Sensor size affects DOF in counterintuitive ways. Because the circle of confusion is directly tied to the sensor size, decreasing the size of the sensor while holding focal length and aperture constant will "decrease" the depth of field (by the crop factor). The resulting image however will have a different field of view. If the focal length is altered to maintain the field of view, the change in focal length will counter the decrease of DOF from the smaller sensor and "increase" the depth of field (also by the crop factor).