Effect sizes for simple (one or two sample) non-parametric tests. Suggested to use ses_calc function instead.

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

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



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


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


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.


confidence level of the interval.


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


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


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


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).


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).


  • 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.