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Date: Thu, 13 May 2010 15:50:42 -0400 (EDT)
From: "Kevin Childs (JIRA)" <jira@apache.org>
To: issues@commons.apache.org
Subject: [jira] Created: (MATH-371)
 PearsonsCorrelation.getCorrelationPValues() precision limited by machine
 epsilon
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PearsonsCorrelation.getCorrelationPValues() precision limited by machine epsilon
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                 Key: MATH-371
                 URL: https://issues.apache.org/jira/browse/MATH-371
             Project: Commons Math
          Issue Type: Bug
    Affects Versions: 2.0
            Reporter: Kevin Childs


Similar to the issue described in MATH-201, using PearsonsCorrelation.getCorrelationPValues() with many treatments results in p-values that are continuous down to 2.2e-16 but that drop to 0 after that.

In MATH-201, the problem was described as such:
> So in essence, the p-value returned by TTestImpl.tTest() is:
> 
> 1.0 - (cumulativeProbability(t) - cumulativeProbabily(-t))
> 
> For large-ish t-statistics, cumulativeProbabilty(-t) can get quite small, and cumulativeProbabilty(t) can get very close to 1.0. When 
> cumulativeProbability(-t) is less than the machine epsilon, we get p-values equal to zero because:
> 
> 1.0 - 1.0 + 0.0 = 0.0

The solution in MATH-201 was to modify the p-value calculation to this:
> p = 2.0 * cumulativeProbability(-t)

Here, the problem is similar.  From PearsonsCorrelation.getCorrelationPValues():
  p = 2 * (1 - tDistribution.cumulativeProbability(t));

Directly calculating the p-value using identical code as PearsonsCorrelation.getCorrelationPValues(), but with the following change seems to solve the problem:
  p = 2 * (tDistribution.cumulativeProbability(-t));


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