The effective hard sphere diameter (EHSD) method has been widely used to calculate both equilibrium and transport properties. Various EHSD explicit equations have been proposed in the literature according to different criteria. In this work a comparison between different expressions has been carried out and suggestions are given following the comparison. As an example of the applications the EHSD method has been applied to the prediction of the selfdiffusion coefficients of the Lennard-Jones fluid, by use of the hard sphere model proposed by Erpenbeck and Wood. It is found that the temperature-dependent Boltzmann EHSD and both temperature-and density-dependent Lado modified Weeks-Chandler-Andersen EHSD give the best results.