gao: Xin Gao's non-parametric multiple test procedure is applied...
In mutoss: Unified multiple testing procedures

Description Usage Arguments Details Value Author(s) References Examples

Xin Gao's non-parametric multiple test procedure is applied to Data. The procedure controls the FWER in the strong sense. Here, only the Many-To-One comparisons are computed.

1 2	gao(formula, data, alpha=0.05, control=NULL, silent=FALSE) gao.wrapper(model, data, alpha, control)

`formula`	Formula defining the statistical model, containing the response and the factors
`model`	Model with formula, containing the response and the factors
`data`	Dataset containing the response and the grouping factor
`alpha`	The level at which the FWER shall be controlled. By default it is alpha=0.05.
`silent`	If true any output on the console will be suppressed.
`control`	The control group for the Many-To-One comparisons. By default it is the first group in lexicographical order.

This function computes Xin Gao's nonparametric multiple test procedures in an unbalanced one way layout. It is based upon the following purely nonparametric effects: Let F_i denote the distribution function of sample i, i=1,…,a, and let G denote the mean distribution function of all distribution functions (G=1/a∑_i F_i). The effects p_i=\int GdF_i are called unweighted relative effects. If p_i>1/2, the random variables from sample i tend (stochastically) to larger values than any randomly chosen number from the whole experiment. If p_i = 1/2, there is no tendency to smaller nor larger values. However, this approach tests the hypothesis H_0^F: F_1=F_j, j=2,…,a formulated in terms of the distribution functions, simultaneously.

A list containing:

`adjPValues`	A numeric vector containing the adjusted pValues
`rejected`	A logical vector indicating which hypotheses are rejected
`confIntervals`	A matrix containing the estimates and the lower and upper confidence bound
`errorControl`	A Mutoss S4 class of type `errorControl`, containing the type of error controlled by the function and the level `alpha`.

Frank Konietschke

Gao, X. et al. (2008). Nonparametric multiple comparison procedures for unbalanced one-way factorial designs. Journal of Statistical Planning and Inference 77, 2574-2591. n The FWER is controlled by using the Hochberg adjustment (Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika 75, 800-802.)

x=c(rnorm(40))
f1=c(rep(1,10),rep(2,10),rep(3,10),rep(4,10))
my.data <- data.frame(x,f1)
result <- gao(x~f1,data=my.data, alpha=0.05,control=2, silent=FALSE)
result <- gao(x~f1,data=my.data, alpha=0.05,control=2, silent=TRUE)
result <- gao(x~f1,data=my.data, alpha=0.05)