There are two main objectives of this paper. One is to review the current Thurstonian models for the conventional and modified triangle and duo‐trio methods. Another objective is to develop Thurstonian models for, and assess the performances of the paired triangle and paired duo‐trio methods with AB and BA pairs. Bradley's models based on the noncentral F distribution for the triangle and duo‐trio methods are revisited and are used to derive the psychometric functions for the paired versions of the triangle and duo‐trio methods. The simulation‐derived psychometric functions for the new methods are also produced. The performances of the new methods in both difference and similarity/equivalence tests are explored and show that the new methods are more powerful than most of the conventional unspecified forced‐choice methods and are similar to the unspecified tetrad.

中文翻译：

---

回顾和发展三角形和二重奏方法以及方法配对版本的瑟斯顿模型

本文有两个主要目标。一种是回顾常规和改进三角法和二重奏法的当前Thurstonian模型。另一个目标是开发Thurstonian模型，并用AB和BA对评估成对的三角形和成对的duo-trio方法的性能。基于非中心F的Bradley模型重新讨论了三角法和双核方法的分布，并用于导出配对的三角法和双核方法的心理测量函数。新方法的模拟派生的心理测量函数也已生成。对差异和相似性/等效性测试中新方法的性能进行了探索，结果表明，新方法比大多数传统的未指定强制选择方法更强大，并且与未指定的四元组相似。