I just know intuitively that a larger f/stop (f/2.8) will yield a shallow DOF and a smaller f/stop (f/16) will yield a longer DOF.
Yes. But. How much different and how does the DoF distribution change.
I think it's a very common amateur mistake to consider DoF only in terms of lens aperture, ignoring the several other factors that affect DoF, particularly the focus point distance.
When I shoot, I am always keenly aware of my focus point distance relative to the lens focal length and aperture I am using.