Introduction to Intersection-union Tests

The Intersection-Union Test (IUT ) has become increasingly popular, especially through its application in bioequivalence testing. Here we will provide a basic introduction and discuss some properties of the IUT . Since this method is based upon a combination of tests, there may be a concern for the need of a multiplicity adjustment to adequately control the overall type-I error rate. We will address this issue by considering two theorems. The first describes how the IUT can be level-α and the second shows under what conditions the test is size-α. Both results do not require any multiplicity adjustment. A simple example from acceptance sampling will be used to apply these theorems, and we will examine Monte Carlo simulations to verify the expected results.