Dominance statistic for two-sample paired data

Calculates a dominance effect size statistic for two-sample paired data with confidence intervals by bootstrap

Usage

pairedSampleDominance(
  formula = NULL,
  data = NULL,
  x = NULL,
  y = NULL,
  ci = FALSE,
  conf = 0.95,
  type = "perc",
  R = 1000,
  histogram = FALSE,
  digits = 3,
  na.rm = TRUE,
  ...
)

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.
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.
digits: The number of significant digits in the output.
na.rm: If TRUE, removes NA values from the input vectors or data frame.
...: Additional arguments.

Value

A small data frame consisting of descriptive statistics, the dominance statistic, and potentially the lower and upper confidence limits.

Details

The calculated Dominance statistic is simply the proportion of observations in x greater the paired observations in y, minus the proportion of observations in x less than the paired observations in y

It will range from -1 to 1, with and 1 indicating that the all the observations in x are greater than the paired observations in y, and -1 indicating that the all the observations in y are greater than the paired observations in x.

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.

This statistic is appropriate for truly ordinal data, and could be considered an effect size statistic for a two-sample paired sign test.

Ordered category data need to re-coded as numeric, e.g. as with as.numeric(Ordinal.variable).

When the statistic is close to 1 or close to -1, or with small sample size, the confidence intervals determined by this method may not be reliable, or the procedure may fail.

VDA is the analogous statistic, converted to a probability, ranging from 0 to 1, specifically, VDA = Dominance / 2 + 0.5

References

https://rcompanion.org/handbook/F_07.html

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

data(Pooh)
Time.1 = Pooh$Likert[Pooh$Time == 1]
Time.2 = Pooh$Likert[Pooh$Time == 2]
library(DescTools)
SignTest(x = Time.1, y = Time.2)
#> 
#> 	Dependent-samples Sign-Test
#> 
#> data:  Time.1 and Time.2
#> S = 1, number of differences = 9, p-value = 0.03906
#> alternative hypothesis: true median difference is not equal to 0
#> 97.9 percent confidence interval:
#>  -2  0
#> sample estimates:
#> median of the differences 
#>                        -1 
#> 
pairedSampleDominance(x = Time.1, y = Time.2)
#>    n Less Equal Greater Dominance  VDA
#> 1 10  0.8   0.1     0.1      -0.7 0.15
pairedSampleDominance(Likert ~ Time, data=Pooh)
#>    n Less Equal Greater Dominance  VDA
#> 1 10  0.8   0.1     0.1      -0.7 0.15