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
x
compositional data of class data.frame or matrix
alpha
significance level
R
Number of Monte Carlo simulations in order to provide p-values.
robustEst
logical
Value
resa list including each test result
checkinformation about the rejection of the null hypothesis
alphathe underlying significance level
infofurther information which is used by the print and summary method.
eststandard for standard estimation and robust for robust estimation
Details
First, the data is transformed using the 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.
References
Anderson, T.W. and Darling, D.A. (1952)
Asymptotic theory of certain goodness-of-fit criteria based
on stochastic processes Annals of Mathematical Statistics, 23
193-212.
Aitchison, J. (1986) The Statistical Analysis of Compositional
Data Monographs on Statistics and Applied Probability. Chapman &
Hall Ltd., London (UK). 416p.