The Anderson-Darling test is an alternative to the chi-square and Kolmogorov-Smirnov goodness of fit tests. 

The normal random numbers were stored in the variable Y1, the double exponential random numbers were stored in the variable Y2, the Cauchy random numbers were stored in the variable Y3, and the lognormal random numbers were stored in the variable Y4. 

  
       ***************************************
       **  anderson darling normal test y1  **
       ***************************************
  
  
               ANDERSON DARLING 1-SAMPLE TEST
               THAT THE DATA COME FROM A NORMAL               DISTRIBUTION
  
 1. STATISTICS:
       NUMBER OF OBSERVATIONS                =     1000
       LOCATION PARAMETER                    =   0.4359940E-02
       SCALE PARAMETER                       =    1.001816
  
       ANDERSON DARLING TEST STATISTIC VALUE =   0.2566688
  
 2. CRITICAL VALUES:
       90         % POINT    =    1.062000
       95         % POINT    =    1.321000
       97.5       % POINT    =    1.591000
       99         % POINT    =    1.959000
  
 3. CONCLUSION (AT THE 5% LEVEL):
       THE DATA DO COME FROM A NORMAL              DISTRIBUTION.
  
  
       ***************************************
       **  anderson darling normal test y2  **
       ***************************************
  
  
               ANDERSON DARLING 1-SAMPLE TEST
               THAT THE DATA COME FROM A NORMAL               DISTRIBUTION
  
 1. STATISTICS:
       NUMBER OF OBSERVATIONS                =     1000
       LOCATION PARAMETER                    =   0.2034888E-01
       SCALE PARAMETER                       =    1.321627
  
       ANDERSON DARLING TEST STATISTIC VALUE =    5.827798
  
 2. CRITICAL VALUES:
       90         % POINT    =    1.062000
       95         % POINT    =    1.321000
       97.5       % POINT    =    1.591000
       99         % POINT    =    1.959000
  
 3. CONCLUSION (AT THE 5% LEVEL):
       THE DATA DO NOT COME FROM A NORMAL              DISTRIBUTION.
  
  
       ***************************************
       **  anderson darling normal test y3  **
       ***************************************
  
  
               ANDERSON DARLING 1-SAMPLE TEST
               THAT THE DATA COME FROM A NORMAL               DISTRIBUTION
  
 1. STATISTICS:
       NUMBER OF OBSERVATIONS                =     1000
       LOCATION PARAMETER                    =    1.503854
       SCALE PARAMETER                       =    35.13059
  
       ANDERSON DARLING TEST STATISTIC VALUE =    287.4414
  
 2. CRITICAL VALUES:
       90         % POINT    =    1.062000
       95         % POINT    =    1.321000
       97.5       % POINT    =    1.591000
       99         % POINT    =    1.959000
  
 3. CONCLUSION (AT THE 5% LEVEL):
       THE DATA DO NOT COME FROM A NORMAL              DISTRIBUTION.
  
  
       ***************************************
       **  anderson darling normal test y4  **
       ***************************************
  
  
               ANDERSON DARLING 1-SAMPLE TEST
               THAT THE DATA COME FROM A NORMAL               DISTRIBUTION
  
 1. STATISTICS:
       NUMBER OF OBSERVATIONS                =     1000
       LOCATION PARAMETER                    =    1.518372
       SCALE PARAMETER                       =    1.719969
  
       ANDERSON DARLING TEST STATISTIC VALUE =    81.64876
  
 2. CRITICAL VALUES:
       90         % POINT    =    1.062000
       95         % POINT    =    1.321000
       97.5       % POINT    =    1.591000
       99         % POINT    =    1.959000
  
 3. CONCLUSION (AT THE 5% LEVEL):
       THE DATA DO NOT COME FROM A NORMAL              DISTRIBUTION.
  
      

1. The first section prints the number of observations and estimates for the location and scale parameters. 
2. The second section prints the upper critical value for the Anderson-Darling test statistic distribution corresponding to various significance levels. The value in the first column, the confidence level of the test, is equivalent to 100(1-). We reject the null hypothesis at that significance level if the value of the Anderson-Darling test statistic printed in section one is greater than the critical value printed in the last column. 
3. The third section prints the conclusion for a 95% test. For a different significance level, the appropriate conclusion can be drawn from the table printed in section two. For example, for  = 0.10, we look at the row for the 90% confidence and compare the critical value 1.062 to the Anderson-Darling test statistic (for the normal data) 0.256. Since the test statistic is less than the critical value, we do not reject the null hypothesis at the  = 0.10 level.

The output from other statistical software programs may look somewhat different than the output above. 

• Is the data from a normal distribution? 
• Is the data from a log-normal distribution? 
• Is the data from a Weibull distribution? 
• Is the data from a exponential distribution? 
• Is the data from a logistic distribution? 

There are many non-parametric and robust techniques that do not make strong distributional assumptions. However, techniques based on specific distributional assumptions are in general more powerful than non-parametric and robust techniques. Therefore, if the distributional assumptions can be validated, they are generally preferred.