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\.
Would that mean that the strength of evidence is the TP/FP ratio ? in that case, it would have the same definition as the relative likelihood. Wouldn't there be a better definition for either one of the notions so that we can easily differentiate them ?