It makes sense when you apply the definition of DOF: area (distance) in front of and behind the focused subject, that still seems to be in focus to our eyes for a given angle of observation of the image. If you use a cropped image, you could be able to distinguish blurred elements that appeared to be in focus in the non-cropped image, just because in the cropped version you are observing them with a higher magnification.
For the same reason and according to the definition, DOF changes with the viewing distance to a printed image. An image that may look to be entirely in focus to your eyes when observed from let's say 10m, could reveal out of focus elements as you get closer to the print.
People stating that DOF doesn't get altered with format, just don't understand the definition of DOF.
On the other hand, Guillermo, if we keep all variables constant, which is the condition you stated in an earlier post, then these changes in viewing distance should not apply.
When isolating a specific quality for comparison, such as DoF and how it may change with sensor size, one should try to keep all other variables constant if possible. If you wish to compare how DoF changes with viewing distance from a print, then that should be a separate experiment in which one should keep not only sensor size, print size, and lens settings constant, but actually use the same camera and lens.
However, there are certain situations when it may not be possible to keep all other variables constant, as is the case when comparing images taken with different size sensors using the same lens, with same settings, from the same position.
If one crops the image from the larger sensor to the same size and aspect ratio of the image from the smaller sensor, then one is effectively comparing equal size sensors. Not much point in that, unless one is comparing some other quality such as the effect on resolution from the different pixel densities of the two sensors, as in a comparison between the Canon 7D and the 5D3.
In order to compare the effect that the larger sensor has on the DoF of a scene, one cannot sensibly crop the scene from the larger sensor in post-processing, because that would constitute a discarding of image information, and scene information, from the larger sensor. That would be really
unscientific. However one should at least try to keep other variables constant, such as lens, aperture, focal length, shooting position, and print viewing distance.
But what about print size? Here we have a dilemma. If the two different size sensors happen to have the same pixel count and the same aspect ratio, we can also achieve equal print size without discarding any image information from one of the sensors and without applying unequal interpolation to the images for printing purposes.
Whilst there certainly are
cameras with different size sensors but similar or identical pixel counts, such as the Canon 1Ds2 and the Nikon D7000, the larger sensor usually has more pixels, so for the sake of clarity on this issue I'd make the following summary.
When comparing the DoF of two different sized sensors, it's not possible to keep all variables constant. The options are:
(1) Keep everything constant except FoV, and print size in circumstances when the two sensors have a different pixel count.
(2) Keep FoV constant by changing focal length of lens used, with the same problem applying to print size in accordance with pixel count.
Take your pick.
In both situations there is at least one additional variable which cannot be constant, apart from the obvious variable of sensor size which is a necessary variable and the basis of the comparison.