Pairwise Vargha and Delaney's A and Cliff's delta

Calculates Vargha and Delaney's A (VDA), Cliff's delta (CD), and the Glass rank biserial coefficient, rg, for several groups in a pairwise manner.

Usage

multiVDA(
  formula = NULL,
  data = NULL,
  x = NULL,
  g = NULL,
  statistic = "VDA",
  digits = 3,
  ...
)

Arguments

formula: A formula indicating the response variable and the independent variable. e.g. y ~ group.
data: The data frame to use.
x: If no formula is given, the response variable.
g: If no formula is given, the grouping variable.
statistic: One of "VDA", "CD", or "rg". This determines which statistic will be evaluated to determine the comparison with the most divergent groups.
digits: The number of significant digits in the output.
...: Additional arguments passed to the wilcox.test function.

Value

A list containing a data frame of pairwise statistics, and the comparison with the most extreme value of the chosen statistic.

Details

VDA and CD are effect size statistic appropriate in cases where a Wilcoxon-Mann-Whitney test might be used. Here, the pairwise approach would be used in cases where a Kruskal-Wallis test might be used. VDA ranges from 0 to 1, with 0.5 indicating stochastic equality, and 1 indicating that the first group dominates the second. CD ranges from -1 to 1, with 0 indicating stochastic equality, and 1 indicating that the first group dominates the second. rg ranges from -1 to 1, depending on sample size, with 0 indicating no effect, and a positive result indicating that values in the first group are greater than in the second.

Be cautious with this interpretation, as R will alphabetize groups in the formula interface if the grouping variable is not already a factor.

In the function output, VDA.m is the greater of VDA or 1-VDA. CD.m is the absolute value of CD. rg.m is the absolute value of rg.

The function calculates VDA and Cliff's delta from the "W" U statistic from the wilcox.test function. Specifically, VDA = U/(n1*n2); CD = (VDA-0.5)*2.

rg is calculated as 2 times the difference of mean of ranks for each group divided by the total sample size. It appears that rg is equivalent to Cliff's delta.

The input should include either formula and data; or var, and group.

Currently, the function makes no provisions for NA values in the data. It is recommended that NAs be removed beforehand.

Note

The parsing of the formula is simplistic. The first variable on the left side is used as the measurement variable. The first variable on the right side is used for the grouping variable.

References

https://rcompanion.org/handbook/F_08.html

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

data(PoohPiglet)
multiVDA(Likert ~ Speaker, data=PoohPiglet)
#> $pairs
#>        Comparison  VDA    CD    rg VDA.m CD.m rg.m
#> 1   Piglet - Pooh 0.05 -0.90 -0.90  0.95 0.90 0.90
#> 2 Piglet - Tigger 0.07 -0.86 -0.86  0.93 0.86 0.86
#> 3   Pooh - Tigger 0.58  0.16  0.16  0.58 0.16 0.16
#> 
#> $comparison
#>      Comparison 
#> "Piglet - Pooh" 
#> 
#> $statistic
#>  VDA 
#> 0.05 
#> 
#> $statistic.m
#> VDA.m 
#>  0.95 
#>