Drick, I have never seen any published formula for the "correct" amount of depth for a dado. I use 1/2 the material thickness for a strong joint, less if it is simply a channel for sliding a panel into. The main thing is to be sure you have enough glue surface to hold the joint together, or to prevent your panel from falling out. On a project like a bird feeder you can cut a 1/8" deep dado to slide a piece of plexiglass into and it will be plenty strong. If you were building a window you would need more support for the glass, perhaps 3/8"? Base your decision on the type of project as well as the material you are using.
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Mike
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