# Trouble interpreting the likelihood ratio chi-squared test statistic

I have obtained a likelihood ratio chi-squared test statistic and I don't know if it is significant or not. Do I:

1. Compare my likelihood ratio chi-squared test statistic with the critical value in the chi-squared distribution table, as you do with a normal Pearson's chi-squared test statistic?

2. Or do I just take the likelihood ratio chi-squared value (i.e., 0.821) and assume because it is greater than 0.05, it is insignificant?

3. Or just read the P-value reported next to the likelihood ratio chi-squared?

• "likelihood ratio", not "ratio likelihood". #3 is the answer. Feb 28, 2016 at 23:00
• Thank you Nick! Sorry for writing it the wrong way round! Feb 28, 2016 at 23:03
• See this video youtube.com/watch?v=HwD7ekD5l0g starting at time (1:00). The p-value is the area to the right of the test statistic. Feb 29, 2016 at 0:48
• Thank you for your help and YouTube link. One last question, when reporting the likelihood ratio chi-square test statistic, do we still use the symbol X2? Or do we write it as Likelihood Ratio X2= 0.035? I can't seem to find a specific symbol for the likelihood ratio chi-sq test statistic, and I do not want to give the impression I have done a Pearson's chi-sq test by just reporting the test statistic as X2= 0.035. Feb 29, 2016 at 14:04
• I would report your sample size, degrees of freedom, chi square statistic and p-value. So long as you state that those results are from a likelihood ratio test there should be no issue with interpretation....I do not think there is a global standard (there may be some standards for specific academic journals or sub-feilds though) Mar 2, 2016 at 3:35

StackExchange doesn't let me reply to your comment in your question since I don't often come here, and this thread is very old, but I did find my way here through Google, so someone else might too.

As Nick Cox said, you're gonna want to use the p-value to interpret it as you would any other χ² test. These statistics have a relationship with the scale of the data you input, so there's no way to readily interpret them by themselves. You can use them to compare; usually to compare models, but nothing stops you from making more creative use such as if you had two equivalent questions and you want to see which one had a better fit (as long as they were on the same scale and had the same n). Some of these statistics are lower (such as χ²) is better, and some are higher is better (such as log-likelihood).

But to answer your question, to report the likelihood ratio chi-squared test statistic people usually use the G, according to this website. However, I must say I'm confused because when this same test is used in item response theory is usually called G² (McKinley, & Mills, 1985). I wish I knew who started using these letters because the oldest article about the test that I read about the test refers to it simply as the LCHI.

Edit: A medicine article I just read reports it as LR (Perneger, 2021). Frankly, you may use any one of these, they are not "wrong", but I'd recommend looking for which one articles in the journal you intend to publish use.

References:

McKinley, R., & Mills, C. (1985). A comparison of several goodness-of-fit statistics. Applied Psychological Measurement, 9, 49-57. Acessed on November 11th, 2022. Available at https://conservancy.umn.edu/handle/11299/102021

Perneger, P. V. (August 2021). How to use likelihood ratios to interpret evidence from randomized trials. Journal of Clinical Epidemiology, 136, 235–242. https://doi.org/10.1016/j.jclinepi.2021.04.010

G., Stephanie. (n.d.) "Likelihood-Ratio Tests (Probability and Mathematical Statistics)" From StatisticsHowTo.com: Elementary Statistics for the rest of us! Acessed on November 11th, 2022. Available at https://www.statisticshowto.com/likelihood-ratio-tests/