Abstract
Recently, a completely nonparametric rank-based approach for inference regarding multivariate data from factorial designs has been introduced, with theoretical results for two different asymptotic settings. Namely, for the situation of few factor levels with large sample sizes at each level, and for the situation of a large number of factor levels with small sample sizes in each group. In this article, we examine in detail how this theory can be translated into practical application. A challenge in this regard has been feasibly implementing consistent covariance matrix estimation in the setting of small sample sizes. The finite sampling distributions are approximated using moment estimators. In order to make the results widely available, we introduce the R package nparMD which performs nonparametric analysis of multivariate data in a two-way layout. Multivariate data in a one-way layout have already been addressed by the npmv package. Similar to the latter, within the nparMD package, there are no assumptions met about the underlying distribution of the multivariate data. The components of the response vector do not necessarily have to be measured on the same scale, but they have to be at least binary or ordinal. Due to the factorial design, hypotheses to be tested include the main effects of both factors, as well as their interaction. The new R package is equipped with two versions of the testing procedure, corresponding to the two asymptotic situations mentioned above.
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The research was supported by Austrian Science Fund (FWF) I 2697-N31.
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Kiefel, M., Bathke, A.C. (2020). Rank-Based Analysis of Multivariate Data in Factorial Designs and Its Implementation in R. In: La Rocca, M., Liseo, B., Salmaso, L. (eds) Nonparametric Statistics. ISNPS 2018. Springer Proceedings in Mathematics & Statistics, vol 339. Springer, Cham. https://doi.org/10.1007/978-3-030-57306-5_26
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DOI: https://doi.org/10.1007/978-3-030-57306-5_26
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