Anderson-Darling test statistics, adjusted with small sample size factor.

The Anderson-Darling test (Stephens, 1974) is used to test if a sample of data came from a population with a specific distribution. It is a modification of the Kolmogorov-Smirnov (K-S) test and gives more weight to the tails than does the K-S test. The K-S test is distribution free in the sense that the critical values do not depend on the specific distribution being tested. The Anderson-Darling test makes use of the specific distribution in calculating critical values. This has the advantage of allowing a more sensitive test and the disadvantage that critical values must be calculated for each distribution. 

The Anderson-Darling test is defined as:

• H0: The data follow a specified distribution.
• Ha: The data do not follow the specified distribution.

The test statistics is defined as: 

where F is the cumulative distribution function of distribution being tested. 

To learn more about A-D test, check the following links:

• hrefhttp://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htmhttp://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htm
• hrefhttp://Src.alionscience.com/pdf/A_DTest.pdfhttp://Src.alionscience.com/pdf/A_DTest.pdf

Note 

The basic assumption is that the data values are sorted in ascending order.

GOFKolmogorov

Statistics Methods