# Wrong result from LLR using Dunning Entropy method

I'm trying to use Dunning's method of calculating LLR to compare word instances between two fulltext indexes. His method uses entropy as part of the calculation.

Dunning's blog post: http://tdunning.blogspot.com/2008/03/surprise-and-coincidence.html

But, although I've implemented it in both Excel and Java and they give the same answers, I believe the answers are wrong.

Two reasons I believe my results are wrong:

1: They don't agree with this online calculator (which uses a different formula): http://ucrel.lancs.ac.uk/llwizard.html

2: They are always negative; that is more disturbing.

Link to my faulty XLS sheet: (hope this is OK) https://www.dropbox.com/s/bnzmk7ttf4mv23k/entropy-and-LLR-suspect-gist.xlsx

Some theories I have:

1: Maybe my contingency table is setup wrong? Dunning talks about an abstract CT, but he doesn't specifically say how to fill it out with term frequencies counts. For example, in my table in cell 1,1 I put the number of times the word "spam" occurs in corpus A, whereas Dunning says "Event A and B together". So, when you have term counts, maybe there's some step to convert those counts into a proper CT?

2: Maybe some misunderstanding about the denominators that I'm using when calculating probability. In Steps 2, 3 and 4 I'm always dividing by the CT grandTotal, maybe that's wrong?

3: Maybe my entropy calculation is not the form that Dunning had in mind, perhaps there's some scaling I'm adding or not adding. I found this page http://mail-archives.apache.org/mod_mbox/mahout-dev/201009.mbox/%3CAANLkTinjgViP5qVdHv3mJ=C53RCrjueWJvNvYEkozGoB@mail.gmail.com%3E where Dunning replied to a question and mentions "un-normalized entropy". But I didn't follow the syntax and conversation well enough to related it back to what I was doing.

https://dl.dropboxusercontent.com/u/36863361/entropy-and-LLR-suspect-gist.xlsx

There are two categories of changes.

a) You need to account for zero counts. Changing ln(Cxx) to ln(if(Cxx=0,1,Cxx)) solves this. The issue is that the limit of p log p is 0 when p=>0, but log p blows up. The special case avoids the problem.

b) My blog was confusing relative to sign. The definition I used for entropy lacked a sign change which I compensated for by inverting the order of the final computation.

• Ted, thank you!!! So I think I'll keep the negative sign in my standard Entropy method, and then reflect the sign changes in the wrap-up formula. – Mark Bennett Feb 27 '14 at 22:34
• Hi Ted, that fixes the sign, but my answers are still 2x off from the online calculator (which may be their issue?) If you go to ucrel.lancs.ac.uk/llwizard.html and do you example of k_11=10 and k_12 = 0, then 10 for both bottom numbers (it subtracts to derive k_21=0, k_22=10), then they return 13.86. But the sheet you uploaded gives 27.726. Being a newb to LLR I'm not sure which is correct, but there's a factor of 2 (or 1/2) floating around somewhere... – Mark Bennett Feb 27 '14 at 23:15
• Found another online calculator that gives the larger result of 27.7259 (in-silico.net/tools/statistics/chi2test), so I guess the UK calculator is wrong... – Mark Bennett Feb 27 '14 at 23:29

27.7 is the correct answer to the [[10,0],[0,10]] case that you mention.

The loss of the factor of two means that they didn't notice the factor of two in the formula. This is a common error.