# rankMANOVA: Rank-based Tests for Multivariate Data in Nonparametric... In smn74/rankMANOVA: Rank-Based Tests for Multivariate Data in Nonparametric Factorial Designs

## Description

The rankMANOVA function calculates an ANOVA-type statistic (ATS) with (wild) bootstrap p-values for nonparametric factorial designs with multivariate data.

## Usage

 ```1 2``` ```rankMANOVA(formula, data, iter = 10000, alpha = 0.05, CPU, seed, resampling = "WildBS") ```

## Arguments

 `formula` A model `formula` object. The left hand side contains the response variables and the right hand side contains the factor variables of interest. An interaction term must be specified. Data must be provided in wide format. `data` A data.frame containing the variables in `formula`. `iter` The number of iterations used for calculating the resampled statistic. The default option is 10,000. `alpha` A number specifying the significance level; the default is 0.05. `CPU` The number of cores used for parallel computing. If omitted, cores are detected via `detectCores`. `seed` A random seed for the resampling procedure. If omitted, no reproducible seed is set. `resampling` The resampling method to be used, one of "bootstrap" (sample-specific bootstrap approach) and "WildBS" (wild bootstrap approach with Rademacher weights). The default is "WildBS".

## Details

Implemented is an ANOVA-type test statistic for testing hypotheses formulated in Mann-Whitney-type effects in nonparametric factorial designs. Statistical inference is based on a wild or a sample-specific bootstrap approach. The unweighted treatment effects considered do not depend on sample sizes and allow for transitive ordering. The package thus provides an extension of the univariate `rankFD` package to multivariate data.

## Value

A `rankMANOVA` object containing the following components:

 `Descriptive` Some descriptive statistics of the data for all factor level combinations. Displayed are the number of individuals per factor level combination and the unweighted treatment effects for each dimension. `Test` The test statistic(s) and p-value(s) based on the chosen bootstrap approach.

## NOTE

The number of bootstrap iterations has been set to 100 in the examples due to runtime restrictions on CRAN. Usually it is recommended to use at least 1000 iterations.

## References

Dobler, D., Friedrich, S., and Pauly, M. (2017). Nonparametric MANOVA in Mann-Whitney effects.

`rankFD`
 ```1 2 3 4 5 6 7``` ``` library(ElemStatLearn) data("marketing") mymar <- marketing[, c("Sex", "Income", "Edu")] mymar2 <- na.omit(mymar) test <- rankMANOVA(cbind(Income, Edu) ~ Sex, data = mymar2, iter=100, resampling = "WildBS", CPU = 1) summary(test) ```