Is the exact test better than the asymptotic test for testing marginal homogeneity in 2 x 2 tables?

McNemar test is commonly used to test for the marginal homogeneity in 2 x 2 contingency tables. McNemar test is an asymptotic test based either on standard normal distribution or on the chi-square distribution. When the total sample size is small, an exact version of McNemar test is available based on the binomial probabilities. The example in the paper came from a clinical study to investigate the effect of epidermal growth factor for children who had microvillus inclusion diseases. There were only six observations available. The test results differ between the exact test and the asymptotic test. It is a common belief that with this small sample size the exact test be used. However, we claim that McNemar test performs better than the exact test even when the sample size is small. In order to investigate the performances of McNemar test and the exact test, we identify the parameters that affect the test results and then perform sensitivity analysis. In addition, through Monte Carlo simulation studies we compare the empirical sizes and powers of these tests as well as other asymptotic tests such as Wald test and the likelihood ratio test.