MCAT content library / Psychology & sociology / Signal detection: sensitivity and the response criterion
A higher hit rate can come with more false alarms. Trace the evidence and the decision rule separately.
About 16 minutes, including the worked examples and checks.
Useful foundations
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Separate the evidence from the decision
A listener reports more faint tones after being told that misses cost extra points. Did hearing improve, or did the listener become more willing to say “present”? Signal detection theory gives these possibilities separate places in an explanation. AAMC includes it within sensory processing and psychophysics.1
Two trials with the same physical stimulus need not produce identical internal evidence. Background noise, sensory variation and the observer’s processing can make the evidence uncertain. Discriminability concerns how distinguishable the signal and noise evidence distributions are. The response criterion is the cutoff used to translate that evidence into a report. A decision can change even when the information available for discrimination stays the same.2
Every response needs its true trial type
First identify whether the experimenter actually presented the signal. Then classify the response. A confident “yes” is not automatically a hit, and a “no” is not automatically a miss.2
| Actual trial | Reports present | Reports absent |
|---|---|---|
| Signal present | Hit | Miss |
| Signal absent | False alarm | Correct rejection |
The hit rate uses signal-present trials as its denominator: hits / (hits + misses). The false-alarm rate uses signal-absent trials: false alarms / (false alarms + correct rejections). These answer different conditional questions. Neither is the fraction of all “present” reports that were correct.
Worked model: identical evidence, two cutoffs
The tone task and all numerical values below are original teaching examples. Suppose a simplified observer assigns each trial an evidence score from 0 to 4. Larger scores favor a tone. The following frequencies summarize 100 signal-present trials and 100 signal-absent trials. Treat these distributions as fixed for the comparison; only the decision rule changes.
| Evidence score | Signal absent: trials | Signal present: trials |
|---|---|---|
| 0 | 40 | 2 |
| 1 | 30 | 8 |
| 2 | 20 | 20 |
| 3 | 8 | 30 |
| 4 | 2 | 40 |
Under the more conservative rule, the observer reports “present” only for scores 3 or 4. Signal-present trials produce 30 + 40 = 70 hits and 30 misses. Signal-absent trials produce 8 + 2 = 10 false alarms and 90 correct rejections. The hit rate is 70%; the false-alarm rate is 10%.
Now lower the cutoff to include score 2. The added bin contains 20 trials of each type. Hits rise to 90, but false alarms also rise to 30. Misses fall to 10 and correct rejections fall to 70. No frequency in the evidence table moved. The decision rule alone changed which bins count as “present.” This is the characteristic tradeoff when a criterion shifts across fixed distributions.3
| Rule | Hits / 100 signal trials | False alarms / 100 noise trials | Overall correct / 200 |
|---|---|---|---|
| Score ≥ 3 | 70 | 10 | 160 / 200 |
| Score ≥ 2 | 90 | 30 | 160 / 200 |
Both rules yield 80% overall accuracy in this balanced example. That equality does not mean the rules make identical errors. One misses more tones; the other reports more tones that were absent. Overall accuracy conceals that difference and also depends on how common each trial type is.
Why a different criterion can be reasonable
Imagine that a miss loses five task points and a false alarm loses one. The conservative rule loses 30 × 5 + 10 = 160 points. The liberal rule loses 10 × 5 + 30 = 80. If the penalties are reversed, the preferred rule reverses: the totals become 80 and 160. The evidence has not improved in either calculation. The task values a different balance of errors.
Signal frequency and the consequences of each response can influence criterion choice. A theory of an optimal decision rule is a prediction under specified payoffs and assumptions; it does not establish that every observer chooses that rule.3 In an experiment, check the actual response pattern after the instructions change.
For example, if tones become uncommon, a participant could obtain high overall accuracy by usually reporting “absent.” To compare detection across blocks, keep the conditional hit and false-alarm rates visible. Otherwise, a change in the mixture of trials can be mistaken for a change in the observer.
What would stronger discrimination look like?
Moving a single cutoff across unchanged ordered evidence cannot simultaneously increase the hit rate and decrease the false-alarm rate. Better separation of signal and noise evidence can permit that combination. An ROC plot places the false-alarm rate on the horizontal axis and the hit rate on the vertical axis; changing the criterion traces a tradeoff for a given discrimination model.3
In the worked model, a “present” rule that accepts a larger set of evidence scores must accept at least as many trials of both types. This provides a direct check on a proposed explanation. If someone explains higher hits and fewer false alarms solely by “saying yes more readily,” their account does not fit this fixed-distribution model.
A real before-and-after table still requires care. The signal may have become louder, attention may have changed, participants may have learned useful features, or the model’s assumptions may fail. Rates support a statement about task performance under the supplied conditions. They do not by themselves locate a receptor change, demonstrate permanent learning or identify the cause of improved separation.
