[
https://issues.apache.org/jira/browse/MATH-201?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]
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: https://issues.apache.org/jira/browse/MATH-201
> 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 n2)
> 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.
--
This message is automatically generated by JIRA.
-
You can reply to this email to add a comment to the issue online.
