In break-junction experiments, the electrical contact between two metal electrodes is broken. When opening the junction, one or more molecules can be trapped between the electrodes and thereby contacted which allows their transport properties to be investigated. Statistical analysis of data plotted in histograms is generally used to determine the values of molecular conductance and the variations therefrom. In this paper, the effect of direct electron tunneling between the metal electrodes on the molecular conductance measurement is discussed. It is shown that this tunneling forms a parallel conductance channel that can influence both the position and the distribution of the apparent molecular conductance extracted from histogram peaks. Criteria to recognize the effect of this form of parallel tunneling path in comparison to the molecular transport path in the experimental data are established. With the help of analytic models and simulations, it will be shown how to disentangle the contributions of several physical variation sources on the resulting position, height, and width of the histogram peaks. Finally, the plotting of 2D histograms is described as a practical method to help distinguish the effects of molecular conductance from those of direct electrode-electrode tunneling. © 2011 American Physical Society.