levene.test: Levene-Brown-Forsythe Test for Homogeneity of Variance...

In visStatistics: Automated Selection and Visualisation of Statistical Hypothesis Tests

Levene-Brown-Forsythe Test for Homogeneity of Variance (center = median)

Description

Performs Levene's test using the Brown-Forsythe modification (median-centred). It tests the null hypothesis that all groups have equal variances by testing whether the absolute deviations from group medians are equal across groups The function reproduces the default behaviour of the leveneTest(y,g,center=median,...) of the car-package.

Usage

levene.test(y, g, data = NULL)

Arguments

y	A numeric response vector.
g	A grouping factor.
data	Optional data frame containing 'y' and 'g'.

Details

For each observation y_{ij} in group i, compute the absolute deviation from the group median:

z_{ij} = |y_{ij} - \tilde{y}_i|

where \tilde{y}_i is the median of group i.

The test statistic is the F-statistic from a one-way ANOVA on the z_{ij} values:

F = \frac{(N-k) \sum_{i=1}^{k} n_i (\bar{z}_i - \bar{z})^2}{(k-1) \sum_{i=1}^{k} \sum_{j=1}^{n_i} (z_{ij} - \bar{z}_i)^2}

where:

• k = number of groups

• N = total sample size

• n_i = sample size of group i

• \bar{z}_i = mean of absolute deviations in group i

• \bar{z} = overall mean of all absolute deviations

Under the null hypothesis of equal variances, the test statistic follows an F-distribution: F \sim F(k-1, N-k).

Value

An object of class "htest" with components:

statistic	the value of the F-statistic.
parameter	degrees of freedom: df1=k-1, df3=N-k, where k is the number of groups and N the total sample size
p.value	the p-value of the test.
method	a character string indicating the test performed.
data.name	a character string giving the name(s) of the data.

References

Brown, M. B., and Forsythe, A. B. (1974). Robust tests for the equality of variances. Journal of the American Statistical Association, 69(346), 364–367. DOI: 10.1080/01621459.1974.10482955

Examples

set.seed(123)
y <- c(rnorm(10), rnorm(10, sd = 2), rnorm(10, sd = 0.5))
g <- factor(rep(1:3, each = 10))
levene.test(y, g)

# Usage with data frame
df <- data.frame(response = y, group = g)
levene.test(response, group, data = df)

# Example with unequal variances (should reject null hypothesis)
set.seed(456)
y_unequal <- c(rnorm(15, sd = 1), rnorm(15, sd = 5), rnorm(15, sd = 0.2))
g_unequal <- factor(rep(c("A", "B", "C"), each = 15))
levene.test(y_unequal, g_unequal)

visStatistics documentation built on May 13, 2026, 1:08 a.m.