`rbs.Rd`

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

- 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 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).

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.