r effect size for Wilcoxon one-sample signed-rank test

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

Usage

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

Arguments

x

A vector of observations.

mu

The value to compare x to, as in wilcox.test

adjustn

If TRUE, reduces the sample size in the calculation of r by the number of observations equal to mu.

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.

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.

The calculated statistic is equivalent to the statistic returned by the wilcoxPairedR function with one group equal to a vector of mu. The author knows of no reference for this technique.

This statistic typically reports a smaller effect size (in absolute value) than does the matched-pairs rank biserial correlation coefficient (wilcoxonOneSampleRC), and may not reach a value of -1 or 1 if there are values tied with mu.

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

When the data are greater than mu, r is positive. When the data are less than mu, r is negative.

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 with mu.

References

https://rcompanion.org/handbook/F_02.html

Author

Salvatore Mangiafico, mangiafico@njaes.rutgers.edu

Examples

X = c(1,2,3,3,3,3,4,4,4,4,4,5,5,5,5,5)
wilcox.test(X, mu=3, exact=FALSE)
#> 
#> 	Wilcoxon signed rank test with continuity correction
#> 
#> data:  X
#> V = 65, p-value = 0.03973
#> alternative hypothesis: true location is not equal to 3
#> 
wilcoxonOneSampleR(X, mu=3)
#>     r 
#> 0.606