Carry the comparison into a new task
Use the same sequence for a visual flash, a remembered word or an inspection task: identify the true states, sort the four outcomes, calculate rates within each true state, and ask what changed. If only payoffs changed while evidence distributions were held fixed, consider a criterion shift. If the pattern cannot arise from that shift, look for a change in available information or a failed assumption. Keep “more reports,” “more correct reports” and “better discrimination” as separate claims.
ACTIVE PRACTICE · SIGNAL DETECTION
Move the Decision Cutoff, Not the Evidence
The original tone task has 100 signal-present and 100 signal-absent trials, with fixed evidence scores 0–4. Present-trial counts are 2, 8, 20, 30, 40; absent-trial counts are 40, 30, 20, 8, 2. Choose when a score is high enough to report “tone present.”
| True condition | Report present | Report absent |
|---|---|---|
| Tone present (100) | hits | misses |
| Tone absent (100) | false alarms | correct rejections |
Hit rate ; false-alarm rate ; accuracy across these 200 balanced trials.
At criterion ≥3: 70 hits and 10 false alarms. The evidence distribution has not changed.
A cutoff of 0 means every trial is called present; 5 means none is. Equal overall accuracy can conceal different kinds of error, and different prevalence changes the accuracy calculation.
Check your reasoning
Choose an answer before opening its feedback. Each option explains the reasoning behind that choice.
Check 1
An observer reports a light whenever its evidence score exceeds a cutoff. The signal-present and signal-absent evidence distributions stay fixed. The cutoff is lowered into a region containing trials from both distributions. Which joint change does this model predict?
A. A lower hit rate and a lower false-alarm rate.
Review this choice. Both rates would fall after raising the cutoff. Lowering it accepts additional scores from both trial types.
B. A lower hit rate and a higher false-alarm rate.
Review this choice. The lower cutoff cannot remove a signal-present score that was previously accepted. Hits increase, together with false alarms.
C. A higher hit rate and a lower false-alarm rate.
Review this choice. This describes a possible improvement in discrimination, but it cannot result solely from accepting a larger set of scores from both unchanged distributions.
D. A higher hit rate and a higher false-alarm rate.
Correct. Lowering the cutoff adds accepted scores from both distributions. More signal trials become hits, and more noise trials become false alarms.
The principle to carry forward
For a criterion-only change, follow which scores move from “absent” to “present” in each true trial type.
Check 2
In matched detection blocks, the hit rate changes from 70% to 85% while the false-alarm rate changes from 30% to 15%. Assume an ordered evidence score and one cutoff in each block. Which conclusion is best supported?
A. A criterion-only shift across fixed evidence distributions is insufficient to explain both changes.
Correct. A lower cutoff increases both rates; a higher cutoff decreases both. The opposing changes require something beyond a criterion-only shift under the stated model.
B. A higher cutoff across fixed evidence distributions explains the improved hit and false-alarm rates.
Review this choice. A higher cutoff can reduce false alarms, but it also removes signal trials from the accepted set and therefore cannot increase hits.
C. A lower cutoff across fixed evidence distributions explains the improved hit and false-alarm rates.
Review this choice. A lower cutoff can increase hits, but it also accepts additional noise scores and therefore cannot reduce false alarms.
D. An unchanged hit-to-false-alarm difference establishes equal discrimination in the two blocks.
Review this choice. The difference is not unchanged: it rises from 40 to 70 percentage points. More fundamentally, an arbitrary rate difference is not a complete model of the evidence distributions.
The principle to carry forward
Identify which model explanation the pattern rules out without assigning an unmeasured biological cause.
Check 3
A task contains 100 signal-present trials and 400 signal-absent trials. The observer makes 80 hits, 20 misses, 80 false alarms and 320 correct rejections. Among all reports of “present,” what fraction are correct?
A. 20%
Review this choice. 80/400 is the false-alarm rate. The question conditions on the response “present,” whose denominator includes both hits and false alarms.
B. 50%
Correct. There are 80 + 80 = 160 “present” reports. Of those, 80 are hits, so 80/160 = 50%.
C. 80%
Review this choice. 80/100 is the hit rate, and 400/500 is overall accuracy here. Neither denominator is all “present” reports.
D. 90%
Review this choice. The supplied counts do not yield 90% for the requested conditional proportion. Build the response-defined denominator before dividing.
The principle to carry forward
A rate among actual signals and a rate among positive reports condition on different sets of trials.
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Related lessons
- Sensory thresholds, adaptation, and habituation
- Psychological Measurement: What Does the Score Mean?
- Experimental Controls: What a Comparison Can Show
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Sources
1. AAMC: Content Category 6A — Sensing the environment