snk: Student - Newman - Keuls rejective test procedure.
In mutoss: Unified multiple testing procedures

Description Usage Arguments Details Value Author(s) References Examples

Student - Newman - Keuls rejective test procedure. The procedure controls the FWER in the WEAK sense.

1 2	snk(formula, data, alpha, MSE=NULL, df=NULL, silent=FALSE) snk.wrapper(model, data, alpha, silent=FALSE)

`formula`	Formula defining the statistical model containing the response and the factor levels.
`model`	Model with formula, containing the response and the factor levels
`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.

This function computes the Student-Newman-Keuls test for given data including p samples. The Newman-Keuls procedure 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 - 1 steps apart are tested at α level of significance and so on. The Newman-Keuls procedure provides an r-mean significance level equal to α for each group of r ordered means, that is, the probability of falsely rejecting the hypothesis that all means in an ordered group are equal to α. It follows that the concept of error rate applies neither on an experimentwise nor on a per comparison basis-the actual error rate falls somewhere between the two. The Newman-Keuls 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.

It should be noted that the Newman-Keuls and Tukey procedures require the same critical difference for the first comparison that is tested. The Tukey procedure uses this critical difference for all the remaining tests, whereas the Newman-Keuls procedure reduces the size of the critical difference, depending on the number of steps separating the ordered means. As a result, the Newman-Keuls test is more powerful than Tukey's test. Remember, however, that the Newman-Keuls procedure does not control the experimentwise error rate at α.

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

Keuls M (1952). "The use of the studentized range in connection with an analysis of variance". Euphytica 1: 112-122

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