powerOneWayTests: Power Simulation for One-Factorial Single Hypothesis Tests

In PMCMRplus: Calculate Pairwise Multiple Comparisons of Mean Rank Sums Extended

Power Simulation for One-Factorial Single Hypothesis Tests

Description

Performs power simulation for one-factorial single hypothesis tests.

Usage

powerOneWayTests(
  mu,
  n = 10,
  errfn = c("Normal", "Lognormal", "Exponential", "Chisquare", "TDist", "Cauchy",
    "Weibull"),
  parms = list(mean = 0, sd = 1),
  test = c("kruskalTest", "leTest", "vanWaerdenTest", "normalScoresTest", "spearmanTest",
    "cuzickTest", "jonckheereTest", "johnsonTest", "oneway.test", "adKSampleTest",
    "bwsKSampleTest", "bwsTrendTest", "mackWolfeTest", "chackoTest", "flignerWolfeTest"),
  alternative = c("two.sided", "greater", "less"),
  var.equal = TRUE,
  dist = NULL,
  alpha = 0.05,
  FWER = TRUE,
  replicates = 1000,
  p = NULL
)

Arguments

mu	numeric vector of group means.
n	number of replicates per group. If n is a scalar, then a balanced design is assumed. Otherwise, n must be a vector of same length as mu.
errfn	the error function. Defaults to "Normal".
parms	a list that denotes the arguments for the error function. Defaults to list(mean=0, sd=1).
test	the test for which the power analysis is to be performed. Defaults to "kwManyOneConoverTest".
alternative	the alternative hypothesis. Defaults to "two.sided", ignored if the selected error function does not use this argument.
var.equal	a logical variable indicating whether to treat the variances in the samples as equal. "TRUE", then a simple F test for the equality of means in a one-way analysis of variance is performed. If "FALSE", an approximate method of Welch (1951) is used, which generalizes the commonly known 2-sample Welch test to the case of arbitrarily many samples. Defaults to "TRUE"; only relevant, if test = "oneway.test", otherwise ignored.
dist	the test distribution. Only relevant for kruskalTest. Defaults's to NULL.
alpha	the nominal level of Type I Error.
FWER	logical, indicates whether the family-wise error should be computed. Defaults to TRUE.
replicates	the number of Monte Carlo replicates or runs. Defaults to 1000.
p	the a-priori known peak as an ordinal number of the treatment group including the zero dose level, i.e. p = \{1, \ldots, k\}. Defaults to NULL. Only relevant, if "mackWolfeTest" is selected.

Details

The linear model of a one-way ANOVA can be written as:

X_{ij} = \mu_i + \epsilon_{ij}

For each Monte Carlo run, the function simulates \epsilon_{ij} based on the given error function and the corresponding parameters. Then the specified test is performed. Finally, Type I and Type II error rates are calculated.

Value

An object with class powerOneWayPMCMR.

See Also

powerMCTests, pwr.anova.test, power.anova.test

Examples

## Not run: 
set.seed(12)
mu <- c(0, 0, 1, 2)
n <- c(5, 4, 5, 5)
parms <- list(mean=0, sd=1)
powerOneWayTests(mu, n, parms, test = "cuzickTest",
alternative = "two.sided", replicates = 1E4)

## Compare power estimation for
## one-way ANOVA with balanced design
## as given by functions
## power.anova.test, pwr.anova.test
## and powerOneWayTest

groupmeans <- c(120, 130, 140, 150)
SEsq <- 500  # within-variance
n <- 10
k <- length(groupmeans)
df <- n * k - k
SSQ.E <- SEsq * df
SSQ.A <- n * var(groupmeans) * (k - 1)
sd.errfn <- sqrt(SSQ.E / (n * k - 1))
R2 <- c("R-squared" = SSQ.A / (SSQ.A + SSQ.E))
cohensf <- sqrt(R2 / (1 - R2))
names(cohensf) <- "Cohens f"

## R stats power function
power.anova.test(groups = k,
                 between.var = var(groupmeans),
                 within.var = SEsq,
                 n = n)

## pwr power function
pwr.anova.test(k = k, n = n, f = cohensf, sig.level=0.05)

## this Monte-Carlo based estimation
set.seed(200)
powerOneWayTests(mu = groupmeans,
                 n = n,
                 parms = list(mean=0, sd=sd.errfn),
                 test = "oneway.test",
                 var.equal = TRUE,
                 replicates = 5E3)

## Compare with effect sizes
R2
cohensf


## End(Not run)

PMCMRplus documentation built on May 29, 2024, 8:34 a.m.