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in my opinion yes if there biting on minnows seems that bigger fish like the bigger bait and if i fish with smaller minnows i catch the smaller fish.
is it better to have bigger sized shiners or smaller sized? i know that "big bait = big fish" but didn't know if i would catch only small junk fish all day if i used small bait.
If you're looking for numbers I'd lean towards smaller bait but if you want a trophy the bigger the better - my best bass through the ice came on a 6" live shiner. Bait in the 5-6" range will be taken by bass around 2lbs regularly used to catch them when fishing big shiners for pike.