Mangiafico's d, or delta MAD

Calculates Mangiafico's d, or delta MAD, which is the difference in medians divided by the pooled median absolute deviation, with confidence intervals by bootstrap

Usage

mangiaficoD(
  formula = NULL,
  data = NULL,
  x = NULL,
  y = NULL,
  correct = FALSE,
  ci = FALSE,
  conf = 0.95,
  type = "perc",
  R = 1000,
  histogram = FALSE,
  reportIncomplete = FALSE,
  verbose = FALSE,
  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 for one group.
y: The response variable for the other group.
correct: If TRUE, applies Hedges' correction.
ci: If TRUE, returns confidence intervals by bootstrap. May be slow.
conf: The level for the confidence interval.
type: The type of confidence interval to use. Can be any of "norm", "basic", "perc", or "bca". Passed to boot.ci.
R: The number of replications to use for bootstrap.
histogram: If TRUE, produces a histogram of bootstrapped values.
reportIncomplete: If FALSE (the default), NA will be reported in cases where there are instances of the calculation of the statistic failing during the bootstrap procedure.
verbose: If TRUE, reports the median difference and MAD.
digits: The number of significant digits in the output.
...: Other arguments passed to mad(). Of particular interest may be the constant= argument.

Value

A single statistic, d. Or a small data frame consisting of d, and the lower and upper confidence limits.

Details

Mangiafico's d, or delta MAD, is an appropriate effect size statistic where Mood's median test, or another test comparing two medians, might be used. Note that the response variable is treated as at least interval.

For normal samples, the result will be somewhat similar to Cohen's d.

The input should include either formula and data; or x, and y. If there are more than two groups, only the first two groups are used.

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

When the data in the first group are greater than in the second group, d is positive. When the data in the second group are greater than in the first group, d is negative.

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

With a small sample size, the confidence intervals determined by this method may not be reliable, or the procedure may fail.

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

Ricca, B.P. and Blaine, B.E. Brief research report: Notes on a nonparametric estimate of effect size. Journal of Experimental Education 90(1):249–258.

https://rcompanion.org/handbook/F_05.html

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

data(Catbus)
mangiaficoD(Steps ~ Gender, data=Catbus, verbose=TRUE)
#> 
#>    Group  Statistic Value
#> 1 female     Median  8000
#> 2   male     Median  7000
#> 3        Difference  1000
#> 4 female        MAD  1480
#> 5   male        MAD  1480
#> 6        Pooled MAD  1480
#> 
#>     d 
#> 0.674 

Nadja = c(5,5,6,6,6,7,7,11,11,11)
Nandor = c(0,1,2,3,4,5,6,7,8,9,10,11)
mangiaficoD(x = Nadja, y = Nandor, verbose=TRUE)
#> 
#>   Group  Statistic Value
#> 1     x     Median  6.50
#> 2     y     Median  5.50
#> 3       Difference  1.00
#> 4     x        MAD  1.48
#> 5     y        MAD  4.45
#> 6       Pooled MAD  3.11
#> 
#>     d 
#> 0.321