r effect size for Wilcoxon two-sample paired signed-rank test

Calculates r effect size for a Wilcoxon two-sample paired signed-rank test; confidence intervals by bootstrap.

Usage

wilcoxonPairedR(
  x,
  g = NULL,
  adjustn = TRUE,
  coin = FALSE,
  ci = FALSE,
  conf = 0.95,
  type = "perc",
  R = 1000,
  histogram = FALSE,
  cases = TRUE,
  digits = 3,
  ...
)

Arguments

x: A vector of observations.
g: The vector of observations for the grouping, nominal variable. Only the first two levels of the nominal variable are used. The data must be ordered so that the first observation of the of the first group is paired with the first observation of the second group.
adjustn: If TRUE, reduces the sample size in the calculation of r by the number of tied pairs.
coin: If FALSE, the default, the Z value is extracted from a function similar to the wilcox.test function in the stats package. If TRUE, the Z value is extracted from the wilcox_test function in the coin package. This method may be much slower, especially if a confidence interval is produced.
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.
cases: By default the N used in the formula for r is the number of pairs. If cases=FALSE, the N used in the formula for r is the total number of observations, as some sources suggest.
digits: The number of significant digits in the output.
...: Additional arguments passed to the wilcoxsign_test function.

Value

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

Details

r is calculated as Z divided by square root of the number of observations in one group. This results in a statistic that ranges from -1 to 1. This range doesn't hold if cases=FALSE.

This statistic typically reports a smaller effect size (in absolute value) than does the matched-pairs rank biserial correlation coefficient (wilcoxonPairedRC), and may not reach a value of -1 or 1 if there are ties in the paired differences.

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, r is positive. When the data in the second group are greater than in the first group, r is negative. Be cautious with this interpretation, as R will alphabetize groups if g is not already a factor.

When r is close to extremes, or with small counts in some cells, the confidence intervals determined by this method may not be reliable, or the procedure may fail.

Acknowledgments

My thanks to Peter Stikker for the suggestion to adjust the sample size for ties.

References

https://rcompanion.org/handbook/F_06.html

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

data(Pooh)
Time1 = Pooh$Likert[Pooh$Time==1]
Time2 = Pooh$Likert[Pooh$Time==2]
wilcox.test(x = Time1, y = Time2, paired=TRUE, exact=FALSE)
#> 
#> 	Wilcoxon signed rank test with continuity correction
#> 
#> data:  Time1 and Time2
#> V = 3.5, p-value = 0.02355
#> alternative hypothesis: true location shift is not equal to 0
#> 
wilcoxonPairedR(x = Pooh$Likert, g = Pooh$Time)
#>      r 
#> -0.777