Statistical testing of clinical trial data leads to acceptance of a hypothesis if a test of the opposite (null) hypothesis (H-0 ) fails to reach a critical probability value. The usual aim is to demonstrate that a new treatment is superior to a comparator, whence H-0 is that the two treatments are the same. By contrast, in studies designed to show that a new treatment is equivalent to an existing therapy, the same principle is satisfied by an amended null hypothesis, that the treatments differ by more than a defined amount. This reversal entails subtle but important logical and practical problems which affect particularly the calculation of sample size. The choice of the limits used to define equivalence is critical to the calculation of sample size in a manner not previously discussed, and in the interpretation of data in relation to the probability of Type I and Type II errors. Investigators, regulatory bodies and institutional ethics committees must ensure that the range of values chosen to indicate equivalence is clinically appropriate and be aware of the effect of this decision on possible errors in accepting or rejecting H-0 .