levene.test {lawstat} | 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 |
trim.alpha |
the fraction (0 to 0.5) of observations to be trimmed from
each end of |
bootstrap |
a logical value identifying whether to implement bootstrap.
The default is |
num.bootstrap |
number of bootstrap samples to be drawn when the |
kruskal.test |
logical value indentifying whether to use the Kruskal–Wallis
statistic. The default option is |
correction.method |
procedures to make the test more robust;
the default option is |
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 |
method |
type of test performed. |
data.name |
a character string giving the name of the data. |
non.bootstrap.p.value |
the |
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
Brown MB, Forsythe AB (1974).
“Robust tests for the equality of variances.”
Journal of the American Statistical Association, 69(346), 364–367.
doi:10.1080/01621459.1974.10482955.
Hines WGS, Hines RJO (2000).
“Increased power with modified forms of the Levene (Med) test for heterogeneity of variance.”
Biometrics, 56(2), 451–454.
doi:10.1111/j.0006-341X.2000.00451.x.
Keyes TK, Levy MS (1997).
“Analysis of Levene's test under design imbalance.”
Journal of Educational and Behavioral Statistics, 22(2), 227–236.
doi:10.3102/10769986022002227.
Levene H (1960).
“Robust Tests for Equality of Variances.”
In Olkin I, others (eds.), Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling.
Stanford University Press, Palo Alto, CA.
Lim T, Loh W (1996).
“A comparison of tests of equality of variances.”
Computational Statistics & Data Analysis, 22(3), 287–301.
doi:10.1016/0167-9473(95)00054-2.
Noguchi K, Gel YR (2010).
“Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives.”
Journal of Nonparametric Statistics, 22(7), 897–913.
doi:10.1080/10485251003698505.
O'Brien RG (1978).
“Robust techniques for testing heterogeneity of variance effects in factorial designs.”
Psychometrika, 43(3), 327–342.
doi:10.1007/BF02293643.
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)