Introductory Biostatistics

then standardize it to obtain

z¼

SmS

sD

wheremS¼0 is the mean ofSunder the null hypothesis and

sS¼

AB

3 NðN 1 Þ

ðN^3 n 13 n^32 n^3 kÞ

 1 = 2

The standardized z score is distributed as standard normal if the null
hypothesis is true. For a one-sided alternative, which is a natural choice for this
type of test, the null hypothesis is rejected at the 5% level ifz> 1 :65 (or
z< 1 :65 if the termsconcordanceanddiscordanceare switched).

Example 6.15 Consider an example concerning the use of seat belts in auto-
mobiles. Each accident in this example is classified according to whether a seat
belt was used and the severity of injuries received: none, minor, major, or death
(Table 6.19). For this study on the use of seat belts in automobiles, an applica-
tion of the method above yields

C¼ð 75 Þð 175 þ 135 þ 25 Þþð 160 Þð 135 þ 25 Þþð 100 Þð 25 Þ

¼ 53 ; 225

D¼ð 65 Þð 160 þ 100 þ 15 Þþð 175 Þð 100 þ 15 Þþð 135 Þð 15 Þ

¼ 40 ; 025

TABLE 6.18

Column Level

Row 1 2  k Total

1 a 1 a 2  ak A
2 b 1 b 2  bk B

Total n 1 n 2  nk N

TABLE 6.19

Extent of Injury Received

Seat Belt None Minor Major Death Total

Yes 75 160 100 15 350
No 65 175 135 25 390

Total 130 335 235 40 740

ORDERED 2
kCONTINGENCY TABLES 231