I think I've seen this mentioned on Geekhack, but back in July 1960, an article was published in The Bell System Technical Journal titled
"Human Factors Engineering Studies of the Design and Use of Pushbutton Telephone Sets, By R. L. DEININGER."
This article (available here:
http://www.beatriceco.com/bti/porticus/bell/pdf/touchtone_hf.pdf ) gives a pretty in-depth description of the experiments done that resulted in the familiar 3x3 + 1 number format used in touch tone phones (and later, smartphones).
Several interesting facts emerge. First, they tested a
lot of formats:

Second, the calculator number pad layout

is measurably inferior to the touchtone layout

though the difference was small.
Third, and most interesting to me, *the 3x3 plus 1 touchtone layout was
NOT the layout most preferred.* Out of the five top designs, two horizontal rows of five keys

had the most preferred votes (the touchtone layout was third), and forth in "least preferred" votes (the touchtone format had the second highest "least preferred" votes). Interestingly enough, while two horizontal rows was the most preferred, two vertical rows were the
least preferred.
I do wish they had tested formats with 0 next to 1, such as

because having the most common numbers on the numeric keypad "home row" might be advantageous for data entry, especially with Enter or Shift/Function under the thumb instead of an enlarged 0 key.
Other possibilities I think would be better test subjects than "The Cross," "The Stairstep," or "The Rainbow" would be things like:

and

Finally, I'd love to see some testing done on a full-size numeric keypad

Preferably with all of the functions of a Goldtouch GTC-0077

I'd be interested to see what other ideas Geekhackers might come up with. I have a Cherry matrix POS board to play on, and it might be fun to try them out.
