Skip to contents

O'Brien's Test of Homogeneity of Variances

Source: R/O.Brien_test.R
O.Brien_test.Rd

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

Usage

O.Brien_test(
  data,
  formula,
  alpha = 0.05,
  silent = FALSE,
  summary = FALSE,
  misc = FALSE,
  transform = function(x) (x - stats::median(x))^2
)

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|

  • y' = (yi - ybar) ^ 2 (default)

  • y' = ln((yi - ybar) ^ 2)

  • y' = sqrt(|yi - ybar|)

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

Note: This test is often regarded as conservative and may have relatively low power to detect heteroscedasticity. The Levene and Brown-Forsythe tests are generally preferred for assessing the homogeneity of variances.

References

O’Brien, R. G. (1981). A simple test for variance effects in experimental designs. Psychological Bulletin, 89(3), 570–574. https://doi.org/10.1037/0033-2909.89.3.570

See also

[Brown_Forsythe_test][Levene_test][O.Neill_Mathews_test]

Examples

df0 <- CYCB1[[1]]
out <- O.Brien_test(df0, cells ~ grp)
#> 
#> ---------------------------------------
#> O'Brien's homogeneity of variance test
#> 
#> Response: cells
#> 
#>           DF        SS       MS Fvalue  pvalue
#> Group      3  46503.18 15501.06 3.7508 0.01576
#> Residuals 57 235564.27  4132.71               
#> Total     60 282067.44                        
#> 
#> #> Group variances are unequal.
#> ---------------------------------------
boxplot(cells ~ grp, df0, horizontal = TRUE)
points(x = df0$cells, y = jitter(as.numeric(df0$grp), amount = 0.15))