Mathematical Psychology
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SDT in Psychophysics

SDT revolutionized psychophysics by replacing the classical threshold concept with a continuous sensitivity measure, showing that detection performance reflects both sensory ability and decision strategy.

Signal Detection Theory was originally developed to address fundamental questions in psychophysics: Can observers detect a fixed signal perfectly on some trials and not at all on others (threshold theory), or is detection performance always graded, reflecting continuous sensory processing corrupted by noise? SDT's answer — continuous processing with a moveable criterion — transformed the field.

Detection and Discrimination

Psychophysical SDT Applications Absolute detection: signal vs. no signal → d′
Discrimination: stimulus A vs. stimulus B → d′(A,B)
Identification: assign stimuli to categories → information transmission

Connection to Weber's Law:
d′ ∝ ΔI/σ, and if σ ∝ I, then d′ ∝ ΔI/I = constant (Weber)

Resolving the Threshold Debate

The classic catch trial analysis demonstrates the SDT framework: when blank (noise-only) trials are included, observers produce false alarms, and the false alarm rate varies with instruction and motivation. This continuous tradeoff between hits and false alarms is predicted by SDT but not by strict threshold theory. The curved ROC functions observed in psychophysical experiments provided definitive evidence against the high-threshold model.

SDT also provided a formal connection between psychophysics and the rest of psychology. The same mathematical framework that describes detecting a faint tone applies to recognizing a face, diagnosing a disease, or evaluating the quality of a product — unifying diverse psychological phenomena under a common quantitative umbrella.

Interactive Calculator

Each row represents a trial: trial_type (signal or noise) and response (yes or no). Computes hit rate, false-alarm rate, d′, criterion c, and β.

Click Calculate to see results, or Animate to watch the statistics update one record at a time.

Related Topics

References

  1. Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. Wiley. https://doi.org/10.1901/jeab.1969.12-475
  2. Swets, J. A., Tanner, W. P., & Birdsall, T. G. (1961). Decision processes in perception. Psychological Review, 68(5), 301–340. https://doi.org/10.1037/h0040547
  3. Swets, J. A. (1961). Is there a sensory threshold? Science, 134(3473), 168–177. https://doi.org/10.1126/science.134.3473.168
  4. Gescheider, G. A. (1997). Psychophysics: The fundamentals (3rd ed.). Lawrence Erlbaum Associates. https://doi.org/10.4324/9780203774458

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