This function extends bartlett.test to a multivariate
response setting. It performs the Bartlett test of homogeneity of variances
for each of a set of response variables, and prints a compact summary.
Bartlett's test is the univariate version of Box's M test for equality of covariance matrices. This function provides a univariate follow-up test to Box's M test to give one simple assessment of which response variables contribute to significant differences in variances among groups.
Usage
bartlettTests(y, ...)
# Default S3 method
bartlettTests(y, group, ...)
# S3 method for class 'formula'
bartlettTests(y, data, ...)
# S3 method for class 'lm'
bartlettTests(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.
- ...
other arguments, passed to
bartlett.test- group
a vector or factor object giving the group for the corresponding elements of the rows of
yfor the default method- data
the data set, for the
formulamethod
Value
An object of classes "anova" and "data.frame", with one observation
for each response variable in y.
References
Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London Series A, 160, 268-282.
See also
boxM for Box's M test for all responses together.
Examples
bartlettTests(iris[,1:4], iris$Species)
#> Bartlett's Tests for Homogeneity of Variance
#>
#> Chisq df Pr(>Chisq)
#> Sepal.Length 16.0057 2 0.0003345 ***
#> Sepal.Width 2.0911 2 0.3515028
#> Petal.Length 55.4225 2 9.229e-13 ***
#> Petal.Width 39.2131 2 3.055e-09 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
data(Skulls, package="heplots")
bartlettTests(Skulls[,-1], Skulls$epoch)
#> Bartlett's Tests for Homogeneity of Variance
#>
#> Chisq df Pr(>Chisq)
#> mb 7.3382 4 0.1191
#> bh 0.7315 4 0.9474
#> bl 3.5155 4 0.4755
#> nh 4.3763 4 0.3575
# formula method
bartlettTests(cbind(mb, bh, bl, nh) ~ epoch, data=Skulls)
#> Bartlett's Tests for Homogeneity of Variance
#>
#> Chisq df Pr(>Chisq)
#> mb 7.3382 4 0.1191
#> bh 0.7315 4 0.9474
#> bl 3.5155 4 0.4755
#> nh 4.3763 4 0.3575