An educated guess might be based on the landing roll distance increasing with at least the square of the landing (ground) speed. Each stage of flaps reduces the recommended approach speed by 3mph (from 85mph approach, flapless) on a PA28.
Assuming you actually manage to touch about 5mph lower than the approach speed, then the increase in landing roll from full flap to no flap would be at least 27%. I say "at least", because I think landing roll increases by more than the square of the speed as brakes are less efficient at high speed, but stand to be corrected. Also, the faster you go the less accurate the touch down (as it's all happening faster in relation to your reaction time).
Edit: missed 24carrot's reply, but would agree the actual increase is likely to be more (rather than less) than the 27% minimum figure I give.