Levenetests2s.mv {smsets}R Documentation

Multiple two-sample Levene tests for the comparison of variation in multivariate data

Description

Performs multiple two-sample Levene tests, based on two-sample t-tests applied to absolute differences around medians for more than one response vector, with corrected significance levels using any of the adjustment methods for multiple comparisons offered by p.adjust. This function includes the argument alternative = useful to specify the type of alternative, either one-sided (lower-/ upper-tail) or two-sided. Effects sizes are also computed with respect to the two-sample t-tests.

Usage

Levenetests2s.mv(
  x,
  group,
  level1,
  alternative = "two.sided",
  var.equal = FALSE,
  P.adjust = "none",
  unit = "units"
)

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.

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

var.equal

a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.

P.adjust

p-value correction method, a character string. Can be abbreviated. See 'Details'.

unit

Physical units of the response variable useful to fully characterize raw effect sizes

Details

This function focuses on the univariate Levene test for the comparison of mean values for two samples, when more than one variable is involved in the data analysis, so that type one error rates ("false significances") in the series of Levene tests are adjusted according to the number of response variables analyzed. The pairwise comparisons between the two levels in group with corrections for multiple testing are made over more than one response vector.

The methods implemented in P.adjust are the same as those contained in the p.adjust.methods: "bonferroni", "holm", "hochberg", "hommel", "BH", (Benjamini-Hochberg) or its alias "fdr" (False Discovery Rate), and "BY" (Benjamini & Yekutieli). The default pass-through option ("none") is also included.

Value

Returns an object of class "Levenetests2s.mv", a list containing the following components:

name A character string describing the function.
medians A list containing two vectors of length p, being p the number of response variables. medians1 and medians2 store the medians for samples 1 (corresponding to level1) and 2, respectively.
absdev.median A list containing two data frames, abs.dev.median1 and abs.dev.median2, corresponding to the absolute deviation around sample medians 1 and 2, respectively
means.absdev A list containing two vectors of length p, (means.absdev1 and means.absdev1), corresponding to the mean absolute deviations around medians for variables 1,...,p, in samples 1 and 2, respectively.
vars.absdev A list containing two vectors of length p, (vars.absdev1 and vars.absdev1), corresponding to the variances of absolute deviations around medians for variables 1,..., p, in samples 1 and 2, respectively.
t.list A list containing p vectors of length 5, each vector containing the t-statistic, the degrees of freedom, the adjusted p-value for the test, the raw effect size estimator: \bar{x}_1 - \bar{x}_2, and the post hoc effect size estimator recommended by Hedges (1981), analogous to Cohen's d, given by |\bar{x}_1 - \bar{x}_2| / \hat{\sigma}. Here \hat{\sigma} = \sqrt{MSE} where MSE is the mean squared error, the estimator of the variance for the difference of means \bar{x}_1 - \bar{x}_2, respectively.
alternative A character string specifying the alternative hypothesis chosen.
var.equal A logical variable indicating whether the two variances were treated as being equal TRUE or not FALSE.
P.adjust A character string indicating the correction method chosen
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.
data the data frame analyzed.

The extractor function print.Levenetests2s.mv returns an annotated output of the Levene tests (or, equivalently, the two-sample t-tests applied to the absolute differences around medians).

Author(s)

Jorge Navarro Alberto, ganava4@gmail.com

References

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

Hedges, L. V. 1981. Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational Statistics 6(2): 107–128.

Examples

data(sparrows)
res.Levene2s.mv <- Levenetests2s.mv(sparrows, Survivorship, "S",
                                alternative = "less", var.equal = TRUE,
                                P.adjust = "bonferroni", unit = "mm")
res.Levene2s.mv


[Package smsets version 1.2.3 Index]