Equivalence tests were conducted with both unilateral test methods (TOST) (Schuirmann reference 10) as well as with the CI approach (Westlake reference 11). Both are valid approaches and the use of one or the other depends on the preference given to the use of a P value or an IC. Equivalence tests are widespread in the pharmaceutical industry, where a new drug, which may have fewer or less expensive side effects to produce, is compared to the standard drug to determine whether the therapeutic effect is equivalent in a predefined area (Midha and McKay 12 reference). If differences in average means (d) are considered with a type t-test, as in the traditional framework, it must be shown that a new drug or method is different (usually in order to be superior). In this case, the zero hypothesis says that there is no difference between treatments, while the alternative hypothesis is that there is a difference. On the basis of this paradigm, introduced by Neyman and Pearson (Reference Neyman and Pearson 13), it can only be shown to ≠0 or that there is insufficient evidence to prove it≠. What is not proven is that the d-0 – that is, the zero hypothesis cannot be proven. With a small sample size, it is difficult to show that ≠0 and an erroneous conclusion that there is no difference (type 2 error) can be made, especially when the difference is small and the variance is significant (Altman and Bland 14 reference). In this situation, we can conclude that both methods agree, because we do not have sufficient power to demonstrate that the difference is statistically significant. On the other hand, there is a sample size for each d, which demonstrates that ≠0, whether or not that difference has practical significance. In this situation, we can conclude that the methods do not match if the difference between them is actually too small to have clinical significance. Thus, statistical significance has nothing to do with practical or clinical significance.
When equivalence is demonstrated, these assumptions are reversed so that the zero indicates that there is a difference (H0:|d|≥∆, hence the difference between methods and ∆ is the pre-established equivalency interval) and the alternative hypothesis is that there is no difference (Ha: |d|<∆), reference Hoen and Heise 15). Equivalence studies require a prior specification of an acceptable equivalency zone. The definition of this area must be based on clinical acceptance of the range of measures. Wellek (Reference Wellek 9) discusses all areas where the equivalence area is unknown, and other arbitrary decisions such as ±10% of the reference product have been used in the physical activity literature (reference Kim, Crouter and Lee 16). In general, this region of equivalence is poorly defined. A review of 332 non-inferior and equivalent pharmaceutical studies found that half of them considered the difference between treatments to be an "irrelevant" difference (Lange reference and Friday 17).