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From "Brent Worden (JIRA)" <>
Subject [jira] Resolved: (MATH-201) T-test p-value precision hampered by machine epsilon
Date Sun, 06 Apr 2008 01:25:24 GMT


Brent Worden resolved MATH-201.

       Resolution: Fixed
    Fix Version/s: 1.3

SVN 645193.

Changes applied.  Thank you for reporting this issue.

> T-test p-value precision hampered by machine epsilon
> ----------------------------------------------------
>                 Key: MATH-201
>                 URL:
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 1.2
>            Reporter: Peter Wyngaard
>            Assignee: Brent Worden
>            Priority: Minor
>             Fix For: 1.3
> The smallest p-value returned by TTestImpl.tTest() is the machine epsilon, which is 2.220446E-16
with IEEE754 64-bit double precision floats.
> We found this bug porting some analysis software from R to java, and noticed that the
p-values did not match up.  We believe we've identified why this is happening in commons-math-1.2,
and a possible solution.
> Please be gentle, as I am not a statistics expert!
> The following method in org.apache.commons.math.stat.inference.TTestImpl currently implements
the following method to calculate the p-value for a 2-sided, 2-sample t-test:
> protected double tTest(double m1, double m2, double v1, double v2,  double n1, double
> and it returns:
>         1.0 - distribution.cumulativeProbability(-t, t);
> at line 1034 in version 1.2.
> double cumulativeProbability(double x0, double x1) is implemented by org.apache.commons.math.distribution.AbstractDisstribution,
and returns:
>         return cumulativeProbability(x1) - cumulativeProbability(x0);
> 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
> An alternative calculation for the p-value of a 2-sided, 2-sample t-test is:
> p = 2.0 * cumulativeProbability(-t)
> This calculation does not suffer from the machine epsilon problem, and we are now getting
p-values much smaller than the 2.2E-16 limit we were seeing previously.

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