# adtest: Anderson-Darling Normality Tests In robCompositions: Compositional Data Analysis

## Anderson-Darling Normality Tests

### Description

This function provides three kinds of Anderson-Darling Normality Tests (Anderson and Darling, 1952).

### Usage

``````adtest(x, R = 1000, locscatt = "standard")
``````

### Arguments

 `x` either a numeric vector, or a data.frame, or a matrix `R` Number of Monte Carlo simulations to obtain p-values `locscatt` standard for classical estimates of mean and (co)variance. robust for robust estimates using ‘covMcd()’ from package robustbase

### Details

Three version of the test are implemented (univariate, angle and radius test) and it depends on the data which test is chosen.

If the data is univariate the univariate Anderson-Darling test for normality is applied.

If the data is bivariate the angle Anderson-Darling test for normality is performed out.

If the data is multivariate the radius Anderson-Darling test for normality is used.

If ‘locscatt’ is equal to “robust” then within the procedure, robust estimates of mean and covariance are provided using ‘covMcd()’ from package robustbase.

To provide estimates for the corresponding p-values, i.e. to compute the probability of obtaining a result at least as extreme as the one that was actually observed under the null hypothesis, we use Monte Carlo techniques where we check how often the statistic of the underlying data is more extreme than statistics obtained from simulated normal distributed data with the same (column-wise-) mean(s) and (co)variance.

### Value

 `statistic ` The result of the corresponding test statistic `method ` The chosen method (univariate, angle or radius) `p.value ` p-value

### Note

These functions are use by `adtestWrapper`.

### Author(s)

Karel Hron, Matthias Templ

### 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.

`adtestWrapper`

### Examples

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