An equivalence hypothesis test formally tests if a population parameter is equivalent to a hypothesized value, that is, practically the same.
An typical parameter hypothesis test can never prove that the parameter is equal to the hypothesized value, it can only ever disprove the null hypothesis of equality. By contrast, an equivalence hypothesis test is of interest when the purpose is to prove that the parameter is equivalent to a hypothesized value, that is the difference is less than some small negligible effect size. An equivalence hypothesis test therefore constructs the null hypothesis of non-equivalence and the goal is to prove the parameter is the equivalent to the hypothesized value.
The null hypothesis states that the parameter is not equivalent to the hypothesized value, against the alternative hypothesis that it is equivalent within the equivalence interval. The hypothesis is tested as a composite of two one-sided t-tests (TOST), H01 tests the hypothesis that parameter is less than the lower bound of the equivalence interval, test H02 that the parameter is greater than the upper bounds of the equivalence interval. The p-value is the greater of the two one sided t-test p-values. When the test p-value is small, you can reject the null hypothesis and conclude the sample is from a population with the parameter practically equivalent to the hypothesized value.
