More generally, suppose we have a medical test that detects a sickness with a 90% true positive rate \(10% false negatives\) and a 30% false positive rate \(70% true negatives\)\. A positive result on this test represents the same strength of evidence as a test with 60% true positives and 20% false positives\. A negative result on this test represents the same strength of evidence as a test with 9% false negatives and 63% true negatives\.
It was unclear when reading this which test "this test" referred to. I ended up figuring out the false negatives and true positives of the 60/20 test instead of the 90/30 test and was subsequently confused because 1:2 != 1:7. This might be an issue with my reading comprehension, but I figured I should mention it anyway.