Introductory Biostatistics

mR¼n 1 m

sR^2 ¼n^21

s^2

n 1

n
n 1

n
 1



The last term of the last equation is called thecorrection factor for finite popu-
lation.
Equivalently, the ranks R 1 ;R 2 ;...;Rn from a combined sample can be
thought of as a standardized representation of the numbersx 1 ;x 2 ;...;xn 1 from
sample 1 andy 1 ;y 2 ;...;yn 2 from sample 2, which preserves all order relation-
ships. Therefore, it is plausible to contruct a test statistic by substituting
R 1 ;R 2 ;...;Rn 1 forx 1 ;x 2 ;...;xn 1 andR 1 ;R 2 ;...;Rn 2 for y 1 ;y 2 ;...;yn 2. The
result is equivalent to Wilcoxon’s rank-sum test.

7.7 NOTES ON COMPUTATIONS

Samples of SAS program instructions were provided for all procedures, at the
end of Examples 7.2, 7.7, 7.9, 7.10, and 7.12. Since allpvalues provided by
SAS are for two-sided alternatives. The one-sample and two-samplettests can
also be implemented easily using Microsoft’s Excel. The first two steps are the
same as in obtaining descriptive statistics: (1) click thepaste function icon,f*,
and (2) clickStatistical. Among the functions available, choose TTEST. A box
appears with four rows to be filled. The first two are for data in the two groups
to be compared; in each you identify the range of cells, say B2:B23. The third
box asking for ‘‘tails,’’ enter ‘‘1’’ (‘‘2’’) for one-sided (two-sided) alternative.
Enter the ‘‘type’’ of test on the last row, ‘‘1’’ (‘‘2’’) for a one-sample (two-sam-
ple)ttest.

EXERCISES

7.1 The criterion for issuing a smog alert is established at greater than 7 ppm

of a particular pollutant. Samples collected from 16 stations in a certain

city give axvalue of 7.84 ppm with a standard deviation ofs¼ 2 : 01

ppm. Do these findings indicate that the smog alert criterion has been

exceeded? State clearly your null and alternative hypotheses and choice

of test size (alpha level).

7.2 The purpose of an experiment is to investigate the e¤ect of vagal nerve

stimulation on insulin secretion. The subjects are mongrel dogs with

varying body weights. Table E7.2 gives the amount of immunoreactive

insulin in pancreatic venous plasma just before stimulation of the left

vagus and the amount measured 5 minutes after stimulation for seven

dogs. Test the null hypothesis that the stimulation of the vagus nerve has

270 COMPARISON OF POPULATION MEANS