levene.test: Levene's Test of Equality of Variances

In lawstat: Tools for Biostatistics, Public Policy, and Law

Levene's Test of Equality of Variances

Description

Tests equality of the k population variances.

Usage

levene.test(
  y,
  group,
  location = c("median", "mean", "trim.mean"),
  trim.alpha = 0.25,
  bootstrap = FALSE,
  num.bootstrap = 1000,
  kruskal.test = FALSE,
  correction.method = c("none", "correction.factor", "zero.removal", "zero.correction")
)

Arguments

y	a numeric vector of data values.
group	factor of the data.
location	the default option is "median" corresponding to the robust Brown–Forsythe Levene-type procedure \insertCiteBrown_Forsythe_1974lawstat; "mean" corresponds to the classical Levene's procedure \insertCiteLevene_1960lawstat, and "trim.mean" corresponds to the robust Levene-type procedure using the group trimmed means.
trim.alpha	the fraction (0 to 0.5) of observations to be trimmed from each end of x before the mean is computed.
bootstrap	a logical value identifying whether to implement bootstrap. The default is FALSE, i.e., no bootstrap; if set to TRUE, the bootstrap method described in \insertCiteLim_Loh_1996;textuallawstat for Levene's test is applied.
num.bootstrap	number of bootstrap samples to be drawn when the bootstrap argument is set to TRUE. The default value is 1000.
kruskal.test	logical value indentifying whether to use the Kruskal–Wallis statistic. The default option is FALSE, i.e., the usual ANOVA statistic is used.
correction.method	procedures to make the test more robust; the default option is "none"; "correction.factor" applies the correction factor described by \insertCiteOBrien_1978;textuallawstat and \insertCiteKeyes_Levy_1997;textuallawstat; "zero.removal" performs the structural zero removal method by \insertCiteHines_Hines_2000;textuallawstat; "zero.correction" performs a combination of the O'Brien's correction factor and the Hines–Hines structural zero removal method \insertCiteNoguchi_Gel_2010lawstat. Note that the options "zero.removal" and "zero.correction" are only applicable when the location is set to "median", otherwise, "none" is applied.

Details

The test statistic is based on the classical Levene's procedure (using the group means), the modified Brown–Forsythe Levene-type procedure (using the group medians), or the modified Levene-type procedure (using the group trimmed means). More robust versions of the test using the correction factor or structural zero removal method are also available. Two options for calculating critical values, namely, approximated and bootstrapped, are available. By default, NAs are omitted from the data.

Value

A list of class "htest" with the following components:

statistic	the value of the test statistic.
p.value	the p-value of the test.
method	type of test performed.
data.name	a character string giving the name of the data.
non.bootstrap.p.value	the p-value of the test without bootstrap method; i.e. the p-value using the approximated critical value.

Note

Instead of the ANOVA statistic suggested by Levene, the Kruskal–Wallis ANOVA may also be applied using this function (see the parameter kruskal.test).

Modified from a response posted by Brian Ripley to the R-help e-mail list.

Author(s)

Kimihiro Noguchi, W. Wallace Hui, Yulia R. Gel, Joseph L. Gastwirth, Weiwen Miao

References

\insertAllCited

See Also

neuhauser.hothorn.test, lnested.test, ltrend.test, mma.test, robust.mmm.test

Examples

data(pot)
levene.test(pot[,"obs"], pot[,"type"], 
            location = "median", correction.method = "zero.correction")
            
## Bootstrap version of the test. The calculation may take up a few minutes 
## depending on the number of bootstrap sampling.
levene.test(pot[,"obs"], pot[,"type"], 
            location = "median", correction.method = "zero.correction", 
            bootstrap = TRUE, num.bootstrap = 500)
            

lawstat documentation built on April 6, 2023, 1:06 a.m.