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it is claimed that the so called G-Test can be used as a replacement for the well-known Chi-squared test. The G-test is defined as: [tex]G = 2\sum_i O_i \cdot \log \left( \frac{O_i}{E_i}\right)[/tex]whereOand_{i}Eare the observed and expected counts in the cell_{i}iof a contingency table.

I see a big problem with this.

Namely, the valueGis directly proportional to the total amountNof observations!

This is easily seen even with the most trivial example of a coin toss. Suppose we want to test wheter a coin is fair or not. We collectN=10samples and we obtain{1 head, 9 tails}.Thus, according to the above formula.G≈7.36

Now suppose we collectN=100samples and we obtain{10 heads, 90 tails}. Well, according to the above formula we now get, exactly ten times more.G≈73.6

So, what is the threshold value forGabove which we reject the null-hypothesis that the coin is fair?

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# Question on G-Test

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