- #1
mnb96
- 715
- 5
Hello,
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]where Oi and Ei are the observed and expected counts in the cell i of a contingency table.
I see a big problem with this.
Namely, the value G is directly proportional to the total amount N of 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 collect N=10 samples and we obtain {1 head, 9 tails}. Thus, according to the above formula G≈7.36.
Now suppose we collect N=100 samples and we obtain {10 heads, 90 tails}. Well, according to the above formula we now get G≈73.6, exactly ten times more.
So, what is the threshold value for G above which we reject the null-hypothesis that the coin is fair?
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]where Oi and Ei are the observed and expected counts in the cell i of a contingency table.
I see a big problem with this.
Namely, the value G is directly proportional to the total amount N of 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 collect N=10 samples and we obtain {1 head, 9 tails}. Thus, according to the above formula G≈7.36.
Now suppose we collect N=100 samples and we obtain {10 heads, 90 tails}. Well, according to the above formula we now get G≈73.6, exactly ten times more.
So, what is the threshold value for G above which we reject the null-hypothesis that the coin is fair?