powerOneWayTests function

Power Simulation for One-Factorial Single Hypothesis Tests

Performs power simulation for one-factorial single hypothesis tests.

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.

Returns

An object with class powerOneWayPMCMR.

Details

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

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.

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)

See Also

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