Abstract
The problem of testing non-inferiority in a 2 x 2 matched-pairs sample is considered. Two exact unconditional tests based on the standard and the confidence interval p-values are proposed. Although tests of non-inferiority have two nuisance parameters under the null hypothesis, the exact tests are defined by reducing the dimension of nuisance parameter space from two to one using the monotonicity of the distribution. The exact sizes and powers of these tests and the existing asymptotic test are considered. The exact tests are found to be accurate in view of their size property. In addition, the exact test based on the confidence interval p-value is more powerful than the other exact test. It is shown that the asymptotic test is inaccurate, that is, its size exceeds the claimed nominal level alpha. Therefore, it recommends a cautious approach in use of the asymptotic test for the problem of testing non-inferiority, particularly when sample sizes are small or moderately large.
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