It's not difficult at all.
TEST#1:
Lets take that 500 watt Fender bass amp described in a thread below. Put an 18ga power cord on it and play a sequence. Now replace that with a 14ga power and play a sequence. Will you hear a difference. I sure hope so!
TEST#2:
Set up your audio amp next to a 50kw AM radio tower - like a hundred feet or so. Use a stock power cord and measure for RFI in the DC rails. Now try a shielded power cord or one with ferrite beads attached. Will the RFI be attentuated? Quite possibly there will be a measurable difference. In some cases the difference may even be audible.
So what exactly were the conditions of the test where you heard the differences? If there were indeed differences, then a logical technical reason can be determined.
It's not magic! And it doesn't take a $1000 plus solution either. A Belden standard 18ga IEC cord is about $3. A shielded version is about $7.
Edits: 04/24/12
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