G Test of Independence

The G test of independence is a likelihood-ratio test of association between two categorical variables, computing twice the sum of observed counts times the log of observed over expected counts.

독립성 G 검정은 관측빈도와 관측/기대 비의 로그를 곱해 합한 값의 두 배로 두 범주형 변수의 연관을 보는 우도비 검정이다.

Instead of Pearson's chi-square, can I use a likelihood-ratio test for my contingency table?

교차표에서 Pearson 카이제곱 대신 우도비 검정을 써도 되나요?

The G test compares observed and expected cell counts through the log-likelihood ratio and refers G to a chi-square distribution with (r − 1)(c − 1) degrees of freedom. Its results are usually close to Pearson's chi-square, and Williams' correction improves the approximation in small samples.

When to use G Test of Independence

• Two categorical variables are cross-tabulated.
• Results should be additive across nested tables or consistent with log-linear models.
• Expected counts are adequate in most cells.

When to use something else

• Many expected counts are below five; use Fisher's exact test.
• The variables are paired measurements on the same units; use McNemar's or the Stuart-Maxwell test.

Assumptions and requirements

• Observations are independent.
• Each observation falls into one cell.
• Expected counts are large enough for the chi-square approximation.

What the analysis reports

• G statistic
• Degrees of freedom
• p value
• Williams-corrected G and p
• Contingency table

How to report it

A G-test of independence indicated a significant association between [variable 1] and [variable 2], G([df], N = [n]) = [G], p = [p].

Related methods

• Chi Square Test
• Fisher's Exact Test
• Cramér's V and Phi Association

Run G Test of Independence on Quorant