wmwpowd {wmwpow}

Precise and Accurate Monte Carlo Power Calculation by Inputting Distributions F and G (wmwpowd)

Description

wmwpowd has two purposes:

1. Calculate the power for a one-sided or two-sided Wilcoxon-Mann-Whitney test with an empirical p-value given two user specified distributions.

2. Calculate p, the P(X<Y), where X represents random draws from one continuous probability distribution and Y represents random draws from another distribution; p is useful for quantifying the effect size that the Wilcoxon-Mann-Whitney test is assessing.

Both 1. and 2. are calculated empirically using simulated data and output automatically.

Usage

wmwpowd(n, m, distn, distm, sides, alpha = 0.05, nsims = 10000)

Arguments

n

Sample size for the first distribution (numeric)

m

Sample size for the second distribution (numeric)

alpha

Type I error rate or significance level (numeric)

distn

Base R’s name for the first distribution and any required parameters ("norm", "beta", "cauchy", "f", "gamma", "lnorm", "unif", "weibull","exp", "chisq", "t", "doublex")

distm

Base R’s name for the second distribution and any required parameters ("norm", "beta", "cauchy", "f", "gamma", "lnorm", "unif", "weibull","exp", "chisq", "t", "doublex")

sides

Options are “two.sided”, “less”, or “greater”. “less” means the alternative hypothesis is that distn is less than distm (string)

nsims

Number of simulated datasets for calculating power; 10,000 is the default. For exact power to the hundredths place (e.g., 0.90 or 90%) around 100,000 simulated datasets is recommended (numeric)

Note

Example of distn, distm: “norm(1,2)” or “exp(1)”

In addition to all continuous distributions supported in Base R, wmwpowd also supports the double exponential distribution from the smoothmest package

The output WMWOdds is p expressed as odds p/(1-p)

Use $ notation to select specific output parameters

The function has been optimized to run through simulations quickly; long wait times are unlikely for n and m of 50 or fewer

References

Mollan K.R., Trumble I.M., Reifeis S.A., Ferrer O., Bay C.P., Baldoni P.L., Hudgens M.G. Exact Power of the Rank-Sum Test for a Continuous Variable, arXiv:1901.04597 [stat.ME], Jan. 2019.