An explorable explanation of Signal Detection Theory

Welcome to d′etectable, an interactive introduction to Signal Detection Theory (SDT). This site uses manipulable diagrams, dynamic tables, and live equations to explain the motivation, conceptualization, and application of SDT.

SDT was originally developed to understand the decisions of radar operators attempting to detect the faint traces of enemy aircraft, bogeys, among the spurious flashes on the radar screen (Marcum, 1947; Peterson, Birdsall, & Fox, 1954; Tanner & Swets, 1954). The fundamental question was: How does a person decide if they are seeing signal or noise?

In answering this question, researchers attempted to decompose the underlying cognitive process into its constituent parts. Then they specified a theory describing these parts in a formal mathematical model. The result was Signal Detection Theory (Green & Swets, 1966).

SDT can be viewed as an early and classic example of computational cognitive neuroscience — the interdisciplinary study of mind, brain, and behavior through the melding of computational, psychological, and neuroscientific approaches. It does this by linking observed behavior to known neural mechanisms through a formal computational account of cognition (Gold & Shadlen, 2007).

SDT simply and elegantly explains patterns found in actual perceptual decision-making data; it makes non-trivial predictions that can be tested; and it fits into a developing understanding of perceptual decision making as neural evidence accumulation (Gold & Shadlen, 2002). Thus the importance of SDT arises from its generality, specificity, and plausibility. As a result, it has been applied to a diverse set of problems, from memory retrieval (Banks, 1970; Berry, Shanks, & Henson, 2008) to medical decision making (Lusted, 1971).

This site approaches SDT from multiple complementary points of view. First, we use SDT to fit your empirical data from an example task, and consider how well the theory accounts for the data. Second, we use SDT to make predictions by running simulations with an SDT-based model performing the task and generating synthetic data. And third, we explore the space of possible results that can be generated by SDT, providing an existence proof for its capabilities.

So let’s get started!