The quintessence of electromagnetic fields propagating in complex environments is its stochastic nature. The canonical test facility to emulate such a complex case is the reverberating chamber (RC). In order to design, test, and model the electromagnetic field in an RC, one must consider the vectorial nature of the field. The electromagnetic field within an RC has a random 3-D structure that must be properly taken into account to analyze it. A robust and basis invariant analysis of the randomness of such 3-D field is here undertaken estimating the polarization purity, i.e., the degree of polarization. In this paper, a new approach, based on the decomposition of the 3-D degree of polarization, is exploited to analyze the electromagnetic field within an RC. Experiments, undertaken exploiting the RC of Universita degli Studi di Napoli Parthenope, formerly Istituto Universitario Navale (IUN), provide a first experimental validation of the aforementioned decomposition in the microwave range of frequency. In addition, such decomposition, being able to sort out information related to the stability of the polarization ellipse and of the direction of propagation, is a key tool to analyze the effectiveness of the stirring process within the RC.