This study aims at overcoming some of the inconsistencies of stabilization diagrams, by applying a novel dispersion analysis framework that relies on the effective modal decomposition of the vibration output's zero-lag covariance matrix, under the assumption of broadband random excitation. A new metric is introduced, which expresses a certain part of the total stochastic vibration energy, and is attributed to each vibration mode. It is then shown how this metric can be integrated into a stabilization diagram, in order to enrich the displayed information and facilitate the model order selection process. In this respect, a vibration mode is identified as structural when it appears stabilized in both its frequency and its dispersion metric. The method's performance is assessed through structural identification problems from both simulated and experimental vibration data, for which subspace and prediction-error based methods are utilized.