There is only one test

You've encountered several types of traditional hypothesis test: t-tests, ANOVA tests, proportion tests, and chi-square tests. You may have noticed that there were similarities in the workflow for performing each test.

Allen Downey proposed that all traditional hypothesis tests were special cases of a generic hypothesis test. He called this the "There is Only One Test" framework, and it forms a "grammar of hypothesis tests", analogous to the "grammar of graphics" implemented by ggplot2.

In which situations will the "There is Only One Test" framework provide p-value and decision rule results that are different than a traditional method like prop_test()?