That specific paper is using a factor of 2 to change the mesh density. I don't know if the numbers represent element edge length or number of elements along an edge, but the factor of 2 is clear.
I prefer to use a set of element edge lengths to plot on the x axis and stress or some other value that is important on the y axis. Three points on the graph may not be enough. You don't have to use a factor of 2, a factor of 1.5 is also good. You also don't have to make it a global element size change, you can apply the size using a Mesh Control such as Sphere of Influence at the location of the peak stress that you are plotting.
Please reply with an image of your model and the initial element size for which you have results.
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