
ANDERSON DARLING K SAMPLE TESTName:
The ksample AndersonDarling statistic is
where
where k is the number of samples (groups), n_{i} is the number of observations in group i, x_{ij} is the jth observation in the ith group, and z_{1}, z_{2} ..., z_{L} are the distinct values in the combined data set ordered from smallest to largest (L is less than n if there are tied observations). Chapter 8 of the MILHDBK17 derives the formulas for the critical values of the AndersonDarling test statistic. These formulas are rather involved and not given here. Dataplot uses the ANDYK routine from the MILHDBK17 to compute the AndersonDarling k sample test.
where <y> is the response variable; <groupid> is group (sample) identifier variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
ANDERSON DARLING K SAMPLE TEST Y1 GROUP SUBSET GROUP > 2
LET ALPHA = <value> with Y denoting the response variable, X denoting the groupid variable, and ALPHA denoting the significance level for the critical value. In addition to the above LET command, builtin statistics are supported for about 20+ different commands (enter HELP STATISTICS for details).
SKIP 25 READ VANGEL32.DAT Y X B SET WRITE DECIMALS 4 ANDERSON DARLING K SAMPLE TEST Y X The following output is generated:AndersonDarling KSample Test for Common Groups Response Variable: Y GroupID Variable: X H0: The Groups Are Homogeneous Ha: The Groups Are Not Homogeneous Summary Statistics: Total Number of Observations: 45 Number of Groups: 3 Minimum Batch Size: 15 Maximum Batch Size: 15 Test Statistic Value: 155.3624 Test Statistic Standard Error: 0.5108 Conclusions (Upper 1Tailed Test)  Null Null Significance Test Critical Hypothesis Hypothesis Level Statistic Region (>=) Conclusion  Homogeneous 50.0% 155.3624 1.1524 REJECT Homogeneous 75.0% 155.3624 1.4969 REJECT Homogeneous 90.0% 155.3624 1.8070 REJECT Homogeneous 95.0% 155.3624 1.9926 REJECT Homogeneous 97.5% 155.3624 2.1536 REJECT Homogeneous 99.0% 155.3624 2.3407 REJECT Homogeneous 99.9% 155.3624 2.7310 REJECT  
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Date created: 6/5/2001 