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markbailey

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Jun 23, 2011

Anderson-Darling Normality Test

JMP provides the Shapiro-Wilk test in the Distribution platform for a departure from a normal distribution. This test has been shown to be more powerful than alternative tests, including the Anderson-Darling test (1). (Note that all such tests have low power with small samples.) Still, you might have a precedent for using the A-D test for normality so this add-in implements it. The test estimates the mean and the standard deviation of the normal distribution by default. Either one of these parameters may instead be specified if known for a test against a particular normal distribution. The test results are appended to a Distribution platform.

Simply open the add-in file to register it with JMP before use. Then, open the data table with the data column to be tested and select Add-Ins > Anderson-Darling Normality Test. Select the data column and click Y, Response. If the mean is known, then select the Known radio button for the Mean and enter the value in the box provided. The same is true for the standard deviation.

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Click OK. An alert window will briefly appear. The p-value for the A square test statistic is computed by a Monte Carlo simulation of 100,000 samples under the null hypothesis.
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The test report is seen at the bottom of the window. The A square and adjusted A square test statistics are reported. The approximate p-value for the second test statistic is computed from a set of four interpolating functions (2).

Note that a previous version (before June 5, 2014) of this test as a script computed the p-value for A square incorrectly and should not be used. Please replace that version with this add-in if you downloaded the version before the correction became available.

References

(1) Razali, Normadiah Modh, and Yap Bee Wah (2011) Power Comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling Tests, Journal of Statistical Modeling and Analytics, 2(1)21-33.

(2 ) R.B. D'Augostino and M.A. Stephens, Eds., 1986, Goodness-of-Fit Techniques, Marcel Dekker.

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