Introductory Biostatistics

In addition,

mR¼

10 ð 10 þ 10 þ 1 Þ

2

¼ 105

and

sR¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð 10 Þð 10 Þð 10 þ 10 þ 1 Þ

12

r

¼ 13 : 23

Substituting these values into the equation for the test statistic, we have

z¼

R
mR

sR

¼

143
105

13 : 23

¼ 2 : 87

Sincez> 1 :96, we reject the null hypothesis at the 5% level. (In fact, since
z> 2 :58, we reject the null hypothesis at the 1% level.) Note that if we use the
sum of the ranks for the other group (heavy smokers), the sum of the ranks is
67, leading to azscore of

67 
 105

13 : 23

¼
2 : 87

and we would come to the same decision.

TABLE 7.4

Nonsmokers Heavy Smokers

Measurement Rank Measurement Rank

0.44 8.5 0.45 10
0.44 8.5 0.25 1
0.43 7 0.40 6
0.56 14 0.27 2
0.85 17 0.34 4
0.68 15 0.62 13
0.96 20 0.47 11
0.72 16 0.30 3
0.92 19 0.35 5
0.87 18 0.54 12

NONPARAMETRIC METHODS 259