sR¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð 21 Þð 22 Þð 43 Þ
24r¼ 28 : 77
leading to a standardizedzscore of
z¼90 115 : 5
28 : 77
¼ 0 : 89
The result indicates that the systolic pressure of the hepatic artery measured
five years after the liver transplant, compared to the measurement at trans-
plant, is lower on the average; however, the di¤erence is not statistically signif-
icant at the 5% level ( 0 : 89 > 1 :96).
Note: An SAS program would include these instructions:
DATA;
INPUT POST PRE;
DIFF = POST - PRE;
DATALINES;
46 35
...
35 27
25 31;
PROC UNIVARIATE;
for which we’ll get, among many other things, the test statistic (SGN RANK)
and thepvalue (Prob>jSj).
7.5 ONE-WAY ANALYSIS OF VARIANCE
Suppose that the goal of a research project is to discover whether there are dif-
ferences in the means of several independent groups. The problem is how we
will measure the extent of di¤erences among the means. If we had two groups,
we would measure the di¤erence by the distance between sample meansðxyÞ
and use the two-samplettest. Here we have more than two groups; we could
take all possible pairs of means and do many two-samplettests. What is the
matter with this approach of doing many two-samplettests, one for each pair
of samples? As the number of groups increases, so does the number of tests to
perform; for example, we would have to do 45 tests if we have 10 groups to
compare. Obviously, the amount of work is greater, but that should not be the
critical problem, especially with technological aids such as the use of calcu-
lators and computers. So what is the problem? The answer is that performing
ONE-WAY ANALYSIS OF VARIANCE 263