Chi-Square Difference Test for Nested Models with a Continuous Outcome Apologies if this is a very basic question - I'm still definitely a beginner when it comes to statistical tests. I understand that chi-square tests are conducted to determine the relationship between two categorical variables or to determine how well a categorical outcome fits a discrete probability distribution.
However, I often come across articles using a chi-square difference test to compare the fit of nested models, even when the outcome is continuous. I'm struggling to understand this a little - how can we calculate a chi-square value for two models to then test if the difference between them is significant if the DV/outcome is continuous?

Chi-square is a distribution, not a test. Chi-square tests are used for things that are chi-square distributed. There are two different things they are used for:

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*The chi-square test of a contingency table (which is what you're thinking of, when you say they are to determine the relationship between two categorical variables).

*Likelihood ratio tests are often also called chi-square tests, because the difference in (-2 *) loglikelihood of two models is chi-square distributed. If I fit a model, and then I add a parameter, I might ask if that parameter significantly improved the models. I can compare the likelihood ratios of the two models because this difference is chi-square distributed.

(Although the first is actually a type of the second.)
