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Frontier Physics involves investigations to the limit of detector sensitivity and the phenomena one searches for can usually be 'mimicked' by other, less interesting ones ('background'). Providing firm results is often not possible, and the claims of discovery are usually accompanied by "statistical significance", traditionally turned by high energy physicists into "number of sigma's".
Meaning and misinterpretation related to the "n-sigma's" will be illustrated, reporting and discussing examples taken from Particle Physics.