\name{adtestWrapper}
\title{ Wrapper for Anderson-Darling tests }
\description{
A set of Anderson-Darling tests (Anderson and Darling, 1952) are applied as proposed by Aitchison
(Aichison, 1986).
}
\usage{
adtestWrapper(x, alpha = 0.05, R = 1000, robustEst = FALSE)
}
\arguments{
\item{x}{ compositional data of class data.frame or matrix }
\item{alpha}{ significance level }
\item{R}{ Number of Monte Carlo simulations in order to provide p-values. }
\item{robustEst}{ logical }
}
\details{
First, the data is transformed using the \sQuote{ilr}-transformation.
After applying this transformation

- all (D-1)-dimensional marginal, univariate distributions are tested using the univariate
Anderson-Darling test for normality.

- all 0.5 (D-1)(D-2)-dimensional bivariate angle distributions are tested using the Anderson-Darling
angle test for normality.

- the (D-1)-dimensional radius distribution is tested using
the Anderson-Darling radius test for normality.
}
\value{
\item{res }{ a list including each test result }
\item{check }{ information about the rejection of the null hypothesis}
\item{alpha}{ the underlying significance level }
\item{info}{ further information which is used by the print and summary method. }
\item{est}{ \dQuote{standard} for standard estimation and \dQuote{robust} for robust estimation }
}
\references{
Anderson, T.W. and Darling, D.A. (1952)
\emph{Asymptotic theory of certain goodness-of-fit criteria based
on stochastic processes} Annals of Mathematical Statistics, \bold{23}
193-212.

Aitchison, J. (1986) \emph{The Statistical Analysis of Compositional
Data} Monographs on Statistics and Applied Probability. Chapman \&
Hall Ltd., London (UK). 416p.
}
\author{ Matthias Templ and Karel Hron }
\keyword{ htest }