AndersonDarlingTest {DescTools} R Documentation

## Anderson-Darling Test of Goodness-of-Fit

### Description

Performs the Anderson-Darling test of goodness-of-fit to a specified continuous univariate probability distribution.

### Usage

AndersonDarlingTest(x, null = "punif", ..., nullname)


### Arguments

 x numeric vector of data values. null a function, or a character string giving the name of a function, to compute the cumulative distribution function for the null distribution. ... additional arguments for the cumulative distribution function. nullname optional character string describing the null distribution. The default is "uniform distribution".

### Details

This command performs the Anderson-Darling test of goodness-of-fit to the distribution specified by the argument null. It is assumed that the values in x are independent and identically distributed random values, with some cumulative distribution function F. The null hypothesis is that F is the function specified by the argument null, while the alternative hypothesis is that F is some other function.

The procedures currently implemented are for the case of a SIMPLE null hypothesis, that is, where all the parameters of the distribution are known. Note that other packages such as 'normtest' support the test of a COMPOSITE null hypothesis where some or all of the parameters are unknown leading to different results concerning the test statistic and the p-value. Thus in 'normtest' you can test whether the data come from a normal distribution with some mean and variance (which will be estimated from the same data).

The discrepancies can be large if you don't have a lot of data (say less than 1000 observations).

### Value

An object of class "htest" representing the result of the hypothesis test.

### Author(s)

Original C code by George Marsaglia and John Marsaglia. R interface by Adrian Baddeley.

### 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.

Anderson, T.W. and Darling, D.A. (1954) A test of goodness of fit. Journal of the American Statistical Association 49, 765–769.

Marsaglia, G. and Marsaglia, J. (2004) Evaluating the Anderson-Darling Distribution. Journal of Statistical Software 9 (2), 1–5. February 2004. https://www.jstatsoft.org/v09/i02

shapiro.test and all other tests for normality.
x <- rnorm(10, mean=2, sd=1)