Introductory Biostatistics

Example 7.9 Refer to the nicotine data of Example 7.6, where measurements
were taken both from a sample of infants who had been exposed to household
smoke and from a sample of unexposed infants. We have:

Unexposed (n 1 ¼7)81112142043111

Rank 1 2 3 4 5 7 11

Exposed (n 2 ¼8) 35 56 83 92 128 150 176 208

Rank 6 8 9 10 12 13 14 15

The sum of the ranks for the group of exposed infants is

R¼ 87

In addition,

mR¼

ð 8 Þð 8 þ 7 þ 1 Þ

2

¼ 64

and

sR¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð 8 Þð 7 Þð 8 þ 7 þ 1 Þ

12

r

¼ 8 : 64

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

z¼

R
mR

sR

¼

87
64

8 : 64

¼ 2 : 66

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; pvalue< 0 :01. (It
should be noted that the sample sizes of 7 and 8 in this example may be not
large enough.)
Note:An SAS program would include these instructions:

260 COMPARISON OF POPULATION MEANS