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Crop factor affects DOF
No, the lens focal length, focusing distance and aperture determine depth of field, also circle of confusion and viewing distance
Wrong. ggreene is correct. Crop factor does affect Depth of Field. You've never done the experiment. Do it, or look at the many examples on the net. I hope I don't have to post links for you.
To make the proper comparison for this paradigm, you have to have the same subject distance (for same perspective), same aperture, same viewing distance, and same print size. Given the same observer, the viewing distance and print size will give the same circle of confusion, due to the visual acuity of the viewer.
You have to change the focal length to compensate for the crop factor, otherwise the pictures will not depict the same thing (one will have more things in the frame).
When you make the same picture by using the same distance, same aperture, adjusted focal length, same print size, and same viewing distance, then the print from the crop factor camera will have more depth of field. It's a fact.
The reason is that circles on the image sensor do not have the same effect as the circles of confusion on the print. The CoC ("blur disks") on the prints are derived from different sized circles on sensor due to the different degree of enlargement.