power.np.wilcoxon | R Documentation |
Calculates power or sample size (only one can be NULL at a time) for non-parametric rank-based tests. The following tests and designs are available:
Wilcoxon Signed-Rank Test (One Sample)
Wilcoxon Rank-Sum or Mann-Whitney U Test (Independent Samples)
Wilcoxon Matched-Pairs Signed-Rank Test (Paired Samples)
Use means.to.d()
to convert raw means and standard deviations to Cohen's d, and d.to.cles()
to convert Cohen's d to the probability of superiority. Note that this interpretation is appropriate only when the underlying distribution is approximately normal and the two groups have similar population variances.
Formulas are validated using G*Power and tables in PASS documentation. However, we adopt rounding convention used by G*Power.
Note that R has a partial matching feature which allows you to specify shortened versions of arguments, such as alt
instead of alternative
, or dist
instead of distribution
.
NOTE: pwrss.np.2means()
function is no longer supported. pwrss.np.2groups()
will remain available for some time.
power.np.wilcoxon(d, null.d = 0, margin = 0,
n2 = NULL, n.ratio = 1, power = NULL, alpha = 0.05,
alternative = c("two.sided", "one.sided", "two.one.sided"),
design = c("independent", "paired", "one.sample"),
distribution = c("normal", "uniform", "double.exponential",
"laplace", "logistic"),
method = c("guenther", "noether"),
ceiling = TRUE, verbose = TRUE, pretty = FALSE)
d |
Cohen's d or Hedges' g. |
null.d |
Cohen's d or Hedges' g under null, typically 0 (zero). |
margin |
margin - ignorable |
n2 |
integer; sample size in the second group (or for the single group in paired samples or one-sample) |
n.ratio |
|
power |
statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as |
alpha |
type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as |
design |
character; "independent" (default), "one.sample", or "paired". |
alternative |
character; direction or type of the hypothesis test: "two.sided", "one.sided", or "two.one.sided". |
distribution |
character; parent distribution: "normal", "uniform", "double.exponential", "laplace", or "logistic". |
method |
character; non-parametric approach: "guenther" (default) or "noether" |
ceiling |
logical; whether sample size should be rounded up. |
verbose |
logical; whether the output should be printed on the console. |
pretty |
logical; whether the output should show Unicode characters (if encoding allows for it). |
parms |
list of parameters used in calculation. |
test |
type of the statistical test (Z- or T-Test). |
df |
degrees of freedom (applies when method = 'guenther'). |
ncp |
non-centrality parameter for the alternative (applies when method = 'guenther'). |
null.ncp |
non-centrality parameter for the null (applies when method = 'guenther'). |
t.alpha |
critical value(s) (applies when method = 'guenther'). |
mean |
mean of the alternative (applies when method = 'noether'). |
null.mean |
mean of the null (applies when method = 'noether'). |
sd |
standard deviation of the alternative (applies when method = 'noether'). |
null.sd |
standard deviation of the null (applies when method = 'noether'). |
z.alpha |
critical value(s) (applies when method = 'noether'). |
power |
statistical power |
n |
sample size ('n' or 'c(n1, n2)' depending on the design. |
Al-Sunduqchi, M. S. (1990). Determining the appropriate sample size for inferences based on the Wilcoxon statistics [Unpublished doctoral dissertation]. University of Wyoming - Laramie
Chow, S. C., Shao, J., Wang, H., and Lokhnygina, Y. (2018). Sample size calculations in clinical research (3rd ed.). Taylor & Francis/CRC.
Lehmann, E. (1975). Nonparameterics: Statistical methods based on ranks. McGraw-Hill.
Noether, G. E. (1987). Sample size determination for some common nonparametric tests. Journal of the American Statistical Association, 82(1), 645-647.
Ruscio, J. (2008). A probability-based measure of effect size: Robustness to base rates and other factors. Psychological Methods, 13(1), 19-30.
Ruscio, J., & Mullen, T. (2012). Confidence intervals for the probability of superiority effect size measure and the area under a receiver operating characteristic curve. Multivariate Behavioral Research, 47(2), 201-223.
Zhao, Y.D., Rahardja, D., & Qu, Y. (2008). Sample size calculation for the Wilcoxon-Mann-Whitney test adjusting for ties. Statistics in Medicine, 27(3), 462-468.
# Mann-Whitney U or Wilcoxon rank-sum test
# (a.k.a Wilcoxon-Mann-Whitney test) for independent samples
## difference between group 1 and group 2 is not equal to zero
## estimated difference is Cohen'd = 0.25
power.np.wilcoxon(d = 0.25,
power = 0.80)
## difference between group 1 and group 2 is greater than zero
## estimated difference is Cohen'd = 0.25
power.np.wilcoxon(d = 0.25,
power = 0.80,
alternative = "one.sided")
## mean of group 1 is practically not smaller than mean of group 2
## estimated difference is Cohen'd = 0.10 and can be as small as -0.05
power.np.wilcoxon(d = 0.10,
margin = -0.05,
power = 0.80,
alternative = "one.sided")
## mean of group 1 is practically greater than mean of group 2
## estimated difference is Cohen'd = 0.10 and can be as small as 0.05
power.np.wilcoxon(d = 0.10,
margin = 0.05,
power = 0.80,
alternative = "one.sided")
## mean of group 1 is practically same as mean of group 2
## estimated difference is Cohen'd = 0
## and can be as small as -0.05 and as high as 0.05
power.np.wilcoxon(d = 0,
margin = c(-0.05, 0.05),
power = 0.80,
alternative = "two.one.sided")
# Wilcoxon signed-rank test for matched pairs (dependent samples)
## difference between time 1 and time 2 is not equal to zero
## estimated difference between time 1 and time 2 is Cohen'd = -0.25
power.np.wilcoxon(d = -0.25,
power = 0.80,
design = "paired")
## difference between time 1 and time 2 is greater than zero
## estimated difference between time 1 and time 2 is Cohen'd = -0.25
power.np.wilcoxon(d = -0.25,
power = 0.80,
design = "paired",
alternative = "one.sided")
## mean of time 1 is practically not smaller than mean of time 2
## estimated difference is Cohen'd = -0.10 and can be as small as 0.05
power.np.wilcoxon(d = -0.10,
margin = 0.05,
power = 0.80,
design = "paired",
alternative = "one.sided")
## mean of time 1 is practically greater than mean of time 2
## estimated difference is Cohen'd = -0.10 and can be as small as -0.05
power.np.wilcoxon(d = -0.10,
margin = -0.05,
power = 0.80,
design = "paired",
alternative = "one.sided")
## mean of time 1 is practically same as mean of time 2
## estimated difference is Cohen'd = 0
## and can be as small as -0.05 and as high as 0.05
power.np.wilcoxon(d = 0,
margin = c(-0.05, 0.05),
power = 0.80,
design = "paired",
alternative = "two.one.sided")
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