In research, policy, and practice, continuous variables are often categorized. Statisticians have generally advised against categorization for many reasons, such as loss of information and precision as well as distortion of estimated statistics. Here, a different kind of problem with categorization is considered: the idea that, for a given continuous variable, there is a unique set of cut points that is the objectively correct or best categorization. It is shown that this is unlikely to be the case because categorized variables typically exist in webs of statistical relationships with other variables. The choice of cut points for a categorized variable can influence the values of many statistics relating that variable to others. This essay explores the substantive trade-offs that can arise between different possible cut points to categorize a continuous variable, making it difficult to say that any particular categorization is objectively best. Limitations of different approaches to selecting cut points are discussed. Contextual trade-offs may often be an argument against categorization. At the very least, such trade-offs mean that research inferences, or decisions about policy or practice, that involve categorized variables should be framed and acted upon with flexibility and humility.

中文翻译：

---

切入点和上下文

在研究、政策和实践中，经常对连续变量进行分类。出于多种原因，统计学家通常建议不要进行分类，例如信息和精度的丢失以及估计统计数据的失真。在这里，考虑了一种不同类型的分类问题：对于给定的连续变量，存在一组独特的切点，即客观上正确或最佳的分类。结果表明，情况不太可能是这样，因为分类变量通常存在于与其他变量的统计关系网络中。分类变量的切点选择会影响将该变量与其他变量相关的许多统计数据的值。本文探讨了在对连续变量进行分类的不同可能切点之间可能出现的实质性权衡，因此很难说任何特定的分类在客观上是最好的。讨论了选择切割点的不同方法的局限性。上下文权衡通常可能是反对分类的论据。至少，这样的权衡意味着涉及分类变量的研究推论或关于政策或实践的决定应该以灵活和谦逊的方式制定和采取行动。