nparms: Nonparametric Test For Multivariate Data With Two-Way Layout...

In nparMD: Nonparametric Analysis of Multivariate Data in Factorial Designs

Nonparametric Test For Multivariate Data With Two-Way Layout Factorial Design - Small Samples

Description

Analysis of multivariate data with two-way completely randomized factorial design - version for small samples. The analysis is based on fully nonparametric, rank-based methods and uses a N(0,1)-approximation for test statistics based on 'Dempster's ANOVA', 'Wilk's Lambda', 'Lawley-Hotelling' and 'Bartlett-Nanda-Pillai' criteria. This approximation is established by the asymptotic distribution of these four statistics under true null-hypothesis if one of the explanatory factors has a large number of levels. The multivariate response is allowed to be ordinal, quantitative, binary or a mixture of the different variable types. The test statistics are constructed using nonparametric relative effect estimators.

Usage

nparms(formula,data)

Arguments

formula	an object of class "formula" with two explanatory variables (factors), see examples.
data	an object of class "data.frame" containing the variables in the formula

Details

This method is only implemented for complete data sets without missing values. The data is analysed for main effects and interaction effect of the explanatory factors. In each case the null hypothesis "no effect" is testet. The explanatory factor that has the higher number of levels is automatically designated as factor "A". The covariance matrix estimation requires at least 4 observations (observation vectors) per factor level combination. As the estimation is very time-consuming for large groups it is performed wih a random selection of observations when a group exceeds a size of 6 observation vectors.

Value

Returns a list of data frames providing the values of the test statistics, p-values, degrees of freedom, factor levels, and groupsize per factor level combination.

References

Kiefel M., Bathke A.C. (2020) Rank-Based Analysis of Multivariate Data in Factorial Designs and Its Implementation in R In: Nonparametric Statistics (285-294) Springer Proceedings in Mathematics & Statistics Springer International Publishing, Cham

Bathke A.C., Harrar S.W. (2016) Rank-Based Inference for Multivariate Data in Factorial Designs. In: Liu R., McKean J. (eds) Robust Rank-Based and Nonparametric Methods. Springer Proceedings in Mathematics & Statistics, vol 168. Springer, Cham

Harrar S.W., Bathke A.C. (2012) A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations (and erratum). In: Annals of the Institute of Statistical Mathematics, 64(1&5):135-165&1087, 2012.

Brunner E., Dette H., Munk A. (1997) Box-Type Approximations in Nonparametric Factorial Designs In: Journal of the American Statistical Association, 92(440):1494-1502

Examples

data(pseudostudy2)
nparms(resp1|resp2|resp3~treatment*age, pseudostudy2)

nparMD documentation built on March 18, 2022, 6:33 p.m.