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Levene's Test of Homogeneity of Variances

Source: R/Levene_test.R
Levene_test.Rd

Performs Levene's test to assess the null hypothesis that the variances are equal across all groups (samples) defined by the independent variable.

Usage

Levene_test(
  data,
  formula,
  alpha = 0.05,
  silent = FALSE,
  summary = FALSE,
  misc = FALSE,
  transform = function(x) abs(x - stats::median(x))
)

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.

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.

References

Levene, H. (1960). Robust tests for equality of variances. In I. Olkin (Ed.), Contributions to probability and statistics: Essays in honor of Harold Hotelling (pp. 278–292). Stanford University Press.

Sharma, D., & Kibria, B. M. G. (2013). On some test statistics for testing homogeneity of variances: A comparative study. Journal of Statistical Computation and Simulation, 83, 1944–1963. https://doi.org/10.1080/00949655.2012.675336

Zhou, Y., Zhu, Y., & Wong, W. K. (2023). Statistical tests for homogeneity of variance for clinical trials and recommendations. Contemporary Clinical Trials Communications, 33, 101119. https://doi.org/10.1016/j.conctc.2023.101119

See also

Brown_Forsythe_test

Examples

df0 <- roGFP[[1]]
out <- Levene_test(df0, ro ~ grp)
#> 
#> ---------------------------------------
#> Levene's homogeneity of variance test
#> 
#> Response: ro
#> 
#>           DF   SS MS Fvalue pvalue
#> Group      3 0.01  0 3.1837 0.0325
#> Residuals 46 0.03  0              
#> Total     49 0.03                 
#> 
#> #> Group variances are unequal.
#> ---------------------------------------
boxplot(ro ~ grp, df0, horizontal = TRUE)
points(x = df0$ro, y = jitter(as.numeric(df0$grp), amount = 0.15))