Eyewitness Identification: A Signal Detection Theory Lab

Memory & Decision

Memory strength d′ (target vs. lure) 1.5

Decision criterion c 0.5

Lineup procedure

Run Witnesses

Hit Miss False alarm Correct rejection

Live Readouts

Hit rate

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False alarm rate

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Estimated d′

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Witnesses run

How it works

Each witness's memory produces a continuous strength of recognition when they view a lineup member. Signal Detection Theory models this as two overlapping Gaussians on that strength axis:

Lure (innocent suspect):  strength ~ N(0, 1)
Target (guilty suspect):  strength ~ N(d′, 1)

The witness says "that's them" whenever the strength exceeds their internal decision criterion c. This single rule produces four outcomes, and their probabilities follow directly from the normal CDF Φ:

Hit rate         H = 1 − Φ(c − d′)   (target present, correctly identified)
False-alarm rate F = 1 − Φ(c)        (target absent, innocent suspect picked)
Miss rate        = 1 − H
Correct rejection = 1 − F

Given empirical H and F from real trials, the discriminability implied by the data can be recovered without knowing the true d′:

d′(estimated) = Φ⁻¹(H) − Φ⁻¹(F)

d′ slider — how distinguishable the guilty suspect's memory trace truly is from an innocent lure; higher separates the two curves.
Criterion c slider — the witness's response bias. A low c means "trigger-happy" identifications (more hits, but more false alarms too); a high c is cautious (fewer false alarms, but more misses).
Sequential procedure — showing faces one at a time (instead of all together) is modelled here as raising the effective criterion, which is the classic empirical finding: sequential lineups cut false identifications of innocent suspects at some cost to hit rate.
Each dot in the 3D scene is one simulated witness: its position along the strength axis is a random draw from the relevant Gaussian, coloured by which of the four outcomes it produced.

Real-world relevance: this exact H/F/d′ framework is what forensic-psychology researchers (e.g. Wells, Loftus, Steblay) use to compare lineup procedures and argue for reform in police identification protocols.

Lure distribution N(0,1) Target distribution N(d′,1) Decision boundary c

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