This outline summarizes major points covered in lecture. It is not intended to replace your own lecture notes.
TSD & Response Bias Summary
Changes in listener sensitivity must be measured under similar conditions of response bias (i.e.
under conditions of constant response bias).
o Such changes are observed as an increase (decrease) in hits and decrease (increase) in
Changes in listener response bias must be measured under conditions of similar listener sensitivity
(i.e. under conditions of constant listener sensitivity).
o Such changes are observed as an increase (decrease) in hits and an increase (decrease) in
false alarms – hits and false alarms go together (change same direction).
Receiver Operator Characteristic (ROC)
Changes in sensitivity, when response bias does not change, are measured and observed as an
increase (decrease) in hits and decrease (increase) in false alarms.
Changes in response bias, when sensitivity does not change, are measured and observed as
increase (decrease) in hits and increase (decrease) in false alarms – hits and false alarms go
Area under ROC curve is a measure of response sensitivity unaffected by listener response bias.
Psychometric function derived from values of the area under the ROC curve (integrate area).
o Calculate area under ROC curve for each stimulus condition.
o As stimulus SPL changes, area under ROC curve will vary between 50%-100%.
o Area under ROC curve increases as S’s performance increases.
o Area under ROC curve indicates how good S’s are at detecting signal.
o Derive psychometric function using the ROC and notice that the mid-point is at 75%.
Alternative Sensitivity Measure: % Correct
An alternative measure of a S sensitivity is percent correct trials for each stimulus condition:
o P(C) = p(hits) x p(signal) + ([1-p(falsealarms]) x p(nosignal))
o P(C) = p(hits) x p(signal) + [p(correctrejection) x p(nosignal)]
If signal is present in 50% of trials (i.e. 50% catch trials), then the above relationship reduces to:
o P(C) = ( p(hits) + (1-p(falsealarms)) ) / 2
o P(C) = ( p(hits) + p(correctrejection) ) / 2
Typically, 2 stimuli are presented to a listener.
Listener is asked to adjust physical dimension of Stimulus #1 to match physical dimension of
E.g. Equal loudness contour: change the loudness of a 500 Hz tone until you perceive it to be
equally loud to a 2000 Hz tone.
Having Ss vary and match different physical dimensions between stimuli allows the experimenter to
determine which aspects of a stimulus make it appear similar (equal) to another stimulus.
Stimulus thresholds define the ranges of detection for parameters of acoustic signals (e.g.
frequency, intensity, phase, etc.)
Thresholds do not capture a Subject’s sensitivity to changes in a stimulus parameter.
Psychophysicists also interested in measuring the smallest difference between physical stimuli
that will just barely cause a difference in sensation.
How does perception scale with changes in stimulus modality and magnitude?
2 famous psychologists looked at the question of how differences in stimulus intensity (magnitude)
map onto perception.
Ernst Heinrich Weber
Devised method for measuring the existence of internal (mental) events; formulated the theory of
signs; with his brother he studied acoustics and wave motion.
Discovered psychology’s 1 empirical constant – Weber Fraction. This concept uses the
awareness of a difference in sensation to measure a difference in sensation.
Psych 3A03 08 November 2012
Week 10 Dr. Paul A. Faure Weber Fraction: the increase in stimulus intensity necessary to produce an increase in sensation is
not a fixed quantity but is a constant proportion of the smaller intensity.
That is, the JND (just noticeable difference) between two stimuli varies proportionally to the smaller
of the two stimuli.
Gustav Theodor Fechner
Studied anatomy under E.H. Weber
Developed first theory of hypothesis testing; technical foundations for descriptive statistics; ideas
about consciousness; first measurement of a features of the mind.
His book Elemente der Psychophysik (1860) describes methods for quantifying the relationships
between sensory stimuli and perception.
Father of modern psychophysics
Research on the accuracy of perceptual representations of physical stimuli considered to be the
bedrock of modern psychophysics.
Realized that the relationships between stimulus events and mental events might be reducible to
Fechner termed the perceptual difference threshold as Just Noticable Difference (JND) threshold.
JND is a psychological entity expressed in units of stimulus magnitude.
JND scale: equal sensation intervals.
Fechner’s Law: magnitude of sensory response (R) increases with logarithm of stimulus intensity
(S) above stimulus threshold (S0). R=k log S
Weber-Fechner Law Incomplete
To a first approximation it describes how changes in perception are related to changes in stimulus
However, the WF Law is incomplete (the so called near misses to Weber’s Law) and is too inflexible
across different sensory modalities.
WF Law now superseded by Steven’s Power Law first formulated by the famous psychologist
Stanley Smith Stevens.
Stevens’ Power Law: subjective scaling of stimulus magnitude relates to physical intensity of
stimulus as an exponential function, not as a logarithmic function.
Scaling procedures designed to obtain information about subjective perception of stimulus.
Scaling procedures attempt to quantify magnitude of subjective experience (loudness, pitch,
location) to actual physical changes in stimulus (SPL, frequency, phase).
Scaling measures are reliable and valid.
Goal of scaling procedures: obtain scale relating perceived magnitude with physical magnitude.
Various types of scaling procedures.
o Ratio Compression
o Cross-Modality Matching
Stevens’ Power Law
P = kS where:
o P = perceived magnitude of stimulus
o S = physical magnitude of stimulus (physical units)
o k = constant
o n = exponent (varies with sensory modality)
When you take the log of both sides of this equation, you get a straight line with a slope of n.
That the data have a linear fit on a log-log plot means that the magnitude of subjective experience is
related to a magnitude of physical stimulus by a power function.
Knowing power function allows experimenter to compute stimulus magnitude for achieving a desired
subjective experience (e.g. doubling loudness).
Measuring Auditory Sensitivity
Psych 3A03 08 N