How to measure and quantify concentration or focus? How can we measure and quantify concentration or focus? For example, if I were to say:


  "If you do Activity X while using Y, you will be more concentrated
  than if you were using Z"


How can I quantify that? And what tests should I do to actually prove that statement? Examples are appreciated.

Background
I am trying to build some different technology products and I want them to help the user stay more focused than they would using a competitor product of the same kind. The only research I've done so far was to build some interfaces and ask the user how they feel.
Short answer
Attention can be quantified with a sustained attention to response task.

Background
I think with focus or concentration you mean sustained attention to a certain task. A sustained attention to response task (SART) (Silverstein &amp; Palumbo, 1998) could be helpful to you (here is a free PsychoPy script). SART seems to be a reliable measure for attention (Smilek et al., 2010). 

Basically SART consists of a set of stimuli (e.g., simple shapes) and the subject is asked to repeatedly give a response (e.g. a button press) when a certain event occurs (e.g. a shape changes color). Reductions in correct rates, increased lapse rates, and/or decreased reaction times all may signal reduced attention to the task. 

Admittedly I am not too familiar with these tests, but I do have a lot of experience with people loosing attention during tedious psychophysical tasks :) I hope the links and references provided here may be of further help.

References
- Silverstein &amp; Palumbo, Computers in Human Behavior (1998); 14(3): 463-75
- Smilek et al., Neuropsychologia (2010); 48(9): 2564-70