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Localization and electron correlation play significant roles in understanding the electronic states of low-dimensional systems. We carried out the tunneling spectroscopy measurements on a crystalline nano-sized island and a disordered two-dimensional metal film. The low temperature zero-bias anomaly was studied using $P\left(E\right)$ theory and statistical analysis of the spatial distribution of the local density of states in both the systems. The effective capacitance and resistance of the tunnel junction extracted from $P\left(E\right)$ theory gives the energy and temperature dependency of the measured ZBA. Statistical analysis reveals the electron correlation effect and the electron correlation length. By combining $P\left(E\right)$ theory and the statistical analysis, we found that the microscopic origin of ZBA formation in the disordered two-dimensional film is strongly related to the electron localization and the correlations.