Introductory Biostatistics

In addition, we have

A¼ 350

B¼ 390

n 1 ¼ 130

n 2 ¼ 335

n 3 ¼ 235

n 4 ¼ 40

N¼ 740

Substituting these values into the equations of the test statistic, we have

S¼ 53 ; 225  40 ; 025

¼ 13 ; 200

sS¼

ð 350 Þð 390 Þ

ð 3 Þð 740 Þð 739 Þ

ð 7403  1303  3353  2353  403 Þ

 1 = 2

¼ 5414 : 76

leading to

z¼

13 ; 200

5414 : 76

¼ 2 : 44

which shows a high degree of significance (one-sidedpvalue¼ 0 :0073). It is
interesting to not that in order to compare the extent of injury from those who
used seat belts and those who did not, we can perform a chi-square test as pre-
sented in Section 6.6. Such an application of the chi-square test yields

X^2 ¼ 9 : 26

with 3 df is 7.81 (for 0: 01 apa 0 :05). Therefore, the di¤erence between the
two groups is significant at the 5% level but not at the 1% level, a lower degree
of significance (compared to thepvalue of 0.0073 above). This is because the
usual chi-square calculation takes no account of the fact that the extent of
injury has a natural ordering: none<minor<major<death. In addition, the
percent of seat belt users in each injury group decreases from level ‘‘none’’ to
level ‘‘death’’:

232 COMPARISON OF POPULATION PROPORTIONS