Paper. Printer paper has clay and such to create a good surface for the ink. It can be informative, but is a bit tougher on the edge compared to other tests. There are two paper tests. A draw stroke, probably the most intuitive and common test and a push cut.
The draw stroke is particularly useful for finding flaws in your edge. As you perform the draw stroke, when you get to said flaw, the cut will often turn into a tear. However, technique is important to consider as you use this test. Generally, people give the paper some stiffness to help them start the cut. The common method is to curve the paper in your grip a bit. The stiffer you have to make the paper to start the cut, the duller your edge. You can also do this test more horizontally or more vertically. Horizontal is easier but masks the edge quality a bit. Vertical cut is more prone to tearing out and so is more revealing.
The push cut can be difficult to get started. It takes a fairly refined edge to push cut paper readily. The paper will usually deflect some at first.
The paper itself matters some too. Newsprint is much more difficult to test your knife in that printer paper or magazine paper. It's more fibrous and prone to tearing. Being able to cut a free hanging piece of newsprint is tricky, but there are some technique tricks here too. mostly about coming in at a downward angle to use gravity and the edge catching the paper to stiffen it up against the grip point. A highly refined edge is important so there is no tearing.
Clearly then, technique, paper and the edge all play into what a paper cutting test can reveal. The paper test can be used to deceive a bit even. It's useful to examine the cut of paper too. how cleanly is it cut. Is there rolling of the edge on the cut, how feathered is the cut and so one.
I'll post some more about the shaving test in a bit. Have to go for now.