Suppose you are researching a new clinical treatment to see if it is at least a good as the current standard of care. This can be achieved using a test of superiority (a type of one-sided test). In this hypothesis, you want to show that the effect size of the treatment, \(\theta_T\), is greater than the reference, \(\theta_R\). Often times, it is not enough to show that \(\theta_t - \theta_r > 0\); it must be shown that \(\theta_T - \theta_R > 0\) is greater than some clinically significant difference that we will denote \(\delta\). We can then express our hypothesis as such:

\[ H_0: \theta_{T} - \theta_{R} \le \delta \text{ versus } H_a: \theta_{T} - \theta_{R} \gt \delta \]The margin, \(\delta\), is this clinically significant difference.

This parameter is used in one-sided tests and obligatory in equivalence tests (read more about hypotheses).

- Chow, S., Shao, J., & Wang, H. (2003),
*Sample size calculations in clinical research,*New York: Marcel Dekker.