LeveneT2 {smsets}R Documentation

Levene's test for two multivariate samples based on Hotelling's T^2 test with extra information

Description

An R function for the comparison of multivariate variation in two samples, which implements Levene's test based on Hotelling's T^2.

Usage

LeveneT2(x, group, level1, var.equal = TRUE)

Arguments

x

A data frame with one two-level factor and p response variables.

group

Two-level factor defining groups. It must be one of the columns in x.

level1

A character string identifying Sample 1. The string must be one of the factor levels in group.

var.equal

A logical variable indicating whether to treat the within-sample covariance matrices of absolute deviations around medians for samples 1 and 2 as equal or not. The default is TRUE. If the within-sample covariance matrices of absolute deviations around medians are not assumed equal (FALSE), Hotelling's T^2 test is performed using the Nel and van der Merwe's (1986) solution to the multivariate Behrens-Fisher problem as implemented in Hotelling package (Curran and Hersh, 2021).

Details

LeveneT2 makes use of Hotelling's T^2 to test the variation in two multivariate samples. This test is an alternative procedure that should be more robust than Box's test which is known to be rather sensitive to the assumption that the samples are from multivariate normal distributions.

In LeveneT2 the data values are transformed into absolute deviations from their respective sample medians

ADM_{ijk} = |x_{ijk}-M_{jk}|

where

x_{ijk} is the value of variable X_{k} for the ith individual in sample j, and

M_{jk} is the median of X_{k} in sample j.

The unequal variation question between samples j = 1 and j = 2 becomes a T^2-test for the difference of the mean ADM vectors.

Value

Returns an object of class "LeveneT2", a list containing the following components:

name A character string describing the function.
medians A list containing two vectors. The first vector medians1 contains the medians for all variables in sample 1 as declared in parameter level1, and the second vector holds the corresponding medians for the other sample.
bygroup.data A list with two data frames matlevel1 and matlevel2 containing the original variables for samples 1 and 2 respectively
absdev.median A list with two data frames abs.dev.median1 and abs.dev.median2 containing the absolute deviations from sample medians for samples 1 and 2, respectively.
LeveneT2.test A list of class hotelling.test containing the list stats and the scalar pval, produced by function hotelling.test implemented in package Hotelling
var.equal a logical variable indicating whether the two variances were treated as being equal TRUE or not FALSE.
group a character string specifying the name of the two-level factor defining groups.
levels.group a vector of length two, showing the two levels in factor group.
data.name a character string giving the name of the data.
variables a character string vector containing the variable names.
data the data frame analyzed.

The extractor function print.LeveneT2 returns an annotated output of the test.

Author(s)

Jorge Navarro Alberto, ganava4@gmail.com

References

Curran, J. and Hersh, T. (2021). Hotelling: Hotelling's T^2 Test and Variants. R package version 1.0-8, https://CRAN.R-project.org/package=Hotelling.

Manly, B.F.J., Navarro Alberto, J.A. and Gerow, K. (2024) Multivariate Statistical Methods. A Primer. 5th Edn. Chapman and Hall/CRC.

Nel, D.G. and van de Merwe, C.A. (1986). A solution to the multivariate Behrens-Fisher problem. Comm. Statist. Theor. Meth., A15, 12, 3719-3736.

Examples

data(sparrows)
LeveneT2.sparrows <- LeveneT2(sparrows, group = Survivorship, level1 = "S",
                              var.equal = TRUE)
# Brief output
LeveneT2.sparrows


[Package smsets version 1.2.3 Index]