Abstract
We consider certain aspects of two ranks statistics. For the non parametric Wilcoxon signed-rank test, power curves for this test are plotted and compared for several population distributions. The power of the Wilcoxon signed-rank test is compared to the power of the sign test. Computations to calculate power are performed using a computer algebra system and an algorithm is presented to perform these computations. Power curves are plotted and compared for small sample sizes. Monte Carlo simulation is used to calculate power curves for larger sample sizes. For the Mann–Whitney rank sum statistic, the distribution of the statistic is considered in the presence of ties, both within a sample and between samples.
This original paper presents research using APPL as the computing environment to explore special situations of two rank statistics. An interesting application using APPL here is creating power curves. Power curves for different distributions are typically not part of an statistical package. This paper was able to use the survival function ability and a few other APPL functions to create exact power curves for different sample sizes for the Wilcoxon test. Some of the discrete processes in APPL can be used also for the Mann–Whitney rank test to find exact distributions, especially in the case of ties in the data. Of interest is the new APPL procedure WMWRV which calculates the exact distribution of H 0 without ties.
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Luckett, D.J., King, S., Leemis, L.M. (2017). Notes on Rank Statistics. In: Glen, A., Leemis, L. (eds) Computational Probability Applications. International Series in Operations Research & Management Science, vol 247. Springer, Cham. https://doi.org/10.1007/978-3-319-43317-2_8
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