PMCMRplus (version 1.9.3)

vanWaerdenManyOneTest: van-der-Waerden's Many-One Comparisons Normal Scores Test

Description

Performs van-der-Waerden's multiple comparison normal scores test with one control.

Usage

vanWaerdenManyOneTest(x, ...)
# S3 method for default
vanWaerdenManyOneTest(
  x,
  g,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = c("single-step", p.adjust.methods),
  ...
)
# S3 method for formula
vanWaerdenManyOneTest(
  formula,
  data,
  subset,
  na.action,
  alternative = c("two.sided", "greater", "less"),
  p.adjust.method = c("single-step", p.adjust.methods),
  ...
)

Arguments

x

a numeric vector of data values, or a list of numeric data vectors.

…

further arguments to be passed to or from methods.

g

a vector or factor object giving the group for the corresponding elements of "x". Ignored with a warning if "x" is a list.

alternative

the alternative hypothesis. Defaults to two.sided.

p.adjust.method

method for adjusting p values (see p.adjust).

formula

a formula of the form response ~ group where response gives the data values and group a vector or factor of the corresponding groups.

data

an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).

subset

an optional vector specifying a subset of observations to be used.

na.action

a function which indicates what should happen when the data contain NAs. Defaults to getOption("na.action").

Value

A list with class "PMCMR" containing the following components:

method

a character string indicating what type of test was performed.

data.name

a character string giving the name(s) of the data.

statistic

lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

lower-triangle matrix of the p-values for the pairwise tests.

alternative

a character string describing the alternative hypothesis.

p.adjust.method

a character string describing the method for p-value adjustment.

model

a data frame of the input data.

dist

a string that denotes the test distribution.

Details

For many-to-one comparisons in an one-factorial layout with non-normally distributed residuals van-der-Waerden's normal scores transformation can be used prior to a many-to-one comparison test. A total of \(m = k-1\) hypotheses can be tested. The null hypothesis H\(_{i}: F_0(x) = F_i(x)\) is tested in the two-tailed test against the alternative A\(_{i}: F_0(x) \ne F_i(x), ~~ 1 \le i \le k-1\). For p.adjust.method = "single-step" the multivariate t distribution is used to calculate p-values (see pmvt). Otherwise, the t-distribution is used for the calculation of p-values with a latter p-value adjustment as performed by p.adjust.

References

Conover, W. J., Iman, R. L. (1979) On multiple-comparisons procedures, Tech. Rep. LA-7677-MS, Los Alamos Scientific Laboratory.

van der Waerden, B. L. (1952) Order tests for the two-sample problem and their power, Indagationes Mathematicae 14, 453--458.

See Also

vanWaerdenTest, vanWaerdenAllPairsTest, pmvt.

Examples

# NOT RUN {
## Data set PlantGrowth
## Global test
vanWaerdenTest(weight ~ group, data = PlantGrowth)

## van-der-Waerden's many-one comparison test
ans <- vanWaerdenManyOneTest(weight ~ group,
                             data = PlantGrowth,
                             p.adjust.method = "holm")
summary(ans)
# }