Note: An SAS program would include these instructions:
DATA;
INPUT GROUP $ SERUMT;
DATALINES;
N .44
...
N .87
F .46
...
F .65
L .37
...
L .51
H .44
...
H .54;
PROC ANOVA;
CLASS GROUP;
MODEL SERUMT = GROUP;
MEANS GROUP;
The last row is an option to provide the sample mean of each group.
7.6 BRIEF NOTES ON THE FUNDAMENTALS
There are two simple, di¤erent, but equivalent ways to view Wilcoxon’s rank-
sum test. In the first approach, one can view the ranksR 1 ;R 2 ;...;Rnfrom a
combined sample,n¼n 1 þn 2 , as forming finite population. The mean and
variance of this finite population are
m¼
Pn
i¼ 1 Ri
n
¼
nþ 1
2
s^2 ¼
Pn
i¼ 1 ðRimÞ
2
n
¼
n^2 1
12
Under the null hypothesis, the rank sumR, from the sample with sizen 1 ,isthe
total from a sample of sizen 1 from the finite population above, so that
BRIEF NOTES ON THE FUNDAMENTALS 269