R: Lu-Smith All-Pairs Comparison Normal Scores Test

normalScoresAllPairsTest {PMCMRplus}

R Documentation

Lu-Smith All-Pairs Comparison Normal Scores Test

Description

Performs Lu-Smith all-pairs comparison normal scores test.

Usage

normalScoresAllPairsTest(x, ...)

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

## S3 method for class 'formula'
normalScoresAllPairsTest(
  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 `NA`s. Defaults to `getOption("na.action")`.

Details

For all-pairs comparisons in an one-factorial layout with non-normally distributed residuals Lu and Smith'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.

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.

References

Lu, H., Smith, P. (1979) Distribution of normal scores statistic for nonparametric one-way analysis of variance. Journal of the American Statistical Association 74, 715–722.