The arthrogram for my shoulder showed no tear in the rotator cuff. But when I went for an MRI, it showed a complete tear. Why didn't the arthrogram show the tear?

The arthrogram is an older test. It is based on the idea that a special dye will leak out if the rotator cuff is torn. If a scar forms over the tear or if the dye can't leak out for some other reason, the test will appear negative. This is known as a "false negative" result, meaning the test appears normal even though the tendon is actually torn. 

A "false positive" is when a test shows there's a problem where there isn't one. For example, because the MRI scan is so sensitive, it can sometimes show what looks like a tear. Yet when surgery is performed to fix the tear, the surgeon may find that the tendon is not torn.

The most accurate test of all is surgical exploration. However, because surgery is costly and has certain risks, doctors prefer to use tests like MRI first to try to confirm the presence of a tear.