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These 2 tests are both test hypothesis that proportions are the same in different nominal variables.
In R, you can find GTest() and chisq.test() for these 2 tests.
Then, when should use G test? When should use Chi-square test?

WhiteGirl
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    @Scortch, from your link,I didn't find any answer correspond to my question – WhiteGirl Jul 07 '17 at 11:33
  • See @gung's answer there, & more details on the differences between score & likelihood-ratio tests by following the link within that answer. – Scortchi - Reinstate Monica Jul 07 '17 at 11:39
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    If possible, you can close this question rather than redirect to a evasive answer. And, you can see that question has no selected answer. – WhiteGirl Jul 07 '17 at 12:20
  • I'd agree with @WhiteGirl that the "duplicate question" doesn't have a satisfactory answer and also asks slightly different questions. – steviesh Jan 30 '18 at 19:35

1 Answers1

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Both these tests use statistics that are approximately chi-squared-distributed. The larger sample, the better approximation.

If your sample is reasonably large G test and chi-square test behave similarly. But with small samples, G test is better. It's statistic follows distribution that is closer to chi-square distribution than chi-square test's distribution, so calculation of p-value is more acurate.

The obvious question is "How small is small sample?". You can find plenty of definitions, rules of thumb and advices in textbooks. Two, I see most otfen are:

  • sample is small, when in contingency table, we have at least one cell with observed count less than 5
  • sample is small, when in contingency table, we have at least one cell with expected count less than 5.

The latter is used in chisq.test(). If it is met R warns about possible approximation problem:

> chisq.test(cbind(c(2,3), c(4,5)))

        Pearson's Chi-squared test with Yates' continuity correction

data:  cbind(c(2, 3), c(4, 5))
X-squared = 3.8347e-32, df = 1, p-value = 1

Warning message:
In chisq.test(cbind(c(2, 3), c(4, 5))) :
  Chi-squared approximation may be incorrect
Łukasz Deryło
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  • If cell count less than 5, should use fisher test? – WhiteGirl Jul 07 '17 at 05:51
  • If Gtest is better than chisq test. Why G test is seldom mentioned in lots of statistic books?Why chisq test listed in R stats package? – WhiteGirl Jul 07 '17 at 05:53
  • I am not sure whether there's a authoritative standard for test selection – WhiteGirl Jul 07 '17 at 05:54
  • I'm not sure too. I just say, R uses it. Fisher test is OK, when your sample is not very large, and contingency table don't have many cells. Otherwise you'll run out of memory fast. Try `fisher.test(cbind(c(12,34,123), c(94,51,321), c(123,456,789)))` and see what happens. And why G test is seldom mentioned? That's a question... :) – Łukasz Deryło Jul 07 '17 at 06:02