Ranked set sampling (RSS) design as a cost-effective sampling is a powerful tool in situations where measuring the variable of interest is costly and time-consuming; however, ranking information about sampling units can be obtained easily through inexpensive and easy to measure characteristics at little or no cost. In this paper, we study RSS data for analysis of an ordinal population. First, we compare the problem of non-representative extreme samples under RSS and commonly-used simple random sampling. Using RSS data with tie information, we propose non-parametric and maximum likelihood estimators for population parameters. Through extensive numerical studies, we investigate the effect of various factors including ranking ability, tie generating mechanisms, the number of categories and population setting on the performance of the estimators. Finally, we apply the proposed methods to the bone disorder data to estimate the proportions of patients with osteopenia and osteoporosis status.

排序集抽样 (RSS) 设计作为一种具有成本效益的抽样，在测量感兴趣的变量既昂贵又耗时的情况下是一种强大的工具；但是，可以通过廉价且易于测量的特性以很少或免费的方式轻松获得有关抽样单位的排名信息。在本文中，我们研究 RSS 数据以分析序数总体。首先，我们比较了RSS下的非代表性极端样本问题和常用的简单随机抽样问题。使用带有领带信息的 RSS 数据，我们提出了总体参数的非参数和最大似然估计器。通过广泛的数值研究，我们调查了各种因素的影响，包括排名能力、平局生成机制、类别数量和人口设置对估计器性能的影响。