Over in the metal work forums I have posted a bunch of run out (RO) measurements of chucks on a DP and a MW Lathe.
Following some leads posted by other members I have done a bunch of checks and come up with some interesting findings that some of you may not be aware of.
Runouts on machinery

Summary
1) The spindle ROs for the DP and MW lathe were both less than 0.005 mm (0.0002")

2) The ROs I measured for my 5 DP chucks ranged from 0.65mm (ie unusable, it was so far out I could easily see the RO) for the original keyed chuck that came with my budget level DP, to 0.025mm (0.001" , fine for WW, OK for MW) for an MT3 keyless chuck from McJing.

3a) Now here's something worth knowing that was pointed out to me by Anorak Bob.
The RO depends on the orientation of the MT arbor in the DP spindle.
For example the Keyless chuck mentioned in 2) above has a RO of 0.025mm in one position but when rotated by 180º it's 0.045mm!

3b) I measured the RO of the keyed chuck mentioned above in 2) on a MW lathe so that I could check the RO at more than just two positions - for this I got between 0.51 and 0.30 mm which shows how much it can vary.

4) The RO depends on which chuck keyhole you use to tighten the chuck.
I only tried this on a 4" 3 jaw, MW lathe chuck but the RO varied from 0.11 to 0.03mm - quite a difference.

If you used a keyed chuck with an MT2 tang in an MT3 adapter in an MT3 DP, you have 3 x 2 x 2 (12) ROs to check to find the optimum RO position.