Signal detection theory in 5 minutes
Accuracy is a misleading summary of performance on a detection task. Two participants can both score 75 % correct and be doing completely different things: one is a careful discriminator, the other says »yes« to everything. Signal detection theory separates those two participants into distinct numbers.
The four outcomes
Every trial lands in one of four cells:
- Hit — signal present, participant says »yes«.
- Miss — signal present, participant says »no«.
- False alarm — signal absent, participant says »yes«.
- Correct rejection — signal absent, participant says »no«.
Hit rate (H) is hits ÷ (hits + misses). False-alarm rate (F) is false alarms ÷ (false alarms + correct rejections). Both are between 0 and 1.
d′ (sensitivity)
d′ = z(H) − z(F), where z() is the inverse standard normal.
d′ is how well the participant can separate signal from noise. A d′ of 0 is chance; 1 is fair; 2 is good; 3+ is expert-level. d′ is independent of where the participant sets their decision threshold — it captures the perceptual quality of the evidence, not the response strategy.
c (bias)
c = −0.5 × (z(H) + z(F)).
c is the participant's response criterion. Negative c means »trigger-happy« (tends to say »yes«); positive c means »conservative« (tends to say »no«). Two participants with the same d′ can have very different c. Reporting only accuracy hides that.
Why it matters
- Publication rigor. Reviewers of perception and memory work expect d′ and c, not raw accuracy.
- Bias detection. If one condition shifts c rather than d′, you have a response-strategy artefact, not a perceptual effect.
- Edge cases. H = 1 or F = 0 sends z() to infinity. Apply a log-linear correction:
H_adj = (hits + 0.5) ÷ (N + 1).
What SciBLIND computes
Every DISCRIMINATION study export includes d_prime and c per participant per condition, with the log-linear correction already applied. The methodology PDF cites the formulas and the correction so your statistical report matches the numbers.