Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 91-108 |
| Number of pages | 18 |
| Journal | Statistical Methods in Medical Research |
| Volume | 12 |
| Issue number | 2 |
| DOIs | |
| State | Published - Mar 2003 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Epidemiology
- Health Information Management
- Nursing(all)
Cite this
Exact unconditional tests for a 2 × 2 matched-pairs design. / Berger, Roger L.; Sidik, K.
In: Statistical Methods in Medical Research, Vol. 12, No. 2, 03.2003, p. 91-108.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Exact unconditional tests for a 2 × 2 matched-pairs design
AU - Berger, Roger L.
AU - Sidik, K.
PY - 2003/3
Y1 - 2003/3
N2 - 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.
AB - 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.
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U2 - 10.1191/0962280203sm312ra
DO - 10.1191/0962280203sm312ra
M3 - Article
VL - 12
SP - 91
EP - 108
JO - Statistical Methods in Medical Research
JF - Statistical Methods in Medical Research
SN - 0962-2802
IS - 2
ER -