The split-up algorithm: a fast symbolic method for computing p-values of distribution-free statistics
- 330 Downloads
Many distribution-free statistics have the drawback that computing exact p-values under the null hypothesis is an intensive task. When the sample sizes are small or the number of ties is large, approximations are often unsatisfactory. Moreover, tables of exact critical values are not available for conditional rank statistics (ties, censoring), for rank statistics with arbitrary regression constants, or for permutation test statistics. In those cases, it is important to have a fast algorithm for computing exact p-values. We present a new algorithm and apply it to a large class of distribution-free one-sample, two-sample and serial statistics. The algorithm is based on splitting the probability generating function of the test statistic into two parts. We compare the speed of this “split-up algorithm” to that of existing procedures and we conclude that our new algorithm is faster in many cases.
KeywordsExact p-values two-sample rank tests signed rank tests rank correlation tests rank autocorrelation tests permutation tests generating functions
I would like to thank Alessandro Di Bucchianico and the referees of this journal for their useful comments on earlier versions of this paper.
- Streitberg, B., and J. Röhmel (1986). Exact distributions for permutation and rank tests: an introduction to some recently published algorithms. Statistical Software Newsletter, 12, 10–17.Google Scholar
- Streitberg, B., and J. Röhmel (1987). Exakte Verteilungen für Rang-und Randomisierungstests im allgemeinen c-Stichprobenproblem. EDV in Medizin und Biologie, 18, 12–19.Google Scholar
- Van de Wiel, M.A. (1996). Computing exact distributions of rank statistics with computer algebra. Master’s thesis, Eindhoven University of Technology, The Netherlands.Google Scholar
- Van de Wiel, M.A. (1998). Exact distributions of two-sample rank statistics and block rank statistics using computer algebra. Technical Report Memorandum COSOR 98-14, Eindhoven University of Technology, The Netherlands.Google Scholar