vanWaerdenAllPairsTest function

van-der-Waerden's All-Pairs Comparison Normal Scores Test

Performs van-der-Waerden all-pairs comparison normal scores test.

vanWaerdenAllPairsTest(x, ...)

## Default S3 method:
vanWaerdenAllPairsTest(
  x,
  g,
  p.adjust.method = c("single-step", p.adjust.methods),
  ...
)

## S3 method for class 'formula'
vanWaerdenAllPairsTest(
  formula,
  data,
  subset,
  na.action,
  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.
• 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").

Returns

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 all-pairs comparisons in an one-factorial layout with non-normally distributed residuals van-der-Waerden's normal scores transformation can be used prior to an all-pairs comparison test. A total of $m = k(k-1)/2$

hypotheses can be tested. The null hypothesis H$_{ij}: F_i(x) = F_j(x)$ is tested in the two-tailed test against the alternative A$_{ij}: F_i(x) \ne F_j(x), ~~ i \ne j$. For p.adjust.method = "single-step" the Tukey's studentized range distribution is used to calculate p-values (see Tukey). 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, vanWaerdenManyOneTest, normOrder.