Nonparametric Methods in Statistics with SAS Applications

ANSARI-BRADLEY TEST FOR SCALE PARAMETER 21

PROC NPAR1WAY DATA=data name AB;

CLASS sample name;

VAR variable name;

EXACT;

RUN;

• Here the option AB stands for the Ansari-Bradley test.

• Besides the exact P-value, SAS also outputs an approximate P-value based on

asymptotic normality of the test statistic C, the mean and variance of which are

computed as follows. Assuming n

1

≤ n

2

, if n = n

1

+ n

2

is even, then E(C) =

n

1

(n + 2)/4 and Var(C) = n

1

n

2

(n

2

−4)/[48(n − 1)] (more generally, Var(C) =

n

1

n

2



16

m

∑

j=1

T

j

r

2

j

−n(n + 2)

2



/[16n(n −1)] in case of m groups of tied observations

of sizes T

1

,...,T

m

with associated ranks r

1

,...,r

m

, respectively); and if n = n

1

+ n

2

is odd, ...