pwrss (version 1.3.1)

power.np.wilcoxon: Power Analysis for Non-parametric Rank-Based Tests (One-Sample, Independent, and Paired Designs)

Description

Calculates power, sample size or effect 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)

Formulas are validated using GPower and tables in the PASS documentation. However, we adopt the rounding convention used by GPower.

Usage

power.np.wilcoxon(
  d = NULL,
  null.d = 0,
  margin = 0,
  req.sign = "+",
  n.ratio = 1,
  n2 = NULL,
  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"),
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)
power.np.wilcox(
  d = NULL,
  null.d = 0,
  margin = 0,
  req.sign = "+",
  n.ratio = 1,
  n2 = NULL,
  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"),
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)

Value

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 \((1-\beta)\).

n

sample size (n or c(n1, n2) depending on the design.

Arguments

d

Cohen's d or Hedges' g.

null.d

Cohen's d or Hedges' g under null, typically 0 (zero).

margin

margin - ignorable d - null.d difference.

req.sign

whether d is smaller or larger than null.d (when minimum detectable prob is of interest).

n.ratio

n1 / n2 ratio (applies to independent samples only)

n2

integer; sample size in the second group (or for the single group in paired samples or one-sample)

power

statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as \(1 - \beta\).

alpha

type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \(\alpha\).

alternative

character; the direction or type of the hypothesis test: "two.sided", "one.sided", or "two.one.sided".

design

character; "independent" (default), "one.sample", or "paired".

distribution

character; parent distribution: "normal", "uniform", "double.exponential", "laplace", or "logistic".

method

character; non-parametric approach: "guenther" (default) or "noether"

ceil.n

logical; whether sample size should be rounded up. TRUE by default.

verbose

1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.

utf

logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Details

• 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.

• NB: pwrss.np.2means() function is depreciated and no longer supported. pwrss.np.2groups() will remain available for some time.

• 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.

References

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.

Examples

# see `?pwrss::power.t.student` for further examples

# 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")