levene.test: 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")
)

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.

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 Brown_Forsythe_1974lawstat; "mean" corresponds to the classical Levene's procedure Levene_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 Lim_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 OBrien_1978;textuallawstat and Keyes_Levy_1997;textuallawstat; "zero.removal" performs the structural zero removal method by Hines_Hines_2000;textuallawstat; "zero.correction" performs a combination of the O'Brien's correction factor and the Hines--Hines structural zero removal method Noguchi_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.

Author

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

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.

References

Examples

Run this code

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)

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