effectsize (version 0.4.4)

rank_biserial: Effect size for non-parametric (rank sum) tests

Description

Compute the rank-biserial correlation, Cliff's delta, rank Epsilon squared, and Kendall's W effect sizes for non-parametric (rank sum) tests.

Usage

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, ...)

Arguments

x

Can be one of:

• A numeric vector, or a character name of one in data.

• A formula in to form of x ~ groups (for rank_biserial() and rank_epsilon_squared()) or x ~ groups | blocks (for kendalls_w()).

• A list of vectors (for rank_epsilon_squared()).

• A matrix of blocks x groups (for kendalls_w()).

y

An optional numeric vector of data values to compare to x, or a character name of one in data. Ignored if x is not a vector.

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 ci is not NULL.

paired

If TRUE, the values of x and y are considered as paired. This produces an effect size that is equivalent to the one-sample effect size on x - y.

verbose

Toggle warnings and messages on or off.

...

Arguments passed to or from other methods.

groups

A vector or factor object giving the group for the corresponding elements of x, or a character name of one in data. Ignored if x is not a vector.

blocks

A vector giving the block for the corresponding elements of x, or a character name of one in data. Ignored if x is not a vector.

Value

A data frame with the effect size (r_rank_biserial, Kendalls_W or rank_epsilon_squared) and its CI (CI_low and CI_high).

Confidence Intervals

Confidence Intervals are estimated using the bootstrap method.

Details

Compute effect sizes for non-parametric (rank sum) tests.

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). See stats::friedman.test. Values range from 0 to 1, with larger values indicating larger differences between groups.

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.

See Also

Other effect size indices: cohens_d(), effectsize(), eta_squared(), phi(), standardize_parameters()

Examples

# NOT RUN {
# 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)
# }
# NOT RUN {
# }