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The good news is that equivalence testing is a popular such scenario in pharmacokinetics, arising, for example, when a pharmaceutical wants to show that their developed generic drug is equivalent to a brand drug. We know that in ordinary hypothesis testing a sufficiently large sample will lead to detecting practically insignificant effects by generating a very small p-value, which is bad news for those relying on classic hypothesis testing!
My colleague Foster Provost from NYU once challenged me how I could trust a statistical method that breaks down with large samples - a poignant thought that eventually led to my co-authored paper Too Big To Fail: Large Samples and the p-value Problem (Lin et al., ISR 2013). In equivalence testing, a very large sample will behave properly: with more data we'll get narrower confidence intervals (more certainty).