bartlett.test {ctest}R Documentation

Bartlett Test for Homogeneity of Variances


Performs Bartlett's test of the null that the variances in each of the groups (samples) are the same.


bartlett.test(x, ...)

## Default S3 method:
bartlett.test(x, g, ...)

## S3 method for class 'formula':
bartlett.test(formula, data, subset, na.action, ...)


x a numeric vector of data values, or a list of numeric data vectors representing the respective samples, or fitted linear model objects (inheriting from class "lm").
g a vector or factor object giving the group for the corresponding elements of x. Ignored if x is a list.
formula a formula of the form lhs ~ rhs where lhs gives the data values and rhs the corresponding groups.
data an optional data frame containing the variables in the model formula.
subset an optional vector specifying a subset of observations to be used.
na.action a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").
... further arguments to be passed to or from methods.


If x is a list, its elements are taken as the samples or fitted linear models to be compared for homogeneity of variances. In this case, the elements must either all be numeric data vectors or fitted linear model objects, g is ignored, and one can simply use bartlett.test(x) to perform the test. If the samples are not yet contained in a list, use bartlett.test(list(x, ...)).

Otherwise, x must be a numeric data vector, and g must be a vector or factor object of the same length as x giving the group for the corresponding elements of x.


A list of class "htest" containing the following components:

statistic Bartlett's K-squared test statistic.
parameter the degrees of freedom of the approximate chi-squared distribution of the test statistic.
p.value the p-value of the test.
method the character string "Bartlett test for homogeneity of variances". a character string giving the names of the data.


Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Statistical Society Series A 160, 268–282.

See Also

var.test for the special case of comparing variances in two samples from normal distributions; fligner.test for a rank-based (nonparametric) k-sample test for homogeneity of variances; ansari.test and mood.test for two rank based two-sample tests for difference in scale.


plot(count ~ spray, data = InsectSprays)
bartlett.test(InsectSprays$count, InsectSprays$spray)
bartlett.test(count ~ spray, data = InsectSprays)

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