Exact unconditional tests for a 2 × 2 matched-pairs design
Exact unconditional tests for a 2 × 2 matched-pairs design
复制标题
2 × 2 配对设计的精确无条件检验
DOI：
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发表时间：
2003
影响因子：
2.3
通讯作者：
Kurex Sidik
中科院分区：
文献类型：
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作者：
Roger L. Berger;Kurex Sidik
研究了二元反应的2×2配对设计中两个比例的比较问题。我们考虑单边的零假设和替代假设。这个问题有两个恼人的参数。利用多项分布的单调性，在计算中将扰参数空间的维度从2降为1，提出了4种基于p值的精确无条件检验。考虑了四种精确检验和另外两种检验--精确条件二项检验和渐近McNemar检验的大小和威力。结果表明，基于可信区间p值的检验比基于标准p值的检验更有效。此外，研究还发现，精确的条件二项检验是保守的，对检验假设的能力不强。此外，渐近的McNemar检验被证明具有不正确的大小；即，其大小大于检验的标称水平。总体而言，基于McNemar统计量和可信区间p值的检验被发现是本次比较中规模正确的检验中最强大的检验。
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.