npmv-package: Nonparametric Comparison of Multivariate Samples

In npmv: Nonparametric Comparison of Multivariate Samples

Description

Performs analysis of one-way multivariate data using nonparametric techniques developed since 2008. Allows for small samples and ordinal variables, or even mixture of the different variable types ordinal, quantitative, binary. Using F-approximations for ANOVA Type, Wilks' Lambda Type, Lawley Hotelling Type, and Bartlett Nanda Pillai Type test statics, as well as a permutation test for each, the package compares the multivariate distributions of the different samples. Also computes nonparametric relative effects and produces plots.

Details

Package:	npmv
Type:	Package
Version:	2.4
Date:	2017-01-08
License:	GPL-2

This package provides the R functions nonpartest and ssnonpartest to compute nonparametric test statistics. The function nonpartest computes the global nonparametric test statistics, their permutation test analogs, and calculates nonparametric relative effects. The function ssnonpartest performs an all-subset algorithm to determine which variables cause significant effects, and between which factor levels. See the examples below for some basic uses and look in the help pages for each function for a much more detailed look.

Warning

The nonparametric methods implemented in the code have been developed for complete data with no missing values.The code automatically produces a warning if there is missing data.

Under certain conditions, the matrices H and G are singular (See literature for explanation of H and G), for example when the number of response variables exceeds the sample size. When this happens, only the ANOVA type statistic can be computed. The code automatically produces a warning if H or G are singular.

Author(s)

Woodrow Burchett, Amanda Ellis, Arne Bathke

Maintainer: Amanda Ellis <[e-mail]>

References

Arne C. Bathke , Solomon W. Harrar, and Laurence V. Madden. "How to compare small multivariate samples using nonparametric tests," Computational Statistics and Data Analysis 52 (2008) 4951-4965

Woodrow W. Burchett, Amanda R. Ellis, Solomon W. Harrar, Arne C. Bathke (2017). "Nonparametric Inference for Multivariate Data: The R Package npmv.," Journal of Statistical Software, 76(4), 1-18.

Brunner E, Domhof S, Langer F (2002), Nonparametric Analysis of Longitudinal Data in Factorial Experiments. Wiley, New York.

Chunxu Liu, Arne C. Bathke, Solomon W. Harrar. "A nonparametric version of Wilks' lambda-Asymptotic results and small sample approximations" Statistics and Probability Letters 81 (2011) 1502-1506

Horst, L.E., Locke, J., Krause, C.R., McMahaon, R.W., Madden, L.V., Hoitink, H.A.J., 2005. Suppression of Botrytis blight of Begonia by Trichoderma hamatum 382 in peat and compost-amended potting mixes. Plant Disease 89, 1195-1200.

Examples

data(sberry)
nonpartest(weight|bot|fungi|rating~treatment,sberry,permreps=1000)
ssnonpartest(weight|bot|fungi|rating~treatment,sberry,test=c(1,0,0,0),alpha=.05,
            factors.and.variables=TRUE)

Example output

$results
                                                  Test Statistic    df1     df2
ANOVA type test p-value                                    2.984  6.836 27.3426
McKeon approx. for the Lawley Hotelling Test               5.769 12.000 12.0000
Muller approx. for the Bartlett-Nanda-Pillai Test          2.501 15.967 41.1641
Wilks Lambda                                               4.166 12.000 24.1033
                                                  P-value
ANOVA type test p-value                             0.019
McKeon approx. for the Lawley Hotelling Test        0.002
Muller approx. for the Bartlett-Nanda-Pillai Test   0.009
Wilks Lambda                                        0.001
                                                  Permutation Test p-value
ANOVA type test p-value                                              0.001
McKeon approx. for the Lawley Hotelling Test                         0.004
Muller approx. for the Bartlett-Nanda-Pillai Test                    0.004
Wilks Lambda                                                         0.002

$releffects
   weight     bot   fungi  rating
3 0.43750 0.59375 0.56250 0.53125
6 0.72656 0.15625 0.48438 0.30469
8 0.44531 0.37500 0.21875 0.53125
9 0.39062 0.87500 0.73438 0.63281


The ANOVA type statistic will be used in the following test 
The Global Hypothesis is significant, subset algorithm will continue 

~Performing the Subset Algorithm based on Factor levels~
The Hypothesis of equality between factor levels  3 6 8 9 is rejected 
The Hypothesis of equality between factor levels  6 8 9 is rejected  
The Hypothesis of equality between factor levels  3 6 9 is rejected  
All appropriate subsets using factor levels have been checked using a closed multiple testing procedure, which controls the maximum overall type I error rate at alpha= 0.05 

~Performing the Subset Algorithm based on Response Variables~ 
 The Hypothesis of equality using response variables  weight bot fungi rating is rejected 
The Hypothesis of equality using response variables  bot fungi rating is rejected 
The Hypothesis of equality using response variables  weight bot fungi is rejected 
The Hypothesis of equality using response variables  bot fungi is rejected  
All appropriate subsets using response variables have been checked using a multiple testing procedure, which controls the maximum overall type I error rate at alpha= 0.05

npmv documentation built on May 2, 2019, 8:32 a.m.