NNature said:
Yes it was kind of sloppy to say "when everything is equal" and not mention framing. In real life you want the same framing no matter what sensor size you use, but I should have included that info as well and not take for granted that everyone would understand that.
The reason we didn't understand that is that you said the opposite. You said, "If you have the same focal length, aperture and distance to the "object" you are photographing...". If those are all the case, you
don't have the same framing. Regardless, it's wrong anyway.
Let's say you adjust one of your constants so that you do have the same framing. Let's use the logical one and adjust focal length by the crop factor.
100mm * 1.6 = 160mm.
7D, 100mm, f/2.8, 10 feet, DOF = 0.32 feet
5D, 160mm, f/2.8, 10 feet, DOF = 0.19 feet
Oops...not the same even with the same framing.
If you want DOF to be the same across formats, and you want to hold framing constant, have have to multiply
both focal length
and f-stop by the crop factor.
f/2.8 * 1.6 = f/4.5
7D, 100mm, f/2.8, 10 feet, DOF = 0.32 feet
5D, 160mm, f/4.5, 10 feet, DOF = 0.30 feet (the difference is caused by round-off error).