Introductory Biostatistics

equals 0, 1, and 2 (observed value; the probabilities for these tables are 0.017,
0.105, and 0.252, respectively).
Note:An SAS program would include these instructions:

DATA;
INPUT CVM DIET COUNT;
CARDS;
112
1223
215
2 2 30;
PROC FREQ;
WEIGHT COUNT;
TABLES CVD*DIET/CHISQ;

The output also includes Pearson’s test (X^2 ¼ 0 :559;p¼ 0 :455) as well.

6.7 ORDERED 2DkCONTINGENCY TABLES

In this section we present an e‰cient method for use with ordered 2
kcon-
tingency tables, tables with two rows and withkcolumns having a certain nat-
ural ordering. We introduced it, in Chapter 1, to provide a descriptive statistic,
thegeneralized odds.
In general, consider an ordered 2
ktable with the frequencies shown in
Table 6.18. The number of concordances is calculated by

C¼a 1 ðb 2 þþbkÞþa 2 ðb 3 þþbkÞþþak 1 bk

The number of discordances is

D¼b 1 ða 2 þþakÞþb 2 ða 3 þþakÞþþbk 1 ak

To perform the test, we calculate the statistic

S¼CD

TABLE 6.17

Type of Diet

Cause of Death High Salt Low Salt Total

Non-CVD 2 (2.92) 23 (22.08) 25
CVD 5 (4.08) 30 (30.92) 35

Total 7 53 60

230 COMPARISON OF POPULATION PROPORTIONS