sim.ssize.wilcox.test: Sample Size for Wilcoxon Rank Sum and Signed Rank Tests

In MKpower: Power Analysis and Sample Size Calculation

Sample Size for Wilcoxon Rank Sum and Signed Rank Tests

Description

Simulate the empirical power of Wilcoxon rank sum and signed rank tests for computing the required sample size.

Usage

sim.ssize.wilcox.test(rx, ry = NULL, mu = 0, sig.level = 0.05, power = 0.8, 
                      type = c("two.sample", "one.sample", "paired"), 
                      alternative = c("two.sided", "less", "greater"),
                      n.min = 10, n.max = 200, step.size = 10, 
                      iter = 10000, BREAK = TRUE)

Arguments

rx	function to simulate the values of x, respectively x-y in the paired case.
ry	function to simulate the values of y in the two-sample case
mu	true values of the location shift for the null hypothesis.
sig.level	significance level (Type I error probability)
power	two-sample, one-sample or paired test
type	one- or two-sided test. Can be abbreviated.
alternative	one- or two-sided test. Can be abbreviated.
n.min	integer, start value of grid search.
n.max	integer, stop value of grid search.
step.size	integer, step size used in the grid search.
iter	integer, number of interations of the simulations.
BREAK	logical, grid search stops when the emperical power is larger than the requested power.

Details

Functions rx and ry are used to simulate the data and functions row_wilcoxon_twosample and row_wilcoxon_onesample are used to efficiently compute the p values of the respective test.

We recommend a two steps procedure: In the first step, start with a wide grid and find out in which range of sample size values the intended power will be achieved. In the second step, the interval identified in the first step is used to find the sample size that leads to the required power setting step.size = 1 and BREAK = FALSE. This approach is applied in the examples below.

Value

Object of class "power.htest", a list of the arguments (including the computed one) augmented with method and note elements.

Author(s)

Matthias Kohl [e-mail]

References

Wilcoxon, F (1945). Individual Comparisons by Ranking Methods. Biometrics Bulletin, 1, 80-83.

See Also

wilcox.test, wilcoxon

Examples

 
  ###############################################################################
  ## two-sample
  ## iter = 1000 to reduce check time
  ###############################################################################
  rx <- function(n) rnorm(n, mean = 0, sd = 1) 
  ry <- function(n) rnorm(n, mean = 0.5, sd = 1) 
  sim.ssize.wilcox.test(rx = rx, ry = ry, n.max = 100, iter = 1000)
  sim.ssize.wilcox.test(rx = rx, ry = ry, n.min = 65, n.max = 70, step.size = 1, 
                        iter = 1000, BREAK = FALSE)
  ## compared to
  power.t.test(delta = 0.5, power = 0.8)
  
  rx <- function(n) rnorm(n, mean = 0, sd = 1) 
  ry <- function(n) rnorm(n, mean = 0.5, sd = 1.5) 
  sim.ssize.wilcox.test(rx = rx, ry = ry, n.max = 100, iter = 1000, alternative = "less")
  sim.ssize.wilcox.test(rx = rx, ry = ry, n.min = 85, n.max = 90, step.size = 1, 
                        iter = 1000, BREAK = FALSE, alternative = "less")
  ## compared to
  power.welch.t.test(delta = 0.5, sd = 1, sd2 = 1.5, power = 0.8, alternative = "one.sided")
  
  rx <- function(n) rnorm(n, mean = 0.5, sd = 1)
  ry <- function(n) rnorm(n, mean = 0, sd = 1)
  sim.ssize.wilcox.test(rx = rx, ry = ry, n.max = 100, iter = 1000, alternative = "greater")
  sim.ssize.wilcox.test(rx = rx, ry = ry, n.min = 50, n.max = 55, step.size = 1, 
                        iter = 1000, BREAK = FALSE, alternative = "greater")
  ## compared to
  power.t.test(delta = 0.5, power = 0.8, alternative = "one.sided")
  
  rx <- function(n) rgamma(n, scale = 10, shape = 1)
  ry <- function(n) rgamma(n, scale = 15, shape = 1)
  sim.ssize.wilcox.test(rx = rx, ry = ry, n.max = 200, iter = 1000)
  sim.ssize.wilcox.test(rx = rx, ry = ry, n.min = 125, n.max = 135, step.size = 1, 
                        iter = 1000, BREAK = FALSE)
  
  ###############################################################################
  ## one-sample
  ## iter = 1000 to reduce check time
  ###############################################################################
  rx <- function(n) rnorm(n, mean = 0.5, sd = 1)
  sim.ssize.wilcox.test(rx = rx, mu = 0, type = "one.sample", n.max = 100, iter = 1000)
  sim.ssize.wilcox.test(rx = rx, mu = 0, type = "one.sample", n.min = 33, n.max = 38, 
                        step.size = 1, iter = 1000, BREAK = FALSE)
  ## compared to
  power.t.test(delta = 0.5, power = 0.8, type = "one.sample")
  
  sim.ssize.wilcox.test(rx = rx, mu = 0, type = "one.sample", n.max = 100, iter = 1000,
                        alternative = "greater")
  sim.ssize.wilcox.test(rx = rx, mu = 0, type = "one.sample", n.min = 25, n.max = 30, 
                        step.size = 1, iter = 1000, BREAK = FALSE, alternative = "greater")
  ## compared to
  power.t.test(delta = 0.5, power = 0.8, type = "one.sample", alternative = "one.sided")
  
  sim.ssize.wilcox.test(rx = rx, mu = 1, type = "one.sample", n.max = 100, iter = 1000,
                        alternative = "less")
  sim.ssize.wilcox.test(rx = rx, mu = 1, type = "one.sample", n.min = 20, n.max = 30, 
                        step.size = 1, iter = 1000, BREAK = FALSE, alternative = "less")
  ## compared to
  power.t.test(delta = 0.5, power = 0.8, type = "one.sample", alternative = "one.sided")
  
  rx <- function(n) rgamma(n, scale = 10, shape = 1)
  sim.ssize.wilcox.test(rx = rx, mu = 5, type = "one.sample", n.max = 200, iter = 1000)
  sim.ssize.wilcox.test(rx = rx, mu = 5, type = "one.sample", n.min = 40, n.max = 50, 
                        step.size = 1, iter = 1000, BREAK = FALSE)
  
  ###############################################################################
  ## paired
  ## identical to one-sample, requires random number generating function 
  ## that simulates the difference x-y
  ## iter = 1000 to reduce check time
  ###############################################################################
  rxy <- function(n) rnorm(n, mean = 0.5, sd = 1)
  sim.ssize.wilcox.test(rx = rxy, mu = 0, type = "paired", n.max = 100, 
                        iter = 1000)
  sim.ssize.wilcox.test(rx = rxy, mu = 0, type = "paired", n.min = 33, 
                        n.max = 38, step.size = 1, iter = 1000, BREAK = FALSE)
  ## compared to
  power.t.test(delta = 0.5, power = 0.8, type = "paired")

MKpower documentation built on April 23, 2023, 1:15 a.m.