To compare distributions of ordinal data such as individuals’ responses on Likert-type scale variables summarizing subjective well-being, we should not apply the toolbox of methods developed for cardinal variables such as income. Instead, we should use an analogous toolbox that accounts for the ordinal nature of the responses. In this article, I review these methods and introduce a new command, ineqord, for undertaking distributional comparisons. As the empirical illustrations demonstrate, ineqord can be used for dominance checks as well as for estimation of indices of polarization and inequality.

中文翻译：

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比较序数数据的分布

为了比较序数数据的分布（例如个人对Likert型量表变量的反应，概述主观幸福感），我们不应应用针对基数变量（如收入）开发的方法的工具箱。相反，我们应该使用一个类似的工具箱来说明响应的顺序性质。在本文中，我将回顾这些方法，并引入一个新命令ineqord，以进行分布比较。如经验例证所示，不等式可用于支配性检查以及极化和不平等指数的估计。