Psych/soc, and one of the few topics there with actual structure to it. It appears in perception passages and in anything involving diagnostic decisions.

The Problem It Solves

Classical psychophysics assumed a fixed sensory threshold — stimuli above it are detected, below it are not. That model fails on a simple observation: whether someone reports detecting a faint stimulus depends on more than the stimulus. It depends on expectations, motivation, and the consequences of being wrong.

Signal detection theory separates these into two independent components: sensitivity (how well you can actually discriminate signal from noise) and response bias (how willing you are to say "yes").

The core claim is that there is always noise in the system. Even with no stimulus present, background neural activity fluctuates. Detection is not "is there a signal" but "is this activity level more likely to have come from noise alone or from signal plus noise."

The Four Outcomes

Two possible states of the world crossed with two possible responses:

	Signal present	Signal absent
Said yes	Hit	False alarm
Said no	Miss	Correct rejection

Hits and correct rejections are correct. Misses and false alarms are the two error types.

This maps directly onto statistics: a false alarm is a Type I error, a miss is a Type II error. And onto medicine: a false alarm is a false positive, a miss is a false negative.

d′ (Sensitivity)

d-prime measures how far apart the noise distribution and the signal-plus-noise distribution are, in standard deviation units.

Higher d′ means the two distributions overlap less and the task is easier — better signal, better sensory system, or better attention. d′ = 0 means the distributions are identical and performance is at chance.

d′ is independent of where you set your criterion. It is a property of the observer's discriminative capacity, not their decision policy.

β (Criterion / Response Bias)

The criterion is the cutoff on the internal evidence axis above which you say "yes."

Shift the criterion left (liberal / low β): more hits, more false alarms. You say yes readily.

Shift the criterion right (conservative / high β): fewer false alarms, more misses. You require strong evidence.

The critical insight: moving the criterion trades hits against false alarms without changing sensitivity. You cannot improve both error types by adjusting your bias. Only increasing d′ does that.

What Moves the Criterion

Payoffs and costs. If missing the signal is catastrophic and false alarms are cheap, you go liberal. A radiologist screening for cancer accepts false positives to avoid misses. A smoke detector is calibrated the same way — occasional false alarms from burnt toast are better than missing a fire.

Prior probability. If signals are rare, you become conservative. This is base rate sensitivity, and failing to account for it is base rate neglect.

Expectations and motivation. Being told to expect a stimulus makes detection more likely — partly a real attentional effect on d′, partly a criterion shift.

The ROC Curve

Plotting hit rate against false alarm rate as the criterion varies gives the receiver operating characteristic curve.

• The diagonal line is chance performance, d′ = 0.
• Curves bowing toward the upper left indicate higher sensitivity.
• Movement along a single curve is a criterion change.
• Movement between curves is a sensitivity change.

Area under the curve summarizes overall sensitivity. This is the same ROC analysis used to evaluate diagnostic tests.

Related Threshold Concepts

Absolute threshold — the minimum stimulus intensity detected 50% of the time. The 50% is there precisely because there is no sharp cutoff.

Difference threshold (JND) — the smallest detectable difference between two stimuli.

Weber's law — the JND is a constant proportion of the original stimulus, not a constant amount. ΔI/I = k. You notice a 1 lb change on a 10 lb weight but not on a 100 lb weight.

Subliminal stimuli fall below the absolute threshold. They can produce measurable priming effects, but the popular claim that they drive complex behavior is not supported.

What Gets Tested

• Classifying a described outcome into hit / miss / false alarm / correct rejection
• Recognizing that a change in payoffs shifts criterion, not sensitivity
• Reading an ROC curve for which observer is more sensitive
• Distinguishing d′ from β when a passage describes an intervention
• The medicine mapping — false positive and false negative

The most common trap: a passage describes participants becoming "better at detecting" something after being told to expect it, and asks whether sensitivity improved. Often the correct answer is that the criterion shifted — hits went up but so did false alarms, which is a bias change, not a sensitivity change. Check whether false alarms moved in the same direction as hits.