Exact unconditional tests for a 2 × 2 matched-pairs design

Roger L. Berger, K. Sidik

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


The problem of comparing two proportions in a 2 × 2 matched-pairs design with binary responses is considered. We consider one-sided null and alternative hypotheses. The problem has two nuisance parameters. Using the monotonicity of the multinomial distribution, four exact unconditional tests based on p-values are proposed by reducing the dimension of the nuisance parameter space from two to one in computation. The size and power of the four exact tests and two other tests, the exact conditional binomial test and the asymptotic McNemar's test, are considered. It is shown that the tests based on the confidence interval p-value are more powerful than the tests based on the standard p-value. In addition, it is found that the exact conditional binomial test is conservative and not powerful for testing the hypothesis. Moreover, the asymptotic McNemar's test is shown to have incorrect size; that is, its size is larger than the nominal level of the test. Overall, the test based on McNemar's statistic and the confidence interval p-value is found to be the most powerful test with the correct size among the tests in this comparison.

Original languageEnglish (US)
Pages (from-to)91-108
Number of pages18
JournalStatistical Methods in Medical Research
Issue number2
StatePublished - Mar 2003

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability
  • Health Information Management


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