Signal detection theory (SDT) and the sequential probability ratio test (SPRT) are two leading models for binary perceptual decision-making in psychology and neuroscience. For initiates in this research area, the foundational relationship between SDT and the SPRT, or between statistical inference models and their mechanistic counterparts, can be unclear because many decision-making models in use today are much extended versions of the original, simpler models that contain the essence of these models’ claims to optimality. For those familiar with the models, it would be useful to have a quantitative comparison between their performance as multi-sample hypothesis tests. In this tutorial review of SDT and the SPRT, we emphasize that SDT and the SPRT differ only in their sampling procedures and so can be viewed as static and dynamic variants from the same family of hypothesis tests. Furthermore, we map the sample efficiency gains of using the SPRT over a multi-sample version of SDT by a novel construction of ROC curves. The goal of this paper is to provide a compact treatise on the statistical underpinnings of SDT and the SPRT, how they relate to the drift–diffusion model (DDM), and what these models imply for the physical implementation of evidence gathering and optimal decision making in biological systems.

信号检测理论 (SDT) 和序列概率比测试 (SPRT) 是心理学和神经科学中二元感知决策的两个主要模型。对于该研究领域的初学者来说，SDT 和 SPRT 之间或统计推理模型与其机制对应物之间的基本关系可能不清楚，因为当今使用的许多决策模型是原始、更简单模型的扩展版本，其中包含这些模型声称最优的本质。对于熟悉这些模型的人来说，将它们作为多样本假设检验的性能进行定量比较会很有用。在本教程回顾 SDT 和 SPRT 中，我们强调，SDT 和 SPRT 仅在采样程序上有所不同，因此可以将其视为来自同一假设检验系列的静态和动态变体。此外，我们通过 ROC 曲线的新构造映射了在 SDT 的多样本版本上使用 SPRT 的样本效率增益。本文的目的是提供一篇关于 SDT 和 SPRT 的统计基础、它们与漂移扩散模型 (DDM) 的关系以及这些模型对证据收集和最佳决策的物理实施的意义的紧凑论文在生物系统中。