# levene.test: Levene's Test of Equality of Variances In vlyubchich/lawstat: Tools for Biostatistics, Public Policy, and Law

 levene.test R Documentation

## 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, `NA`s 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

`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)

``````

vlyubchich/lawstat documentation built on April 17, 2023, 12:47 a.m.