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Yes, there have been tests of the propagation of medium frequency radio waves using field strength measurements of actual AM broadcast stations to confirm the theoretical predictions, dating back to the 1930s, or maybe earlier. The calculations have been found to be at least approximately correct, but there is a lot of scatter in the results.
The problem is that the material of the earth is not homogeneous, and the surface is not smooth, except for still water. The conductivity and dielectric constant of the earth nornally varies with depth, and is different in different surface areas. So the measured results are different in different regions, even if the nominal electrical constants of the soil are numerically the same. Something that is usually ignored is that the electrical constants actually vary with frequency. It is common practice to consider the electrical constants to be truly constant instead of variable, which they actually are.