Non-inferiority of a diagnostic test to the standard or the optimum test is a common issue in medical research.In this paper, we consider the problem of comparing two proportions in a 2 × 2 matched-pairs design with binary responses and propose a new test based on the standard p-value.The size and power of the asymptotically normal test and Sidiks unconditional exact test are considered.Simulation experiments demonstrate that our new testbased on the p-value is more powerful than Sidiks unconditional exact test.In addition, it is found that the exact conditional binomial test is conservative and not powerful for testing the hypothesis.Moreover, the asymptotically normal test is shown to have incorrect size; that is, its size is larger than the nominal level of the test.Overall, our new test based on the p-value is found to be the most powerful test with the correct size among the tests in this comparison.Also, we introduce a method based on simulation studies to determine the sample size.