If your machine has what is called a ballscrew compensation table as part of the control parameters, it is only a matter of mapping the screw with a high resolution dial indicator to a known good standard. The dial indicator should have at least the same resolution as the axis being checked. Screw compensation tables may have variables that can map the screw at stations every XXmm-Xcm or .XXXin-1in. Each station within that table will get a +/- offset value to compensate that portion of the screw. You end up with a table of say 10 numbers that may be + .018mm, -.023mm and so on. What ever the deviation from the commanded verses actual against the standard ends up being input data for the compensation table. It is also a good idea to map it in both travel directions, since you may find backlash or greater ball path wear affect in some places more than others. Considering this is done in a no load condition, there may still be some additional deviation under load besides the normal way wear and machine deflection.
OEM's will usually do laser mapping on a ballscrew and many OEM's retain the original mapping of the screws as stored parameters for the compensation table in their archives. As long as the screw has not been replaced and wear isn't excessive, it would be easier to request a backup copy than mapping it yourself. There is still some peace of mind in knowing if there are any faulty areas of concern. At best, you end up taking the happy medium for the compensation table correction value on any given station along the screw, but you have only one backlash compensation value for the entire screw.
No compensation formulas that I know of for the equipment I have worked on. Unless someone is taking some other miniscule anomoly into account to compensate for.