mutoss (version 0.1-13)

gao: Xin Gao's non-parametric multiple test procedure is applied to Data.

Description

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.

Usage

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

Value

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.

Author

Frank Konietschke

Arguments

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.

Details

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 \(i, i=1,\ldots,a,\) and let \(G\) denote the mean distribution function of all distribution functions \((G=1/a\sum_i F_i)\). 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 \(H_0^F: F_1=F_j, j=2,\ldots,a\) formulated in terms of the distribution functions, simultaneously.

References

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.)

Examples

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)