wmwpowp {wmwpow}

Precise and Accurate Monte Carlo Power Calculation by Inputting P (wmwpowp)

Description

wmwpowp has two purposes:

1. Calculate the power for a one-sided or two-sided Wilcoxon-Mann-Whitney test with an empirical Monte Carlo p-value given one user specified distribution and p (defined as P(X<Y)).

2. Calculate the parameters of the second distribution. It is assumed that the second population is from the same type of continuous probability distribution as the first population.

Power is calculated empirically using simulated data and the parameters are calculated using derived mathematical formulas for P(X<Y).

Usage

wmwpowp(n, m, distn, k = 1, p = NA, wmwodds = NA, sides, alpha = 0.05, nsims = 10000)

Arguments

n

Sample size for the first distribution (numeric)

m

Sample size for the second distribution (numeric)

p

The effect size, i.e., the probability that the first random variable is less than the second random variable (P(X<Y)) (numeric)

alpha

Type I error rate or significance level (numeric)

distn

Base R’s name for the first distribution (known as X in the above notation) and any required parameters. Supported distributions are normal, exponential, and double exponential ("norm","exp", "doublex"). User may enter distribution without parameters, and default parameters will be set (i.e., "norm" defaults to "norm(0,1)"), or user may specify both distribution and parameters (i.e., "norm(0,1)").

sides

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

k

Standard deviation (SD) scalar for use with the normal or double exponential distribution options. The SD for distm is computed as k multiplied by the SD for distn. Equivalently, k is the ratio of the SDs of the second and first distribution (k = SDm/SDn). Default is k=1 (equal SDs) (numeric)

wmwodds

The effect size expressed as odds = p/(1-p). Either p or wmwodds must be input (numeric)

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)

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.

Examples

# We want to calculate the statistical power to compare the distance between mutations on a DNA 
# strand in two groups of people. Each group (X and Y) has 10 individuals. We assume that the 
# distance between mutations in the first group is exponentially distributed with rate 3. We assume
# that the probability that the distance in the first group is less than the distance in the second 
# group (i.e., P(X<Y)) is 0.8. The desired type I error is 0.05.

wmwpowp(n = 10, m = 10, distn = "exp(3)", p = 0.8, sides = "two.sided", alpha = 0.05)