Policy Favored
Highest
Education Level
No
Restrictions
on Smoking
Smoking Allowed
in Designated
Areas Only
No
Smoking
at All Total
Grade school 15 40 10 65
High school 15 100 30 145
College graduate 5 44 23 72
Total 35 184 63 300
26 DESCRIPTIVE METHODS FOR CATEGORICAL DATA