To expand upon my previous post, the problem with many of Howard's examples attempting to support his assertion that format is unattached to DoF, is that essentially they are all saying that A=A, or if A=B then B=A.
There's no great insight here. If I cut a print in half, then of course that half is the same as the half before it was cut, but that half is clearly not the same as the uncut whole.
As BJL has mentioned, if we are comparing the perception of DoF on 2 prints, we should keep the prints which are under comparison the same size to reduce the number of variables. We should also not vary the quality of the viewer's eyesight or the viewing distance to the 2 prints.
Howard has brought up these subjective variables time and again. They are really just a smokescreen.
I shall now attempt a definitive proof that changing format can directly affect the perception of DoF on a print when comparing equal size prints of the same subject and same FoV.
I'll use a range of f stops that are more familiar to users of 35mm, rather than 4x5 format.
I'll use Howard's example of a full height figure. Here's the scene; Howard standing in front of a huge tree with spreading canopy. The background stretches to a theoretical infinity, mountains on the horizon, other trees and tall grass in between. Howard is very close to the tree trunk, in fact leaning back on it. I have a prime lens which, from a convenient position, takes in a good portion of the scene in front of me. No need to crop smaller than the camera's format. I calculate that f4 is sufficient to get all of Howard sharp on a good size print, from the tip of his nose to the patch of ground he is standing on, to the hair at the back of his head, to the tree trunk he is leaning against. For good measure, I use f5.6, just in case I later want to make a large print of a crop.
However, I'm a bit concerned about the close foliage at the top of the frame, which at f5.6 is definitely going to be out-of-focus. The mountains and other trees in the background will also be OoF, so I take another shot at f13 to get everything looking sharp, even in a large print.
I make a 16x24 print of each shot. The one at f5.6, as expected, has a shallow DoF, but the one at f13 appears equally sharp from corner to corner. (I'm actually using the Canon TS-E 45mm which has a larger than usual image circle and produces a reasonably good result from corner to corner.)
I show Howard the 2 prints and he agrees (as anyone would) that the f13 shot has much greater DoF, but Howard doesn't like all the distracting foliage and asks me to make a crop of just him against the tree trunk, which I do, cropping to a panoramic aspect ratio of 3:1, vertically orientated.
I crop both images. I'm not sure why I bothered cropping both images, but Howard told me that cropping or changing format does not change DoF, so I expected one print might still exhibit greater DoF than the other. (Not really ).
Lo and behold! I find that both prints, still both equal in size, now have identical DoF.
By changing just one variable, the format, I have changed the DoF on the final result, the print. Of course, by cropping I have changed the composition and FoV, but that's what cropping does when you use the same lens. It's unavoidable. The cropped print is also smaller than the uncropped print, but again, that's what cropping does.
Perhaps we could summarise this principle as follows.
If 2 prints of the same scene have equal DoF, cropping to a different format will also result in 2 prints with the same DoF. However, if 2 prints have an unequal DoF, then cropping (ie. changing format) can change that inequality.