Oh yeah you can.
Add that variable to your testing. Just make sure you know how to tamp in the first place and you do it with a correctly sized tamper. If you don't and you can't, skip it.
We have a couple tampers made by a fellow Canadian of yours, Reg Barber. In my opinion, they are easily the best you can buy. He is retired now. Any device that offers to tamp for you, run away from it.
-Mike
Maybe if I can find a stump or piece of wood that I can whittle down to an appropriate diameter.
