Introductory Biostatistics

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 ðRi
mÞ

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