Using a suite of cosmology simulations of a sample of >120 galaxy clusters with log (M sub( DM, vir)) less than or equal to 14.5. We compare clusters that form in purely dark matter (DM) run and their counterparts in hydro-runs and investigate four independent parameters that are normally used to classify dynamical state. We find that the virial ratio ... in hydro-dynamical runs is ~10 per cent lower than in the DM run, and there is no clear separation between the relaxed and unrelaxed clusters for any parameter. Further, using the velocity dispersion deviation parameter ..., which is defined as the ratio between cluster velocity dispersion ... and the theoretical prediction ..., we find that there is a linear correlation between the virial ratio ... and this ... parameter. We propose to use this ... parameter, which can be easily derived from observed galaxy clusters, as a substitute of the ... parameter to quantify the cluster dynamical state. (ProQuest: ... denotes formulae/symbols omitted.)