Welsch test procedure...
In mutoss: Unified multiple testing procedures

Description Usage Arguments Value Author(s) References Examples

REGWQ - Ryan / Einot and Gabriel / Welsch test procedure This function computes REGWQ test for given data including p samples. It is based on a stepwise or layer approach to significance testing. Sample means are ordered from the smallest to the largest. The largest difference, which involves means that are r = p steps apart, is tested first at α level of significance; if significant, means that are r <p steps apart are tested at a different α level of significance and so on. Compare to the Student- Newman-Keuls test, the α levels are adjusted for the p-1 different layers by the formula α_p=α, if p=k or p=k-1, α_p = 1-(1-α)^{p/k} otherwise. It might happen that the quantiles are not descending in p. In this case, they are adapted by c_k = max_{2≤q r ≤q k} c_r, k=2,…,p. The REGWQ procedure, like Tukey's procedure, requires equal sample n's. However, in this algorithm, the procedure is adapted to unequal sample sized which can lead to still conservative test decisions.

1	regwq(formula, data, alpha, MSE=NULL, df=NULL, silent=FALSE)

`formula`	Formula defining the statistical model containing the response and the factors
`data`	dataset containing the response and the grouping factor
`alpha`	The level at which the error should be controlled. By default it is alpha=0.05.
`MSE`	Optional for a given variance of the data
`df`	Optional for a given degree of freedom
`silent`	If true any output on the console will be suppressed.

A list containing:

`adjPValues`	A numeric vector containing the adjusted pValues
`rejected`	A logical vector indicating which hypotheses are rejected
`statistics`	A numeric vector containing the test-statistics
`confIntervals`	A matrix containing only the estimates
`errorControl`	A Mutoss S4 class of type `errorControl`, containing the type of error controlled by the function.

Frank Konietschke

Hochberg, Y. & Tamhane, A. C. (1987). Multiple Comparison Procedures, Wiley.

x = rnorm(50)
grp = c(rep(1:5,10))
dataframe <- data.frame(x,grp)
result <- regwq(x~grp, data=dataframe, alpha=0.05,MSE=NULL, df=NULL, silent = TRUE)
result <- regwq(x~grp, data=dataframe, alpha=0.05,MSE=NULL, df=NULL, silent = FALSE)
result <- regwq(x~grp, data=dataframe, alpha=0.05,MSE=1, df=Inf, silent = FALSE) # known variance
result <- regwq(x~grp, data=dataframe, alpha=0.05,MSE=1, df=1000, silent = FALSE) # known variance