Compute the rankbiserial correlation, Cliff's delta, rank Epsilon squared, and Kendall's W effect sizes for nonparametric (rank sum) tests.
rank_biserial( x, y = NULL, data = NULL, mu = 0, ci = 0.95, iterations = 200, paired = FALSE, verbose = TRUE, ... ) cliffs_delta( x, y = NULL, data = NULL, mu = 0, ci = 0.95, iterations = 200, verbose = TRUE, ... ) rank_epsilon_squared(x, groups, data = NULL, ci = 0.95, iterations = 200, ...) kendalls_w( x, groups, blocks, data = NULL, ci = 0.95, iterations = 200, verbose = TRUE, ... )
x  Can be one of:


y  An optional numeric vector of data values to compare to 
data  An optional data frame containing the variables. 
mu  a number indicating the value around which (a)symmetry (for onesample or paired samples) or shift (for independent samples) is to be estimated. See stats::wilcox.test. 
ci  Confidence Interval (CI) level 
iterations  The number of bootstrap replicates for computing confidence intervals. Only applies when 
paired  If 
verbose  Toggle warnings and messages on or off. 
...  Arguments passed to or from other methods. 
groups, blocks  A factor vector giving the group / block for the
corresponding elements of 
A data frame with the effect size (r_rank_biserial
,
rank_epsilon_squared
or Kendalls_W
) and its CI (CI_low
and
CI_high
).
The rankbiserial correlation is appropriate for nonparametric 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
matchedpairs rankbiserial correlation) and for two independent samples
case, that would normally be tested with MannWhitney's U Test (giving
Glass' rankbiserial 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. (Cliff's delta is an alias to the
rankbiserial correlation in the two sample case.)
The rank Epsilon squared is appropriate for nonparametric tests of
differences between 2 or more samples (a rank based ANOVA). See
stats::kruskal.test. Values range from 0 to 1, with larger values
indicating larger differences between groups.
Kendall's W is appropriate for nonparametric tests of differences between
2 or more dependent samples (a rank based rmANOVA), where each group
(e.g.,
experimental condition) was measured for each block
(e.g., subject). This
measure is also common as a measure of reliability of the rankings of the
groups
between raters (blocks
). See stats::friedman.test. Values range
from 0 to 1, with larger values indicating larger differences between groups
/ higher agreement between raters.
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 are estimated using the bootstrap method.
Cureton, E. E. (1956). Rankbiserial correlation. Psychometrika, 21(3), 287290.
Glass, G. V. (1965). A ranking variable analogue of biserial correlation: Implications for shortcut item analysis. Journal of Educational Measurement, 2(1), 9195.
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, 11IT.
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.
Other effect size indices:
cohens_d()
,
effectsize()
,
eta_squared()
,
phi()
,
standardize_parameters()
# \donttest{ # twosample tests  A < c(48, 48, 77, 86, 85, 85) B < c(14, 34, 34, 77) rank_biserial(A, B)#> r (rank biserial)  95% CI #>  #> 0.79  [0.25, 1.00]x < c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) y < c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) rank_biserial(x, y, paired = TRUE)#> r (rank biserial)  95% CI #>  #> 0.78  [0.33, 1.00]# onesample tests  x < c(1.15, 0.88, 0.90, 0.74, 1.21) rank_biserial(x, mu = 1)#> r (rank biserial)  95% CI #>  #> 0.07  [1.00, 0.87] #> #>  Deviation from a difference of 1.# anova tests  x1 < c(2.9, 3.0, 2.5, 2.6, 3.2) # control group x2 < c(3.8, 2.7, 4.0, 2.4) # obstructive airway disease group x3 < c(2.8, 3.4, 3.7, 2.2, 2.0) # asbestosis group x < c(x1, x2, x3) g < factor(rep(1:3, c(5, 4, 5))) rank_epsilon_squared(x, g)#> Epsilon2 (rank)  95% CI #>  #> 0.06  [0.01, 0.71]wb < aggregate(warpbreaks$breaks, by = list( w = warpbreaks$wool, t = warpbreaks$tension ), FUN = mean ) kendalls_w(x ~ w  t, data = wb)#> Warning: Variable `x.A` contains only two different values. Consider converting it to a factor.Variable `x.B` contains only two different values. Consider converting it to a factor.#> Warning: Variable `x.A` contains only two different values. Consider converting it to a factor.Variable `x.B` contains only two different values. Consider converting it to a factor.#> Warning: Variable `x.A` contains only two different values. Consider converting it to a factor.Variable `x.B` contains only two different values. Consider converting it to a factor.#> Kendall's W  95% CI #>  #> 0.11  [0.11, 1.00]# }