Levene's Test for Homogeneity of Variance

Computes Levene's test for homogeneity of variance across groups.

LeveneTest(y, ...)

# S3 method for class 'formula'
LeveneTest(formula, data, ...)
# S3 method for class 'lm'
LeveneTest(y, ...)
# Default S3 method
LeveneTest(y, group, center=median, ...)

Arguments

y

response variable for the default method, or a lm or formula object. If y is a linear-model object or a formula, the variables on the right-hand-side of the model must all be factors and must be completely crossed.

group

factor defining groups.

center

The name of a function to compute the center of each group; mean gives the original Levene's test; the default, median, provides a more robust test (Brown-Forsythe-Test).

formula

a formula of the form lhs ~ rhs where lhs gives the data values and rhs the corresponding groups.

data

an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).

...

arguments to be passed down, e.g., data for the formula and lm methods; can also be used to pass arguments to the function given by center (e.g., center=mean and trim=0.1 specify the 10% trimmed mean).

Value

returns an object meant to be printed showing the results of the test.

Note

This function was previously published as leveneTest() in the library(car) and has been integrated here without logical changes.

References

Fox, J. (2008) Applied Regression Analysis and Generalized Linear Models, Second Edition. Sage.

Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage.

See also

fligner.test for a rank-based (nonparametric) \(k\)-sample test for homogeneity of variances; mood.test for another rank-based two-sample test for a difference in scale parameters; var.test and bartlett.test for parametric tests for the homogeneity in variance.

ansari_test in package coin for exact and approximate conditional p-values for the Ansari-Bradley test, as well as different methods for handling ties.

Author

John Fox jfox@mcmaster.ca; original generic version contributed by Derek Ogle
adapted from a response posted by Brian Ripley to the r-help email list.

Examples

## example from ansari.test:
## Hollander & Wolfe (1973, p. 86f):
## Serum iron determination using Hyland control sera
ramsay <- c(111, 107, 100, 99, 102, 106, 109, 108, 104, 99,
            101, 96, 97, 102, 107, 113, 116, 113, 110, 98)
jung.parekh <- c(107, 108, 106, 98, 105, 103, 110, 105, 104,
            100, 96, 108, 103, 104, 114, 114, 113, 108, 106, 99)

LeveneTest( c(ramsay, jung.parekh),
  factor(c(rep("ramsay",length(ramsay)), rep("jung.parekh",length(jung.parekh)))))
#> Levene's Test for Homogeneity of Variance (center = median)
#>       Df F value Pr(>F)
#> group  1  1.7865 0.1893
#>       38               

LeveneTest( c(rnorm(10), rnorm(10, 0, 2)), factor(rep(c("A","B"),each=10)) )
#> Levene's Test for Homogeneity of Variance (center = median)
#>       Df F value Pr(>F)
#> group  1  0.1475 0.7055
#>       18               

if (FALSE) { # \dontrun{
# original example from package car

with(Moore, LeveneTest(conformity, fcategory))
with(Moore, LeveneTest(conformity, interaction(fcategory, partner.status)))

LeveneTest(conformity ~ fcategory * partner.status, data = Moore)
LeveneTest(conformity ~ fcategory * partner.status, data = Moore, center = mean)
LeveneTest(conformity ~ fcategory * partner.status, data = Moore, center = mean, trim = 0.1)

LeveneTest(lm(conformity ~ fcategory*partner.status, data = Moore))
} # }