R Language for The Project Management Course — AUG University “part 7”

Anderson-Darling Test(A²):

The hypotheses for the AD-test are:

  • H0: The data comes from a specified distribution.
  • H1: The data does not come from a specified distribution.

Perform AD by Hand:

  1. Using this formula, calculate the AD Statistic:
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AD-Test Example in Excel:

Step1: Enter your data like the following (page 25 in the slides):

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Step 2: calculate 2i -1

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Step3: Calculate ln(f(xi)), — x is A-Z order —

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Step3: Calculate ln(1-f(x)): x is Z-A order

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Step4: Calculate (2i-1) *( ln(f(x))+ ln(1-F(Xn-i+1)))

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Step5: Caluclate S value

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Step6: Calculate A² value

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Step6: Calculate A² critical value

  • From this table, choose the nearest n value to your n data which is 9. This means we choose n =10
  • After that, find the cross cell between %5 and n =10
  • A² critical value is 0.683
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Step7: Compare A² with the A² critical value

  • If A² < A² critical value then, you can consider your data distributed as a normal distribution.
  • If A² > A² critical value then, your data is not distributed as a normal distribution.

or

AD-Test in R:

ad.test(x)

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Hunger for Knowledge, adventure, and risk enthusiastic. Software engineering student

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