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Brown-Forsythe Test of Homogeneity of Variances

Source: R/Brown_Forsythe_test.R
Brown_Forsythe_test.Rd

Performs Brown-Forsythe test to assess the null hypothesis that the variances are equal across all groups (samples) defined by the independent variable.

Usage

Brown_Forsythe_test(
  data,
  formula,
  alpha = 0.05,
  silent = FALSE,
  summary = FALSE,
  misc = FALSE,
  transform = function(x) abs(x - stats::median(x)),
  method = c("MBF", "BF")
)

Arguments

data

A data frame containing the variables specified in the formula.

formula

A formula of the form DV ~ IV, where DV is the dependent (response) variable and IV is the independent (grouping) variable.

alpha

A numeric value specifying the significance level. Must be between 0 and 1. Default is 0.05.

silent

A logical value. If FALSE (default), results are printed to the console. If TRUE, no output is printed.

summary

A logical value (default: FALSE). If TRUE, a summary table for the input data is returned.

misc

A logical value. If FALSE (default), only essential parameters are returned. If TRUE, additional auxiliary parameters are included in the output.

transform

A function used to transform the response variable into deviations from a specified location measure.

method

A character specifying either "MBF" (default) or "BF".

Value

A list containing the test statistics, p-value, degrees of freedom, and optionally a summary table and/or auxiliary parameters, depending on the values of summary and misc.

Details

transform The concept is similar to ANOVA procedure (transform the response variable to residuals before analysis). Possible transformation are:

  • y' = |yi - ybar| (default)

  • y' = (yi - ybar) ^ 2

  • y' = ln((yi - ybar) ^ 2)

  • y' = sqrt(|yi - ybar|)

The ybar could be either mean, median (default), or trimmed-mean.

method

  • "BF": The original Brown–Forsythe test proposed by Brown and Forsythe (1974), a modification of Levene's test that uses the median instead of the mean.

  • "MBF" The modified Brown–Forsythe test proposed by Mehrotra (1997), which adjusts the degrees of freedom and consequently yields an approximate F-distribution of F(f1, f2) rather than F(k - 1, N - k). Compared with the original version (BF), this modification tends to reduce the Type I error rate at the cost of a higher Type II error rate.

References

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

Mehrotra, D. V. (1997). Improving the Brown–Forsythe solution to the generalized Behrens–Fisher problem. Communications in Statistics—Simulation and Computation, 26, 1139–1145. https://doi.org/10.1080/03610919708813431

See also

Levene_test

Examples

df0 <- roGFP[[1]]
out <- Brown_Forsythe_test(df0, ro ~ grp)
#> 
#> --------------------------------------------
#> Brown-Forsythe homogeneity of variance test
#> 
#> Response: ro
#> 
#>              DF   SS   MS Fvalue  pvalue
#> Group      1.96 0.01 0.01 3.9769 0.02918
#> Residuals 32.86 0.05    0               
#> Total     34.81 0.06                    
#> 
#> #> Group variances are unequal.
#> --------------------------------------------
boxplot(ro ~ grp, df0, horizontal = TRUE)
points(x = df0$ro, y = jitter(as.numeric(df0$grp), amount = 0.15))