P/S 05 · Psychophysics and signal detection
Thresholds and Decisions
Interpret absolute and difference thresholds, Weber’s law and signal detection data.
Passage
Psychophysics is the study of how physical stimuli relate to the sensations they produce. The absolute threshold is the lowest intensity of a stimulus that a person can detect, usually defined as the intensity detected on half of the trials. The difference threshold, or just-noticeable difference (JND), is the smallest change in a stimulus that a person can detect. According to Weber’s law, the JND is a constant fraction of the starting intensity. Signal detection theory adds that detecting a faint stimulus depends on two things: the person’s sensitivity to the signal, and the person’s response criterion, which is how much evidence the person needs before saying that the signal is present.
Part 1. In a hearing experiment, 40 adults listen through headphones to short bursts of a tone at different intensities, in a quiet room. On each trial they say whether they heard the tone. Table 1 shows the percentage of trials on which the tone was reported at each intensity.
Table 1. Detection of a tone at different intensities.
| Tone intensity (dB) | Percentage of trials with a ‘yes’ response |
|---|---|
| 0 | 5 |
| 10 | 20 |
| 20 | 50 |
| 30 | 80 |
| 40 | 98 |
Part 2. In a second experiment, participants lift a standard weight and then a comparison weight and report whether the second one felt heavier. The researchers find the smallest difference that participants detect on 75% of the trials. Table 2 shows the JND for three standard weights.
Table 2. Difference thresholds for lifted weights.
| Standard weight (g) | JND (g) |
|---|---|
| 100 | 2 |
| 200 | 4 |
| 400 | 8 |
Part 3. In a third experiment, the tone from Part 1 is set to a faint, constant level, and it is presented on half of the trials. On the other half of the trials, only background noise is presented. Participants say ‘yes’ if they think the tone was present. A hit is a ‘yes’ on a trial with the tone, and a false alarm is a ‘yes’ on a trial without it. Across three conditions, the researchers change only the pay-off for responses. In the neutral condition, correct answers are worth the same. In the liberal condition, a hit is worth more than a correct rejection. In the conservative condition, a false alarm is penalized heavily. Table 3 shows the results.
Table 3. Hit and false alarm rates in three pay-off conditions.
| Condition | Hit rate (%) | False alarm rate (%) |
|---|---|---|
| Neutral | 70 | 15 |
| Liberal | 90 | 40 |
| Conservative | 45 | 5 |
The researchers point out that the participants’ ability to separate the tone from the noise, as measured by a statistic that combines the hit and false-alarm rates, is about the same in all three conditions. They also note that all participants were tested in a quiet room, with no distracting sounds, and that the order of the three conditions was varied across participants.
Questions
Question 1 of 6
Based on Table 1, what is the absolute threshold for the tone?
At 0 dB the tone is reported on only 5% of trials, which is much less than half.
The tone was reported on 20% of trials at 10 dB, which is less than the 50% used in the definition.
At 40 dB the tone is reported on 98% of trials, well above the criterion of half.
Why the answer is what it is
The absolute threshold is the intensity detected on 50% of trials. In Table 1, the response rate at 20 dB is 50%.
Review: Sensation & Perception · Hearing & Sound · Somatosensation
Question 2 of 6
Based on Table 2, what is the JND likely to be for a standard weight of 500 g?
This is 1% of 500 g. In Table 2 the JND is 2% of the standard weight at every weight.
This is the JND for the 400 g weight. A heavier standard weight should have a larger JND.
This would be a JND of 4%, which is twice the fraction observed.
Why the answer is what it is
In each row the JND is 2% of the standard weight (2 ÷ 100, 4 ÷ 200, 8 ÷ 400). By Weber’s law, the JND for 500 g is 0.02 × 500 = 10 g.
Review: Sensation & Perception · Hearing & Sound · Somatosensation
Question 3 of 6
Which statement best describes the principle shown by Table 2?
The JND doubles when the standard weight doubles. It is not constant.
The larger JND for heavier weights means that a bigger change is needed. A given change is harder to detect.
The smallest JND is 2 g. People can detect much smaller differences than 100 g.
Why the answer is what it is
In Weber’s law, ΔI/I is constant. Here the JND is 2% of the standard weight at all three weights, so the amount that must be added grows in proportion to the starting weight.
Review: Sensation & Perception · Hearing & Sound · Somatosensation
Question 4 of 6
In Part 3, going from the neutral condition to the liberal condition raises both the hit rate and the false alarm rate. What is the best interpretation?
The passage says that only the pay-off changed, and the tone stayed at the same level.
If sensitivity had improved, hits would rise while false alarms would stay the same or fall.
Random responding would produce about the same hit rate and false-alarm rate, not a hit rate of 90%.
Why the answer is what it is
Both rates rose because the pay-off encouraged participants to say ‘yes’ on weaker evidence. This is a shift in response criterion, not in sensitivity, which the passage says stayed about the same.
Review: Sensation & Perception · Hearing & Sound · Somatosensation
Question 5 of 6
Which change would be expected in the conservative condition compared with the neutral condition?
Table 3 shows fewer hits (45%), and the passage says that sensitivity is similar in all conditions.
This is the pattern of the liberal condition. In the conservative condition, participants are penalized for false alarms.
The rates differ because the pay-off changes the response criterion. The hit rate falls from 70% to 45%.
Why the answer is what it is
A penalty for false alarms makes people more cautious. They say ‘yes’ only when they are fairly sure, so both hits and false alarms fall (70 to 45 and 15 to 5).
Review: Sensation & Perception · Hearing & Sound · Somatosensation
Question 6 of 6
A participant who lifts a weight for several minutes stops noticing the pressure of the handle on the skin of the hand. This is an example of:
A false alarm is a ‘yes’ response when the stimulus is not present.
The example concerns touch and a constant stimulus, not the threshold for a tone.
A fading sensation is a decrease in response, not an increase in sensitivity.
Why the answer is what it is
Sensory receptors respond strongly to a change and less to a constant stimulus. The fading of the pressure sensation from an unchanging handle is sensory adaptation.
Review: Sensation & Perception · Hearing & Sound · Somatosensation
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