Introductory Biostatistics

Example 6.3 A study in Maryland identified 4032 white persons, enumerated
in a uno‰cial 1963 census, who became widowed between 1963 and 1974.
These people were matched, one to one, to married persons on the basis of
race, gender, year of birth, and geography of residence. The matched pairs were
followed to a second census in 1975. The overall male mortality is shown in
Table 6.3. An application of McNemar’s chi-square test (two-sided) yields

X^2 ¼

ð 292  210 Þ^2

292 þ 210

¼ 13 : 39

It can be seen that the null hypothesis of equal mortality should be rejected at
the 0.05 level (13: 39 > 3 :84).

6.3 COMPARISON OF TWO PROPORTIONS

Perhaps the most common problem involving categorical data is the compari-
son of two proportions. In this type of problem we have two independent
samples of binary dataðn 1 ;x 1 Þandðn 2 ;x 2 Þwhere then’s are adequately large
sample sizes that may or may not be equal. Thex’s are the numbers of ‘‘posi-
tive’’ outcomes in the two samples, and we consider the null hypothesis

H 0 :p 1 ¼p 2

expressing the equality of the two population proportions.
To perform a test of significance forH 0 , we proceed with the following steps:

1. Decide whether a one-sided test, say,

HA:p 2 >p 1

or a two-sided test,

HA:p 10 p 2

is appropriate.

TABLE 6.3

Married Men

Widowed Men Dead Alive

Dead 2 292

Alive 210 700

COMPARISON OF TWO PROPORTIONS 213