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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 Thu, 11 Oct 2012 17:21:03 GMT

    [ https://issues.apache.org/jira/browse/MATH-878?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13474336#comment-13474336
] 

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

1. The array of convenience methods seems excessive.  For instance, all that 
{code}
boolean gTestGoodnessOfFit(final double[] expected, final long[] observed,
            final double alpha)
{code}
adds is a single comparison against alpha.

2. For all the vast number of convenience routines, you don't include the 2 x 2 test that
returns a signed square root of G^2 where the sign indicates higher or lower frequency than
expected.

3. This doesn't seem to integrate into the Commons Math framework for this kind of test.

                
> 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.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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