Nonparametric Methods in Statistics with SAS Applications

42 HYPOTHESES TESTING FOR SEVERAL SAMPLES

The critical value from Table A.5 for k = 3, n = 10, and

α

= 0.05 is 6.2. For

α

= 0.01,

it is 9.6. Thus, the null hypothesis H

0

:

θ

A

=

θ

B

=

θ

C

is rejected even at the 0.01 level

of significance and the conclusion is that tasted beer brands differ in preference rat-

ings.

To conduct the Friedman rank test in SAS, we use the code

data beer;

input taster brand $ rating @@;

datalines;

1 A 4 1 B 5 1 C 8 2 A 3 2 B 7 2 C 6 3 A 2 3 B 8 3 C 8

4 A 5 4 B 7 4 C 9 5 A 1 5 B 3 5 C 6 6 A 4 6 B 4 6 C 6

7 A 3 7 B 6 7 C 8 8 A 2 8 B 5 8 C 5 9 A 2 9 B 7 9 C 9

10 A 6 10 B 4 10 C 5

;

proc sort data=beer;

by taster;

run;

proc rank data=beer out=ranked;

var rating;

by taster;

ranks rank;

run;

proc freq data=ranked;

table taster*brand*rank/noprint cmh;

run; ...