Is Cochran-Armitage Test the most appropriate test?

[Carla Jorge]

I want to determine the correlation between a categorical (with 2 categories) and an ordinal variable (sum of multiple likert items). Is Cochran-Armitage Test the most appropriate test?

[Mike Lacy]

Any two-category variable is ordinal as well as nominal. (e.g., Even if the two categories were "dog" and "cat," the "dog" category indicates "more dog" than the cat category does.) I'd therefore suggest using an ordinal-ordinal measure of association. Goodman and Kruskal's Gamma is built-in to -tabulate twoway-, but there are very good reasons to prefer Somers' D, which is available as a well-documented user-written package. See -ssc describe somersd-.

While I personally would support treating your sum of Likert items as ordinal, many people would be quite satisfied to see that treated as a continuous (interval) variable, so doing that would open up many possibilities.