*PROC CAPABILITY and General Statements* |

## Signed Rank Statistic

The signed rank statistic *S* is computed as

where *r*_{i}^{+} is the rank of |*x*_{i}| after discarding
values of *x*_{i} = 0, and *n* is the number of nonzero
*x*_{i} values. Average ranks are used for tied values.
If , the significance of *S* is computed from
the exact distribution of *S*, where the distribution
is a convolution of scaled binomial distributions.
When *n* > 20, the significance of *S* is computed by
treating

as a Student *t* variate with *n* - 1 degrees of
freedom. V is computed as

where the sum is over groups tied in absolute value
and where *t*_{i} is the number of values in the *i*^{ th}
group (Iman 1974, Conover 1980). The null hypothesis
tested is that the mean (or median) is zero, assuming
that the distribution is symmetric. Refer to Lehmann (1975).

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.