The authors illustrate the difficulties involved in obtaining a valid statistical significance in clinical studies especially when the prior probability of the hypothesis under scrutiny is low. Since the prior probability of a research hypothesis is directly related to its scientific plausibility, the commonly used frequentist statistics, which does not take into account this probability, is particularly unsuitable for studies exploring matters in various degree disconnected from science such as complementary alternative medicine (CAM) interventions. Any statistical significance obtained in this field should be considered with great caution and may be better applied to more plausible hypotheses (like placebo effect) than that examined — which usually is the specific efficacy of the intervention.Since achieving meaningful statistical significance is an essential step in the validation of medical interventions, CAM practices, producing only outcomes inherently resistant to statistical validation, appear not to belong to modern evidence-based medicine.