pwrss.np.2groups {pwrss}

Difference between Two Groups (Non-parametric Tests for Independent and Paired Samples)

Description

Calculates statistical power or minimum required sample size (only one can be NULL at a time) to test difference between two groups. Although means and standard deviations are some of the arguments in the function below, what is actually being tested is the difference between mean ranks. First, the mean difference is converted into Cohen's d, and then into probability of superiority, which is the probability of an observation in group 1 being higher than an observation in group 2. Probability of superiority can be extracted as pwrss.np.2groups()$parms$prob1. This parameterization, expressed as means and standard deviations, helps in making comparisons and switching back and forth between parametric and non-parametric tests.

For standardized mean difference (Cohen's d) set mu1 = d and use defaults for mu2, sd1, and sd2. If pooled standard deviation (psd) is available set sd1 = psd.

Formulas are validated using Monte Carlo simulation, G*Power, and tables in PASS documentation.

Usage

pwrss.np.2groups(mu1 = 0.20, mu2 = 0,
                sd1 = ifelse(paired, sqrt(1/(2*(1-paired.r))), 1), sd2 = sd1,
                margin = 0, alpha = 0.05, paired = FALSE, paired.r = 0.50,
                kappa = 1, n2 = NULL, power = NULL,
                alternative = c("not equal", "greater", "less",
                                "non-inferior", "superior", "equivalent"),
                distribution = c("normal", "uniform", "double exponential",
                                 "laplace", "logistic"),
                method = c("guenther", "noether"),
                verbose = TRUE)

Arguments

mu1

expected mean in the first group

mu2

expected mean in the second group

sd1

expected standard deviation in the first group

sd2

expected standard deviation in the second group

paired

if TRUE paired samples

paired.r

correlation between repeated measures for paired samples (e.g., pretest and posttest)

n2

sample size in the second group (or for the single group in paired samples)

kappa

n1/n2 ratio (applies to independent samples only)

power

statistical power (1-\beta)

alpha

probability of type I error

margin

non-inferority, superiority, or equivalence margin (margin: boundry of mu1 - mu2 that is practically insignificant)

alternative

direction or type of the hypothesis test: "not equal", "greater", "less", "equivalent", "non-inferior", or "superior"

distribution

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

method

non-parametric method: "guenther" (default) or "noether"

verbose

if FALSE no output is printed on the console

Value

parms

list of parameters used in calculation

test

type of the statistical test (z or t test)

df

degrees of freedom

ncp

non-centrality parameter

power

statistical power (1-\beta)

n

sample size

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.

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

# 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
pwrss.np.2means(mu1 = 0.25, mu2 = 0, power = 0.80,
                alternative = "not equal")

## difference between group 1 and group 2 is greater than zero
## estimated difference is Cohen'd = 0.25
pwrss.np.2means(mu1 = 0.25, mu2 = 0, power = 0.80,
                alternative = "greater")

## 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
pwrss.np.2means(mu1 = 0.25, mu2 = 0.15,
                margin = -0.05, power = 0.80,
                alternative = "non-inferior")

## 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
pwrss.np.2means(mu1 = 0.25, mu2 = 0.15,
                margin = 0.05, power = 0.80,
                alternative = "superior")

## 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
pwrss.np.2means(mu1 = 0.25, mu2 = 0.25,
                margin = 0.05, power = 0.80,
                alternative = "equivalent")


# 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
pwrss.np.2means(mu1 = 0, mu2 = 0.25, power = 0.80,
                paired = TRUE, paired.r = 0.50,
                alternative = "not equal")

## difference between time 1 and time 2 is greater than zero
## estimated difference between time 1 and time 2 is Cohen'd = -0.25
pwrss.np.2means(mu1 = 0, mu2 = 0.25, power = 0.80,
                paired = TRUE, paired.r = 0.50,
                alternative = "greater")

## 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
pwrss.np.2means(mu1 = 0.15, mu2 = 0.25, margin = 0.05,
                paired = TRUE, paired.r = 0.50, power = 0.80,
                alternative = "non-inferior")

## 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
pwrss.np.2means(mu1 = 0.15, mu2 = 0.25, margin = -0.05,
                paired = TRUE, paired.r = 0.50, power = 0.80,
                alternative = "superior")

## 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
pwrss.np.2means(mu1 = 0.25, mu2 = 0.25, margin = 0.05,
                paired = TRUE, paired.r = 0.50, power = 0.80,
                alternative = "equivalent")