Data Analysis Papers

Exact Methods in the NPAR1WAY Procedure
Anupama Narayanan and Donna Watts, SUGI Proceedings, 1996


Exact nonparametric methods have an advantage over asymptotic methods since they remain valid for very small sample sizes, as well as for data that are sparse, skewed, or heavily tied. However, computing exact p-values by direct enumeration can be very time-consuming, and may be infeasible for many problems. Over the past few years, many new algorithms for exact computations have been published. Beginning with Release 6.11 of the SAS System, exact p-values are available in the NPAR1WAY procedure. This procedure uses Mehta and Patel’s network algorithm, substantially reducing the computational effort required.

The NPAR1WAY procedure computes exact p-values for the simple linear rank statistics based on Wilcoxon scores, median scores, Van der Waerden scores, and Savage scores. Exact p-values are computed for these statistics when the data are classified into two levels (two-sample tests), and when the data are classified into more than two levels (multi-sample tests). For the two-sample case, the simple linear rank statistics listed above correspond to the Wilcoxon-Mann-Whitney, Median, Van der Waerden, and Savage tests, respectively. For the multi-sample case, the NPAR1WAY procedure gives exact p-values for the Kruskal-Wallis, Brown-Mood, k-sample Van der Waerden, and k-sample Savage tests.