If you already know there’s an error , a weaker test can be more useful than a stronger test, because it localizes where the bug is more. If you’re trying to determine correctness , though, stronger tests are better. I wonder if there’s a way to speed up test suites using this. If P is stronger than Q, there’s no point to running Q if P already passed.
I also wonder if this gives us a way of formalizing “integration test”. It’s not clear what distinguishes a “unit” from an “integration” test, but I think any good categorization would have a single integration test imply a set of weaker unit tests.