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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 18:51:04 GMT

    [ https://issues.apache.org/jira/browse/MATH-878?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13475237#comment-13475237
] 

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

{quote}
2. I added rootLogLikelihoodRatio using your code from mahout. Could you help me with the
rationale description comments. Unfortunately the quoted discussion is no longer available
in internet. I'll be better perhaps add some info in-line in the comments.
{quote}
There is some more permanent discussion on the root LLR test here:

http://mail-archives.apache.org/mod_mbox/mahout-user/201001.mbox/%3Cc7d45fc71001121120r6b0482aat345014770ed32744@mail.gmail.com%3E

And see the response to Wataru's comment here:

http://tdunning.blogspot.com/2008/03/surprise-and-coincidence.html

If I can squeeze some time, I will write you some purpose-built rationale text, but you should
be able to lift some of my other comments with small changes.
                
> 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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