Analysis of Hadron Propagators with One Thousand Configurations on a ${24}^3\times 64$ Lattice at $\beta =6.0$

Statistical properties of effective mass are analyzed. We show from a general ground that effective mass as a function of time should not exhibit long plateaux whatever high statistics simulations are made: the mass should fluctuate beyond the one standard deviation of error bars after a few time slices for large times where the ground state dominates. This explains the difficulty of obtaining long plateaux experienced in previous simulations. Implications of the observation for global ${\chi }^2$ fits are discussed, and results for hadron masses are presented.