Guys...
Sensor size does not change DoF.
Aperture diameter and subject distance change dof or to say it better blur circle (pic related).
Focal length doesnt matter BUT focal length indirectly affects aperture diameter. F-number is Focal length / apertureO or apertureO is F / f.
50mm / f/1.8 = 27,8mm AO
Cropfactor between Fullframe and APS-C sensor size is 1,5x so to get the same framing, from the same distance. 50mm /1,5 = 33,3mm.
33,3mm / f/1.8 = 18,5mm AO
You stand at the same distance, have the same framing, have the same f-number but because the actual AO is larger on the 50mm the blurcircle is larger->dof is more shallow.
Divide the f-number by the crop factor as well and you get the equivalent f-number to get the same actuall AO->the same actually blurcircle->dof
f/1,8 / 1,5 = f/1,2 -> 33,3mm / f/1,2 = 27,8mmO
In the end end, in real world, sensor size AFFECTS dof because you would have to use another lens with a faster aperture. Which just arent available if you consider fast lenses, so you will mostly get shallower dof on FF. If shot wide open! 2.8 on FF? 1,8 on APS-C.
Same goes for medium format. Most lenses have an actually max aperture diameter smaller than fullframe lenses, giving greater dof.
Helpfull link:
http://yedlin.net/lens_blur.html 