Suppose you have some imperfect test function : is this cat picture cute? For n-many cat pictures (where is the collection of cat pictures under test) our test will produce many results, some true, some false, as to to the cutest of the cat in the picture
Now, it's easy to imagine that some cats are truly cute (effectively no question), truly not-cute (or falsely cute). Yet we have a test that is imperfect. What is to stop our test from incorrectly rate "not-cute" a cute cat or incorrectly rate "cute" a not-cute cat!
Sensitivity is the measure of how many truly cute cat pictures are among all cat pictures rated "cute".
Allow for a change in notation:
a truly cute cat
a truly not-cute cat
a not-cute cat rated as "cute"
a cute cat rated as "not-cute"
Sensitivity then is given by the following equation:
Alternately, the plain English of our example so far:
Sensitivity is the ratio of cats evaluated as "cute" to all of the cats that were truly cute.
Sensitivity is a common measure in applied statistics, as well as modern machine learning, though it often goes by another name: recall.
In either case, we may often want to "improve our test sensitivity" or "live with false positives, but we can't have a false negative". In both cases, the above measurement is what's being referenced: by decreasing the number of false-negative results produces a shrinking denominator, thereby improving the fraction ever towards .