Introductory Biostatistics

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