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From "Ted Dunning (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-878) G-Test (Log-Likelihood ratio - LLR test) in math.stat.inference
Date Fri, 12 Oct 2012 18:29:04 GMT

    [ https://issues.apache.org/jira/browse/MATH-878?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13475216#comment-13475216
] 

Ted Dunning commented on MATH-878:
----------------------------------

{quote}
Could you provide pls. some reference data for rootLogLikelihoodRatio test?
{quote}
>From Mahout (with a few extras added just now)
{code}
  @Test
  public void testRootLogLikelihood() {
    // positive where k11 is bigger than expected.
    assertTrue(LogLikelihood.rootLogLikelihoodRatio(904, 21060, 1144, 283012) > 0.0);

    // negative because k11 is lower than expected
    assertTrue(LogLikelihood.rootLogLikelihoodRatio(36, 21928, 60280, 623876) < 0.0);

    assertEquals(Math.sqrt(2.772589), LogLikelihood.rootLogLikelihoodRatio(1, 0, 0, 1), 0.000001);
    assertEquals(-Math.sqrt(2.772589), LogLikelihood.rootLogLikelihoodRatio(0, 1, 1, 0), 0.000001);
    assertEquals(Math.sqrt(27.72589), LogLikelihood.rootLogLikelihoodRatio(10, 0, 0, 10),
0.00001);

    assertEquals(Math.sqrt(39.33052), LogLikelihood.rootLogLikelihoodRatio(5, 1995, 0, 100000),
0.00001);
    assertEquals(-Math.sqrt(39.33052), LogLikelihood.rootLogLikelihoodRatio(0, 100000, 5,
1995), 0.00001);

    assertEquals(Math.sqrt(4730.737), LogLikelihood.rootLogLikelihoodRatio(1000, 1995, 1000,
100000), 0.001);
    assertEquals(-Math.sqrt(4730.737), LogLikelihood.rootLogLikelihoodRatio(1000, 100000,
1000, 1995), 0.001);

    assertEquals(Math.sqrt(5734.343), LogLikelihood.rootLogLikelihoodRatio(1000, 1000, 1000,
100000), 0.001);
    assertEquals(Math.sqrt(5714.932), LogLikelihood.rootLogLikelihoodRatio(1000, 1000, 1000,
99000), 0.001);
  }
{code}
                
> G-Test (Log-Likelihood ratio - LLR test) in math.stat.inference
> ---------------------------------------------------------------
>
>                 Key: MATH-878
>                 URL: https://issues.apache.org/jira/browse/MATH-878
>             Project: Commons Math
>          Issue Type: New Feature
>    Affects Versions: 3.1, 3.2, 4.0
>         Environment: Netbeans
>            Reporter: Radoslav Tsvetkov
>              Labels: features, test
>             Fix For: 3.1
>
>         Attachments: MATH-878_gTest_12102012.patch, MATH-878_gTest.patch, vcs-diff16294.patch
>
>   Original Estimate: 24h
>  Remaining Estimate: 24h
>
> 1. Implementation of G-Test (Log-Likelihood ratio LLR test for independence and goodnes-of-fit)
> 2. Reference: http://en.wikipedia.org/wiki/G-test
> 3. Reasons-Usefulness: G-tests are tests are increasingly being used in situations where
chi-squared tests were previously recommended. 
> The approximation to the theoretical chi-squared distribution for the G-test is better
than for the Pearson chi-squared tests. In cases where Observed >2*Expected for some cell
case, the G-test is always better than the chi-squared test.
> For testing goodness-of-fit the G-test is infinitely more efficient than the chi squared
test in the sense of Bahadur, but the two tests are equally efficient in the sense of Pitman
or in the sense of Hodge and Lehman. 

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