# Margins

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).

## References

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