@Reference(authors="T. W. Anderson, D. A. Darling", title="Asymptotic theory of certain \'goodness of fit\' criteria based on stochastic processes", booktitle="Annals of mathematical statistics 23(2)", url="https://doi.org/10.1214/aoms/1177729437", bibkey="doi:10.1214/aoms/1177729437") public class AndersonDarlingTest extends java.lang.Object
This is a test against normality / goodness of fit. I.e. you can use it to reject the hypothesis that the data is normal distributed. Such tests are sensitive to data set size: on small samples, even large deviations could be bychance and thus not allow rejection. On the other hand, on large data sets even a slight deviation can be unlikely to happen if the data were indeed normal distributed. Thus, this test is more likely to fail to reject small data sets even when they intuitively do not appear to be normal distributed, while it will reject large data sets that originate from a distribution only slightly different from the normal distribution.
Before using, make sure you have understood statistical tests, and the difference between failuretoreject and acceptance!
The data size should be at least 8 before the results start getting somewhat reliable. For large data sets, the chance of rejecting the normal distribution hypothesis increases a lot: no real data looks exactly like a normal distribution.
References:
T. W. Anderson, D. A. Darling
Asymptotic theory of certain 'goodness of fit' criteria based on stochastic
processes
Annals of mathematical statistics 23(2)
M. A. Stephens
EDF Statistics for Goodness of Fit and Some Comparisons
Journal of the American Statistical Association 69(347)
Modifier  Constructor and Description 

private 
AndersonDarlingTest()
Private constructor.

Modifier and Type  Method and Description 

static double 
A2Noncentral(double[] sorted)
Test a sorted but not standardized data set.

static double 
A2StandardNormal(double[] sorted)
Test a sorted data set against the standard normal distribution.

static double 
removeBiasNormalDistribution(double A2,
int n)
Remove bias from the AndersonDarling statistic if the mean and standard
deviation were estimated from the data, and a normal distribution was
assumed.

private AndersonDarlingTest()
public static double A2StandardNormal(double[] sorted)
Note: the data will be compared to the standard normal distribution, i.e. with mean 0 and variance 1.
The data size should be at least 8 before the results start getting somewhat reliable. For large data sets, the chance of rejecting increases a lot: no real data looks exactly like a normal distribution.
sorted
 Sorted input data.public static double A2Noncentral(double[] sorted)
The data size should be at least 8!
sorted
 Sorted input data.@Reference(authors="M. A. Stephens", title="EDF Statistics for Goodness of Fit and Some Comparisons", booktitle="Journal of the American Statistical Association, Volume 69, Issue 347", url="https://doi.org/10.1080/01621459.1974.10480196", bibkey="doi:10.1080/01621459.1974.10480196") public static double removeBiasNormalDistribution(double A2, int n)
A2
 A2 statisticn
 Sample sizeCopyright © 2019 ELKI Development Team. License information.