R: Wrapper for Anderson-Darling tests

adtestWrapper {robCompositions} | R Documentation

## 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)

    ## S3 method for class 'adtestWrapper'
    print(x, ...)

    ## S3 method for class 'adtestWrapper'
    summary(object, ...)

### 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
`...` | additional parameters for print and summary passed through
`object` | an object of class adtestWrapper for the summary method

### 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.

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.

### Value

`res` | a list including each test result
`check` | information about the rejection of the null hypothesis
`alpha` | the underlying significance level
`info` | further information which is used by the print and summary method.
`est` | “standard” for standard estimation and “robust” for robust estimation

### Author(s)

Matthias Templ and Karel Hron

### 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.

### See Also

`adtest`, `pivotCoord`

### Examples

    data(machineOperators)
    a <- adtestWrapper(machineOperators, R=50) # choose higher value of R
    a
    summary(a)

[Package robCompositions version 2.0.9 Index]