Department of Statistics and O.R., Complutense University of Madrid, Madrid, Spain.
Department of Agriculture, Crop Production and Rural Environment, University of Thessaly, Volos, Greece.
Biom J. 2020 Oct;62(6):1574-1588. doi: 10.1002/bimj.201900272. Epub 2020 May 25.
Alternative hypotheses for order restrictions, such as umbrella or inverse umbrella (a.k.a tree) orderings, have been studied extensively in the literature, although less so when the studied response for each individual is the presence or absence of the event of interest. Two families of test statistics for solving the problem of testing against an umbrella or a tree ordering when the responses are binomial proportions are studied in this work and their asymptotic distributions are derived. A simulation study is conducted to compare the empirical power of some members of the derived families of test statistics with competing approaches. The methodology developed here was driven by an applied problem arising in stored products research where despite universal mortality in the case of doses of 1000 ppm of the insecticide phosphine, unexpected survival was noted at higher doses.
替代有序限制的假设，如伞形或反向伞形（又称树）排序，在文献中已经得到了广泛的研究，尽管在研究每个个体的响应是感兴趣事件的存在或不存在时，研究得较少。当响应是二项式比例时，这项工作研究了两种用于解决针对伞形或树形排序检验的检验统计量的族，并且推导出了它们的渐近分布。进行了一项模拟研究，以比较推导的检验统计量族的一些成员与竞争方法的经验功效。这里开发的方法学是由储存产品研究中出现的一个应用问题驱动的，尽管在剂量为 1000ppm 的杀虫剂磷化氢的情况下普遍存在死亡率，但在更高剂量下却观察到了意外的存活。
