nparcomp: An R Software Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals

One-way layouts, i.e., a single factor with several levels and multiple observations at each level, frequently arise in various fields. Usually not only a global hypothesis is of interest but also multiple comparisons between the different treatment levels. In most practical situations, the distribution of observed data is unknown and there may exist a number of atypical measurements and outliers. Hence, use of parametric and semiparametric procedures that impose restrictive distributional assumptions on observed samples becomes questionable. This, in turn, emphasizes the demand on statistical procedures that enable us to accurately and reliably analyze one-way layouts with minimal conditions on available data. Nonparametric methods offer such a possibility and thus become of particular practical importance. In this article, we introduce a new R package nparcomp which provides an easy and user-friendly access to rank-based methods for the analysis of unbalanced one-way layouts. It provides procedures performing multiple comparisons and computing simultaneous confidence intervals for the estimated effects which can be easily visualized. The special case of two samples, the nonparametric Behrens-Fisher problem, is included. We illustrate the implemented procedures by examples from biology and medicine.

[1]  L. Hothorn,et al.  A Unified Approach to Simultaneous Rank Test Procedures in the Unbalanced One-way Layout , 2001 .

[2]  Edgar Brunner,et al.  Nonparametric methods in factorial designs , 2001 .

[3]  Luigi Salmaso,et al.  A new nonparametric approach for multiplicity control:Optimal Subset procedures , 2005, Comput. Stat..

[4]  Luigi Salmaso,et al.  Permutation Tests for Complex Data , 2010 .

[5]  Edgar Brunner,et al.  A studentized permutation test for the non-parametric Behrens-Fisher problem , 2007, Comput. Stat. Data Anal..

[6]  C. Dunnett A Multiple Comparison Procedure for Comparing Several Treatments with a Control , 1955 .

[7]  Marco Marozzi,et al.  Nonparametric Simultaneous Tests for Location and Scale Testing: A Comparison of Several Methods , 2013, Commun. Stat. Simul. Comput..

[8]  Gang Li,et al.  Nonparametric multiple comparison procedures for unbalanced one-way factorial designs , 2008 .

[9]  Luigi Salmaso,et al.  Nonparametric Multi-focus Analysis for Categorical Variables , 2004 .

[10]  Edgar Brunner,et al.  Are Multiple Contrast Tests Superior to the ANOVA? , 2013, The international journal of biostatistics.

[11]  A. Genz,et al.  Computation of Multivariate Normal and t Probabilities , 2009 .

[12]  Luigi Salmaso,et al.  A permutation test for umbrella alternatives , 2011, Stat. Comput..

[13]  E Shirley,et al.  A non-parametric equivalent of Williams' test for contrasting increasing dose levels of a treatment. , 1977, Biometrics.

[14]  Robert G. D. Steel,et al.  A Rank Sum Test for Comparing All Pairs of Treatments , 1960 .

[15]  Frank Bretz An extension of the Williams trend test to general unbalanced linear models , 2006, Comput. Stat. Data Anal..

[16]  Edgar Brunner,et al.  Nonparametric Hypotheses and Rank Statistics for Unbalanced Factorial Designs , 1997 .

[17]  J. Neher A problem of multiple comparisons , 2011 .

[18]  A. Genz,et al.  On the Numerical Availability of Multiple Comparison Procedures , 2001 .

[19]  Ludwig A. Hothorn,et al.  Evaluation of Toxicological Studies Using a Nonparametric Shirley-Type Trend Test for Comparing Several Dose Levels with a Control Group , 2012 .

[20]  John H. Skillings,et al.  Nonparametric Stepwise Multiple Comparison Procedures , 1985 .

[21]  Williams Da,et al.  The comparison of several dose levels with a zero dose control. , 1972 .

[22]  T. Hothorn,et al.  Multiple Comparisons Using R , 2010 .

[23]  E. Brunner,et al.  The Nonparametric Behrens‐Fisher Problem: Asymptotic Theory and a Small‐Sample Approximation , 2000 .

[24]  Chihiro Hirotsu,et al.  TWO‐WAY CHANGE‐POINT MODEL AND ITS APPLICATION , 1997 .

[25]  Luigi Salmaso,et al.  Weighted methods controlling the multiplicity when the number of variables is much higher than the number of observations , 2006 .

[26]  Ludwig A. Hothorn,et al.  Nonparametric Evaluation of Quantitative Traits in Population-Based Association Studies when the Genetic Model is Unknown , 2012, PloS one.

[27]  Marco Marozzi,et al.  Some notes on the location–scale Cucconi test , 2009 .

[28]  Luigi Salmaso,et al.  FDR- and FWE-controlling methods using data-driven weights , 2007 .

[29]  Y. Hochberg A sharper Bonferroni procedure for multiple tests of significance , 1988 .

[30]  Luigi Salmaso,et al.  A review and some new results on permutation testing for multivariate problems , 2012, Stat. Comput..

[31]  Edgar Brunner,et al.  Rank-based multiple test procedures and simultaneous confidence intervals , 2012 .

[32]  T. Hothorn,et al.  Simultaneous Inference in General Parametric Models , 2008, Biometrical journal. Biometrische Zeitschrift.

[33]  F. Konietschke,et al.  Simultane Konfidenzintervalle für nichtparametrische relative Kontrasteffekte , 2009 .

[34]  R. H. Browne,et al.  The t-Test p Value and Its Relationship to the Effect Size and P(X>Y) , 2010 .