This a quote from Analog Devices...
So having started by telling me to "ignore" their data sheets, you now wish to use them in an appeal to authority argument.
A higher ENOB means that voltage levels recorded in an analog to digital conversion are more accurate.
You seem to be reading something more into that than there is stated. Yes, better resolution can contribute to better accuracy , that does not mean resolution IS accuracy, which is what you seem to be implying it says.
Resolution has nothing to do with accuracy.
Wrong again, as you would say. Resolution is one factor that contributes to (or limits) accuracy.
You may increase resolution by dithering and oversampling, thereby improving accuracy within the limit of the quantisation error you had previously. If you have 0.5LSB of quantisation error you cannot improve the quantisation error by more than 0.5 LSB. Neither will oversampling correct non-linearaity or gain errors. The major part of the 1.5 LSB errors reducing the basic 10b sample.
You may also remove gaussain noise by oversampling. But if your noise is not gaussian it will NOT be correctly removed. There will remain a bias in the result, the sign and magnitude of which you will not be able to know. If you do not know the nature of the noise you are injecting by waving a piece of wire around, you cannot know what will be left after oversampling. You will therefore have degraded the S/N of the result (notwithstanding the limited improvement gained by dithering).
That is why I suggested that, since you seem to have got a very clean signal, a suitable cyclic perturbation signal would be better than arbitrary, uncharacterised noise.
This is so basic, I don't see why I am having to lay this out for a third time.
If you see something wrong with my argument I'd be more impressed if you could say where it was wrong rather than pretending app. notes are some kind of text book on methodology or saying "bah! go back to school" and questioning my credentials.
I deliberately left that last comment short. Yet you ignore it. I'll ask again...
ENOB specifies the number of bits in the digitized signal above the noise floor, this is accuracy.
Your arduino with a 3LSB offset is less accurate. Does it have any less ENOBs because of that offset?