Levene Tests of Homogeneity of Variances

This function extends leveneTest to a multivariate response setting. It performs the Levene test of homogeneity of variances for each of a set of response variables, and prints a compact summary.

Usage

leveneTests(y, ...)

# Default S3 method
leveneTests(y, group, center = median, ...)

# S3 method for class 'formula'
leveneTests(y, data, ...)

# S3 method for class 'lm'
leveneTests(y, ...)

Arguments

y: A data frame or matrix of numeric response variables for the default method, or a model formula for a multivariate linear model, or the multivariate linear model itself. In the case of a formula or model, the variables on the right-hand-side of the model must all be factors and must be completely crossed.
...: arguments to be passed down to leveneTest, 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) other arguments.
group: a vector or factor object giving the group for the corresponding elements of the rows of y for the default method
center: The name of a function to compute the center of each group; mean gives the original Levene's (1960) test; the default, median, provides a more robust test suggested by Brown and Forsythe (1974).
data: the data set, for the formula method

Value

An object of classes "anova" and "data.frame", with one observation for each response variable in y.

References

Levene, H. (1960). Robust Tests for Equality of Variances. In Olkin, I. et al. (Eds.), Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, Stanford University Press, 278-292.

Brown, M. B. & Forsythe, A. B. (1974). Robust Tests For Equality Of Variances Journal of the American Statistical Association, 69, 364-367.

Author

Michael Friendly

Examples


leveneTests(iris[,1:4], iris$Species)
#> Levene's Tests for Homogeneity of Variance (center = median)
#> 
#>              df1 df2 F value    Pr(>F)    
#> Sepal.Length   2 147  6.3527  0.002259 ** 
#> Sepal.Width    2 147  0.5902  0.555518    
#> Petal.Length   2 147 19.4803 3.129e-08 ***
#> Petal.Width    2 147 19.8924 2.261e-08 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# handle a 1-column response?
leveneTests(iris[,1, drop=FALSE], iris$Species)
#> Levene's Tests for Homogeneity of Variance (center = median)
#> 
#>              df1 df2 F value   Pr(>F)   
#> Sepal.Length   2 147  6.3527 0.002259 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

data(Skulls, package="heplots")
leveneTests(Skulls[,-1], Skulls$epoch)
#> Levene's Tests for Homogeneity of Variance (center = median)
#> 
#>    df1 df2 F value Pr(>F)
#> mb   4 145  1.0367 0.3905
#> bh   4 145  0.7171 0.5816
#> bl   4 145  0.6797 0.6071
#> nh   4 145  1.0418 0.3878

# formula method
leveneTests(cbind(mb, bh, bl, nh) ~ epoch, data=Skulls)
#> Levene's Tests for Homogeneity of Variance (center = median)
#> 
#>    df1 df2 F value Pr(>F)
#> mb   4 145  1.0367 0.3905
#> bh   4 145  0.7171 0.5816
#> bl   4 145  0.6797 0.6071
#> nh   4 145  1.0418 0.3878

# use 10% trimmed means
leveneTests(cbind(mb, bh, bl, nh) ~ epoch, data=Skulls, trim = 0.1)
#> Levene's Tests for Homogeneity of Variance (center = median: 0.1)
#> 
#>    df1 df2 F value Pr(>F)
#> mb   4 145  1.0367 0.3905
#> bh   4 145  0.7171 0.5816
#> bl   4 145  0.6797 0.6071
#> nh   4 145  1.0418 0.3878


# mlm method
skulls.mod <- lm(cbind(mb, bh, bl, nh) ~ epoch, data=Skulls)
leveneTests(skulls.mod)
#> Levene's Tests for Homogeneity of Variance (center = median)
#> 
#>    df1 df2 F value Pr(>F)
#> mb   4 145  1.0367 0.3905
#> bh   4 145  0.7171 0.5816
#> bl   4 145  0.6797 0.6071
#> nh   4 145  1.0418 0.3878