This paper develops a new test, the trinomial test, for pairwise ordinal data samples to improve the power of the sign test by modifying its treatment of zero differences between observations, thereby increasing the use of sample information. Simulations demonstrate the power superiority of the proposed trinomial test statistic over the sign test in small samples in the presence of tie observations. We also show that the proposed trinomial test has substantially higher power than the sign test in large samples and also in the presence of tie observations, as the sign test ignores information from observations resulting in ties.

hypothesis testing, non-parametric test, sign test, test statistics, ties, trinomial test
Hypothesis Testing (jel C12), Semiparametric and Nonparametric Methods (jel C14), Simulation Methods; Monte Carlo Methods; Bootstrap Methods (jel C15)
Erasmus School of Economics
Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus School of Economics

Bian, G, McAleer, M.J, & Wong, W.-K. (2010). A Trinomial Test for Paired Data When There are Many Ties (No. EI 2010-68). Report / Econometric Institute, Erasmus University Rotterdam (pp. 1–18). Erasmus School of Economics. Retrieved from