For the simulation of micro-heterogeneous materials the FE2-method provides incorporation of the mechanical behavior at the microscale in a direct manner by taking into account a microscopic boundary value problem based on a representative volume element (RVE). A main problem of this approach is the high computational cost, when we have to deal with RVEs that are characterized by a complex geometry of the individual constituents. This leads to a large number of degrees of freedom and history variables at the microscale which needs a large amount of memory, not to mention the high computation time. Therefore, methods that reduce the complexity of such RVEs play an important role for efficient direct micro-macro transition procedures. In this contribution we focus on random matrix-inclusion microstructures and analyze several statistical measures with respect to their influence on the characterization of the inclusion phase morphology. For this purpose we apply the method proposed in Balzani and Schr¨oder (2008); Balzani et al. (2009a), where an objective function is minimized which takes into account differences between statistical measures computed for the original binary image of a given real microstructure and a simplified statistically similar representative volume element (SSRVE). The analysis with respect to the capability of the resulting SSRVEs to reflect the mechanical response in some simple independent virtual experiments allows for an estimation of the importance of the investigated statistical measures.