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From "Radoslav Tsvetkov (JIRA)" <>
Subject [jira] [Commented] (MATH-878) G-Test (Log-Likelihood ratio - LLR test) in math.stat.inference
Date Fri, 12 Oct 2012 11:03:03 GMT


Radoslav Tsvetkov commented on MATH-878:

Thanks Ted for your interest and quick comments. 

I added rootLogLikelihoodRatio as proposed by you using your code from 
mahout. I kept the name as it is more commonly in use for this 
On your comments:

1. Usually commons.math has more convenience methods. For example 
ChiSquare has much more. As I'm your opinion and allowed myself to 
provide less. Concerning gTestGoodnessOfFit - let not forget that 
majority of users are not interested at all at p-Values and G-values, 
all they want to know is: true or false (can they reject the null or 
not). ChiSquateTEst provides exactly the same functionality and it is in
 commons since 1.2 - so it seems a good thing.

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.

3. The G-Tests are fully integrated in the commons TestUtils 
framework as all other ChiSquarem, Anova etc ... With this patch I added some more test cases.
On request.
Could you provide pls. some reference data for rootLogLikelihoodRatio test?

> G-Test (Log-Likelihood ratio - LLR test) in math.stat.inference
> ---------------------------------------------------------------
>                 Key: MATH-878
>                 URL:
>             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, vcs-diff56368.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:
> 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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