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In recent years, the interest in probabilistic real-time has grown, as a response to the limitations of traditional static Worst-Case Execution Time (WCET) methods, in performing timing analysis of applications running on complex systems, like multi/many-cores and COTS platforms. The probabilistic theory can partially solve this problem, but it requires strong guarantees on the execution time traces, in order to provide safe probabilistic-WCET estimations. These requirements can be verified through suitable statistical tests, as described in this paper. In this work, we identify also challenges and problems of using statistical testing procedures in probabilistic real-time computing, proposing a unified test procedure based on a single index called Probabilistic Predictability Index (PPI). An experimental campaign has been carried out, considering both synthetic and realistic datasets, and the analysis of the impact of the Linux PREEMPT_RT patch on a modern complex platform as a use-case of the proposed index.