The statistics of optimal decision making: Exploring the relationship between signal detection theory and sequential analysis

Thom Griffith*, Sophie Anne Baker, Nathan F. Lepora

*Corresponding author for this work

Research output: Contribution to journalReview article (Academic Journal)peer-review

13 Citations (Scopus)
75 Downloads (Pure)


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.

Original languageEnglish
Article number102544
JournalJournal of Mathematical Psychology
Early online date19 May 2021
Publication statusPublished - Aug 2021

Bibliographical note

Funding Information:
This work was supported by a Leverhulme Trust Research Leadership Award ( RL-2016-039 ) to Prof. Nathan Lepora.

Publisher Copyright:
© 2021 The Author(s)


  • Drift–diffusion model
  • Perceptual decision making
  • ROC analysis
  • Sequential probability ratio test
  • Signal detection theory


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