Levene's Test (Median) for Equality of Variance

Source: R/levene.R

This function performs the Levene's test for equality of variance using the median. This is also known as the Brown-Forsythe test.

levene_test(data = NULL, x, groups, alpha = 0.05, modcv = FALSE)

Arguments

data

a data.frame

x

the variable in the data.frame or a vector on which to perform the Levene's test (usually strength)

groups

a variable in the data.frame that defines the groups

alpha

the significance level (default 0.05)

modcv

a logical value indicating whether the modified CV approach should be used.

Value

Returns an object of class levene. This object has the following fields:

  • call the expression used to call this function

  • data the original data supplied by the user

  • groups a vector of the groups used in the computation

  • alpha the value of alpha specified

  • modcv a logical value indicating whether the modified CV approach was used.

  • n the total number of observations

  • k the number of groups

  • f the value of the F test statistic

  • p the computed p-value

  • reject_equal_variance a boolean value indicating whether the null hypothesis that all samples have the same variance is rejected

  • modcv_transformed_data the data after the modified CV transformation

Details

This function performs the Levene's test for equality of variance using median (also known as the Brown-Forsythe test). The data is transformed as follows:

$$w_{ij} = \left| x_{ij} - m_i \right|$$

Where \(m_i\) is median of the \(ith\) group. An F-Test is then performed on the transformed data.

When modcv=TRUE, the data from each group is first transformed according to the modified coefficient of variation (CV) rules before performing Levene's test.

References

“Composite Materials Handbook, Volume 1. Polymer Matrix Composites Guideline for Characterization of Structural Materials,” SAE International, CMH-17-1G, Mar. 2012.

NIST/SEMATECH e-Handbook of Statistical Methods, https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm, 2024.

Brown, M. B. and Forsythe, A. B. (1974), Journal of the American Statistical Association, 69, pp. 364-367.

Examples

library(dplyr)

carbon.fabric.2 %>%
  filter(test == "FC") %>%
  levene_test(strength, condition)
#> 
#> Call:
#> levene_test(data = ., x = strength, groups = condition)
#> 
#> n = 91           k = 5            
#> F = 3.883818     p-value = 0.00600518 
#> Conclusion: Samples have unequal variance ( alpha = 0.05 )
#> 
##
## Call:
## levene_test(data = ., x = strength, groups = condition)
##
## n = 91          k = 5
## F = 3.883818    p-value = 0.00600518
## Conclusion: Samples have unequal variance ( alpha = 0.05 )