In these "statistical notes", equivalence and non-inferiority randomized controlled clinical trials (RCCT) are considered. Equivalence trials are designed to confirm the absence of a meaningful difference between the effect of two treatments. Non-inferiority trials are designed to prove that the new treatment is no less effective than an existing one: it may be more effective or it may have a similar effect. In this note the attention is addressed to suitable criteria for the choice of the tolerance margin epsilon, i.e. the largest difference which is clinically acceptable, so that a difference bigger than that would matter in practice. In particular, the procedures for the determination of the margin epsilon, used by the authors of the non-inferiority RCCT COBALT and INJECT, are presented and discussed in detail. The ethical implications of equivalence and non-inferiority RCCT are here considered and the reader is repeatedly invited to consider the appropriateness of the basic arguments asserted by the supporters of this kind of studies.