mutoss (version 0.1-12)

regwq: REGWQ - Ryan / Einot and Gabriel / Welsch test procedure...

Description

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 \(\alpha\) level of significance; if significant, means that are \(r <p\) steps apart are tested at a different \(\alpha\) level of significance and so on. Compare to the Student- Newman-Keuls test, the \(\alpha\) levels are adjusted for the p-1 different layers by the formula \(\alpha_p=\alpha\), if p=k or p=k-1, \(\alpha_p = 1-(1-\alpha)^{p/k}\) otherwise. It might happen that the quantiles are not descending in p. In this case, they are adapted by \(c_k = max_{2\leq r \leq k} c_r, k=2,\ldots,p\). 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.

Usage

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

Value

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.

Author

Frank Konietschke

Arguments

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.

References

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

Examples

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