If you want to prove that two means are equal, or that a mean equals a target value, and if you can define exactly what size difference is important in your field, you may want to use an equivalence test instead of a standard t-test.

How do you demonstrate equivalence?

Demonstrating equivalence requires defining a difference Δ that is considered significant and then demonstrating with high confidence the difference is less than Δ. Equivalence tests are based on confidence intervals.

What is the main objective behind equivalence testing?

Equivalence tests are a variation of hypothesis tests used to draw statistical inferences from observed data. In equivalence tests, the null hypothesis is defined as an effect large enough to be deemed interesting, specified by an equivalence bound.