New software for computation exact distribution of a multivariate nonparametric partially order set test statistic

Abstract

Exact nonparametric methods in statistical methods have an advantage over asymptotic methods, since they remain valid for very small sample sizes. It is often said that the coherence of an association between a treatment and outcomes is important in judging whether the association is causal. In this study we obtain exact distribution for multivariate Nonparametric Poset (partially order set) test statistic that was developed by Rosenbaum (1994). This test is applicable to detect a coherent association in observational studies. We designed an algorithm for calculating the exact distribution of the Poset test statistic which is feasible with respect to time and memory constraints on commonly available PCs. For establishing these algorithms, the enumeration method will be used and critical values for one side significance level (α=0.05, α=0.01) are computed. In addition to them the complexity of the algorithms will be discussed. Although, the computational algorithm is fast, the time for computation exact distribution can be prohibitive, depending on the number of sample sizes in two groups, the speed and memory of your computer.