PLEASE PEOPLE!! DO NOT REMOVE THE BATTERY CABLE WHILE THE CAR IS RUNNING.
Modern automobiles Use the battery as a capacitor, to help iron out voltage ripples that are small, and easily absorbed by the relatively large battery. if you remove that battery from the curcuit, it is possible that voltage spikes and dips can fry ANY electronic component in the system. PLEASE DONT DO THIS. It works fine on any car without a computer, IE pre-80 something (depends on model) BUT CAN CAUSE many electrical problems, from killing voltage regulators to outright killing the ECU.
PLEASE DONT DO THIS, USE A VOM to check your alternator, or take it to someone who knows how to test it. If you take it to a mechanic that pulls the cable off while the car is running, you should start running..... to another mechanic.