Clustered binary data occur frequently in many application areas. When analyzing data of this form, ignoring key features, such as the intracluster correlation, may lead to inaccurate inference, e.g., inflated Type I error rates. For clustered binary data, Gerard and Schucany (Comput Stat Data Anal 51:4622–4632, 2007) proposed an exact test for examining whether the marginal probability of a response differs from 0.5, which is the null hypothesis considered in the classic sign test. This new test maintains the specified Type I error rate and has more power, when compared to both the classic sign and permutation tests. The test statistic proposed by these authors equally weights the observed data from each cluster, regardless of whether the clusters are of equal size. To further improve the performance of the Gerard and Schucany test, a weighted test statistic is proposed and two weighting schemes are investigated. Seeking to further improve the performance of the proposed test, empirical Bayes estimates of the cluster-level success probabilities are utilized. These adaptations lead to 5 new tests, each of which are shown through simulation studies to be superior to the Gerard and Schucany (Comput Stat Data Anal 51:4622–4632, 2007) test. The proposed tests are further illustrated using data from a chemical repellency trial.

中文翻译：

---

通过加权和未加权测试统计对聚集二进制数据进行基于精确排列的符号测试

聚集的二进制数据经常出现在许多应用领域。在分析这种形式的数据时，忽略关键特征，例如集群内相关性，可能会导致不准确的推理，例如夸大的 I 类错误率。对于聚类二元数据，Gerard 和 Schucany（Comput Stat Data Anal 51:4622–4632, 2007）提出了一种精确检验，用于检查响应的边际概率是否不同于 0.5，这是经典符号检验中考虑的零假设。与经典的符号和置换测试相比，此新测试保持指定的 I 类错误率并具有更高的功效。这些作者提出的检验统计量对来自每个集群的观测数据进行同等加权，而不管这些集群的大小是否相同。为了进一步提高 Gerard 和 Schucany 测试的性能，提出了加权检验统计量并研究了两种加权方案。为了进一步提高所提出的测试的性能，使用了集群级成功概率的经验贝叶斯估计。这些调整导致了 5 个新测试，每个测试都通过模拟研究显示优于 Gerard 和 Schucany (Comput Stat Data Anal 51:4622–4632, 2007) 测试。建议的测试使用来自化学排斥试验的数据进一步说明。通过模拟研究表明，每一项都优于 Gerard 和 Schucany（Comput Stat Data Anal 51:4622–4632, 2007）测试。建议的测试使用来自化学排斥试验的数据进一步说明。通过模拟研究表明，每一项都优于 Gerard 和 Schucany（Comput Stat Data Anal 51:4622–4632, 2007）测试。建议的测试使用来自化学排斥试验的数据进一步说明。