rbs {TOSTER}R Documentation

Non-parametric standardized effect sizes (replicates of ses_calc)

Description

Effect sizes for simple (one or two sample) non-parametric tests.

Usage

rbs(x, y = NULL, mu = 0, conf.level = 0.95, paired = FALSE)

np_ses(
  x,
  y = NULL,
  mu = 0,
  conf.level = 0.95,
  paired = FALSE,
  ses = c("rb", "odds", "cstat")
)

Arguments

x

a (non-empty) numeric vector of data values.

y

an optional (non-empty) numeric vector of data values.

mu

a number indicating the value around which (a-)symmetry (for one-sample or paired samples) or shift (for independent samples) is to be estimated. See [stats::wilcox.test].

conf.level

confidence level of the interval.

paired

a logical indicating whether you want to calculate a paired test.

ses

Rank-biserial (rb), odds (odds), and concordance probablity (cstat).

Details

This method was adapted from the effectsize R package. The rank-biserial correlation is appropriate for non-parametric tests of differences - both for the one sample or paired samples case, that would normally be tested with Wilcoxon's Signed Rank Test (giving the **matched-pairs** rank-biserial correlation) and for two independent samples case, that would normally be tested with Mann-Whitney's *U* Test (giving **Glass'** rank-biserial correlation). See [stats::wilcox.test]. In both cases, the correlation represents the difference between the proportion of favorable and unfavorable pairs / signed ranks (Kerby, 2014). Values range from '-1' indicating that all values of the second sample are smaller than the first sample, to '+1' indicating that all values of the second sample are larger than the first sample.

In addition, the rank-biserial correlation can be transformed into a concordance probability (i.e., probability of superiority) or into a generalized odds (WMW odds or Agresti's generalized odds ratio).

## Ties When tied values occur, they are each given the average of the ranks that would have been given had no ties occurred. No other corrections have been implemented yet.

# Confidence Intervals Confidence intervals for the standardized effect sizes are estimated using the normal approximation (via Fisher's transformation).

Value

Returns a list of results including the rank biserial correlation, logical indicator if it was a paired method, setting for mu, and confidence interval.

References

- Cureton, E. E. (1956). Rank-biserial correlation. Psychometrika, 21(3), 287-290.

- Glass, G. V. (1965). A ranking variable analogue of biserial correlation: Implications for short-cut item analysis. Journal of Educational Measurement, 2(1), 91-95.

- Kendall, M.G. (1948) Rank correlation methods. London: Griffin.

- Kerby, D. S. (2014). The simple difference formula: An approach to teaching nonparametric correlation. Comprehensive Psychology, 3, 11-IT.

- King, B. M., & Minium, E. W. (2008). Statistical reasoning in the behavioral sciences. John Wiley & Sons Inc.

- Cliff, N. (1993). Dominance statistics: Ordinal analyses to answer ordinal questions. Psychological bulletin, 114(3), 494.

- Tomczak, M., & Tomczak, E. (2014). The need to report effect size estimates revisited. An overview of some recommended measures of effect size.


[Package TOSTER version 0.7.1 Index]