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Here is my result on 5D3 & 70-200 f/2.8 II.
@200mm, white LED light (~5000K)
-9 to +7, avg = -1
@200mm, halogen light (~3000K)
-7 to +9, avg = +1
@70mm, white LED light
-11 to +5, avg = -3
@70mm, halogen light
-5 to +11, avg = +3
I used the same target, brightness, tripod, etc. I just turned on one light, and switched off the other light. These numbers were very consistent and reproducible.
I have known this but phase detection focus shifts with light temperature. A couple of years ago, I returned 3 camera bodies and after months of frustration testing 6 camera bodies and lenses, I finally realized that focus shifts depending on light temperature. Under warm incandescent light, cameras front-focuses (or move in that direction). Under whiter light such as LEDs and florescent lights, cameras back-focus. Even outdoors, there is a shift going from sunlight to shade, mid-day to dawn/dusk. I don't know why this can't be compensated in camera electronics since auto-balance sensor can measure color temperature.
I have to say the 5D3 focus accuracy in various conditions is much, much better than the 7D for example but if you examine closely, you can get frustrated with any camera. I am happy with my camera/lens combination in this case. The MFA average is exactly zero.
The Dot-tune method seems to work well but I don't believe in the MFA since the value changes with light temperature, distance, and with focal length (in case of zoom lens). If you set the MFA to any value other than 0, it will make things worse in some other conditions. If my camera/lens need MFA, I would send them back and get them calibrated. I do understand that it can be beneficial if your camera/lens is offset to one direction but in my experience, focus consistency gets worse when MFA is enabled and set to a non-zero value.