powerOneWayTests: 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

numeric vector of group means.

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.

the a-priori known peak as an ordinal number of the treatment group including the zero dose level, i.e. $p = {1, \dots, k}$ . Defaults to NULL. Only relevant, if "mackWolfeTest" is selected.

Value

An object with class powerOneWayPMCMR.

Details

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

$X_{i j} = μ_{i} + ϵ_{i j}$

For each Monte Carlo run, the function simulates $ϵ_{i j}$ 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

Run this code

# 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

# }
# NOT RUN {
# }

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