Evidence for Skilled Abacus Operator being faster than someone with a calculator
"does anyone have any evidence for or against the old claim that a skilled abacus operator can produce results faster than someone using a handheld calculator?"
I'm glad you specified "skilled abacus operator" rather than specifying operating on an actual abacus.
The very skilled abacus operators don't even the abacus; they begin with the physical abacus, but as they progress they use a model of one inside their head to do the calculation, instead of having to accept the delay of physically manipulating a real abacus.
Here's a skilled abacus operator (not using an actual abacus - that'd be too slow!) summing 10 four digit numbers in three seconds:
http://www.youtube.com/watch?v=3g63WR_PelY&t=0m55s
Here's a Guardian piece on the championships. 15 three digit numbers flashed up in 1.70 seconds , and the skilled abacus operator summed them.
https://www.theguardian.com/science/alexs-adventures-in-numberland/2012/oct/29/mathematics