A set of Anderson-Darling tests (Anderson and Darling, 1952) are applied as proposed by Aitchison (Aichison, 1986).
adtestWrapper(x, alpha = 0.05, R = 1000, robustEst = FALSE)# S3 method for adtestWrapper
print(x, ...)
# S3 method for adtestWrapper
summary(object, ...)
a list including each test result
information about the rejection of the null hypothesis
the underlying significance level
further information which is used by the print and summary method.
“standard” for standard estimation and “robust” for robust estimation
compositional data of class data.frame or matrix
significance level
Number of Monte Carlo simulations in order to provide p-values.
logical
additional parameters for print and summary passed through
an object of class adtestWrapper for the summary method
Matthias Templ and Karel Hron
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.
A print and a summary method are implemented. The latter one provides a similar output is proposed by (Pawlowsky-Glahn, et al. (2008). In addition to that, p-values are provided.
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 and Hall Ltd., London (UK). 416p.
adtest, pivotCoord
data(machineOperators)
a <- adtestWrapper(machineOperators, R=50) # choose higher value of R
a
summary(a)
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