Effect size for non-parametric (rank sum) tests
Compute the rank-biserial correlation, Cliff's delta, rank Epsilon squared, and Kendall's W effect sizes for non-parametric (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 one-sample 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 |
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. (Cliff's delta is an alias to the
rank-biserial correlation in the two sample case.)
The rank Epsilon squared is appropriate for non-parametric 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 non-parametric 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.
A data frame with the effect size (r_rank_biserial,
rank_epsilon_squared or Kendalls_W) and its CI (CI_low and
CI_high).
Confidence Intervals are estimated using the bootstrap method.
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.
Other effect size indices:
cohens_d(),
effectsize(),
eta_squared(),
phi(),
standardize_parameters()
# two-sample tests -----------------------
A <- c(48, 48, 77, 86, 85, 85)
B <- c(14, 34, 34, 77)
rank_biserial(A, B)
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)
# one-sample tests -----------------------
x <- c(1.15, 0.88, 0.90, 0.74, 1.21)
rank_biserial(x, mu = 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)
wb <- aggregate(warpbreaks$breaks,
by = list(
w = warpbreaks$wool,
t = warpbreaks$tension
),
FUN = mean
)
kendalls_w(x ~ w | t, data = wb)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.