parametric anova for unequal variance + Bartlett Test of Homogeneity of Variances

Example

x <- c(10,11,15,8,16,12,20)
y <- c(10,14,18,25,28,30,35)

d <- c(x,y)
f <- as.factor(c(rep("a",7), rep("b",7)))

# Unequal variance:

t.test(x,y)$p.value
t.test(d~f)$p.value

# Equal variance:

t.test(x,y, var.equal=TRUE)$p.value
t.test(d~f, var.equal=TRUE)$p.value

anova(lm(d~f))[[5]]
summary(aov(lm(d~f)))[[1]][5]
summary(lm(d~f))[[4]][8]

## Not assuming equal variances
oneway.test(extra ~ group, data = sleep)
## Assuming equal variances
oneway.test(extra ~ group, data = sleep, var.equal = TRUE)
## which gives the same result as
anova(lm(extra ~ group, data = sleep)) # not for (smallest var)*4 < (largest var)


Details

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.

Value

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 of homogeneity of variances".

data.name
a character string giving the names of the data.

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

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.

Examples

require(graphics)

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