Compute Wilcoxon effect size (r
) for:
onesample test (Wilcoxon onesample signedrank test);
paired twosamples test (Wilcoxon twosample paired signedrank test) and
independent twosamples test ( MannWhitney, twosample ranksum test).
It can also returns confidence intervals by bootstap.
The effect size r
is calculated as Z
statistic divided by
square root of the sample size (N) (\(Z/\sqrt{N}\)). The Z
value is
extracted from either coin::wilcoxsign_test()
(case of one or
pairedsamples test) or coin::wilcox_test()
(case of independent
twosamples test).
Note that N
corresponds to total sample size for independent samples
test and to total number of pairs for paired samples test.
The r
value varies from 0 to close to 1. The interpretation values
for r commonly in published litterature and on the internet are: 0.10
 < 0.3
(small effect), 0.30  < 0.5
(moderate effect) and >=
0.5
(large effect).
wilcox_effsize( data, formula, comparisons = NULL, ref.group = NULL, paired = FALSE, alternative = "two.sided", mu = 0, ci = FALSE, conf.level = 0.95, ci.type = "perc", nboot = 1000, ... )
data  a data.frame containing the variables in the formula. 

formula  a formula of the form 
comparisons  A list of length2 vectors specifying the groups of
interest to be compared. For example to compare groups "A" vs "B" and "B" vs
"C", the argument is as follow: 
ref.group  a character string specifying the reference group. If specified, for a given grouping variable, each of the group levels will be compared to the reference group (i.e. control group). If 
paired  a logical indicating whether you want a paired test. 
alternative  a character string specifying the alternative
hypothesis, must be one of 
mu  a number specifying an optional parameter used to form the null hypothesis. 
ci  If TRUE, returns confidence intervals by bootstrap. May be slow. 
conf.level  The level for the confidence interval. 
ci.type  The type of confidence interval to use. Can be any of "norm",
"basic", "perc", or "bca". Passed to 
nboot  The number of replications to use for bootstrap. 
...  Additional arguments passed to the functions

return a data frame with some of the following columns:
.y.
: the y variable used in the test.
group1,group2
: the compared groups in the pairwise tests.
n,n1,n2
: Sample counts.
effsize
: estimate of the effect
size (r
value).
magnitude
: magnitude of effect size.
conf.low,conf.high
: lower and upper bound of the effect size
confidence interval.
Maciej Tomczak and Ewa Tomczak. The need to report effect size estimates revisited. An overview of some recommended measures of effect size. Trends in Sport Sciences. 2014; 1(21):1925.
if(require("coin")){ # Onesample Wilcoxon test effect size ToothGrowth %>% wilcox_effsize(len ~ 1, mu = 0) # Independent twosamples wilcoxon effect size ToothGrowth %>% wilcox_effsize(len ~ supp) # Pairedsamples wilcoxon effect size ToothGrowth %>% wilcox_effsize(len ~ supp, paired = TRUE) # Pairwise comparisons ToothGrowth %>% wilcox_effsize(len ~ dose) # Grouped data ToothGrowth %>% group_by(supp) %>% wilcox_effsize(len ~ dose) }#>#>#> #>#>#> #>#> # A tibble: 6 x 8 #> .y. group1 group2 effsize supp n1 n2 magnitude #> * <chr> <chr> <chr> <dbl> <fct> <int> <int> <ord> #> 1 len 0.5 1 0.719 OJ 10 10 large #> 2 len 0.5 2 0.846 OJ 10 10 large #> 3 len 1 2 0.398 OJ 10 10 moderate #> 4 len 0.5 1 0.846 VC 10 10 large #> 5 len 0.5 2 0.845 VC 10 10 large #> 6 len 1 2 0.795 VC 10 10 large