W2
Threshold
E-module - Threshold
After the e-modules, the student is expected to:
Understand and explain different concepts and definitions of thresholds
Understand, explain, and apply different methods of measuring thresholds
Understand, apply and interpret different psychophysical functions in relation to thresholds
E-module – Thresholds: the laws of Weber, Fechner and Stevens
A psychophysical function describes the relationship between the psychophysical function and
perceived intensity of a sensory stimulus.
Weber’s law
This law states that the amount of a physical stimulus which is needed to increase to be ‘just
perceivably different’ is a constant linear ratio.
Delta intensity/intensity = constant (k) over the range of possible concentrations
A definition of the Weber fraction is the ‘Just-Noticeable-Difference’ (JND) = the difference between
two stimuli that can be detected or perceived in 50% of the cases.
For both glucose and fructose, Weber's Fraction is between 0.10 and 0.15 (or 10-15%). This means
that when you have a solution with 10 grams of glucose per 100 grams, an increase in concentration
of ~10%, to 11 grams glucose per 100 grams, is just perceivably more sweet. Similarly, with 30 grams
per 100 grams, you would need an increase of 3 grams (10%, or a fraction of 0.10), to 33 grams per
100 grams, for it to be just perceivably more sweet.
Fechner’s law
Fechner’s law is built upon Weber’s law and states that the subjective sensation is proportional to the
logarithm of the stimulus intensity.
,By adding up JNDs, you can construct a psychophysical function between physical stimulus intensity
(or concentration) and perceived sensory intensity. If you do that, the perceived intensity (S) is a
linear function of the logarithm of the concentration (𝐼).
!Note that the concentrations on the x-axis for Fechner’s law are plotted on a logarithmic scale.
The psychophysical function according to Fechner’s law is linear in a semi-log plot (a plot that has one
logarithmic axis).
Stevens’ law
Stevens’ power law – method of magnitude estimation. People could easily rate the intensity of one
stimulus in proportion to the intensity of another stimulus.
An example of a magnitude estimation instruction is: 'Please taste this solution. This standard
solution has a standard intensity of 10. Now, please assign the intensities of the other stimuli that you
are going to taste in proportion to the standard stimulus. If the presented stimulus is twice as sweet
as the standard stimulus, then you assign the value of 20. If it is half as sweet, then assign the value
of 5.'
This yields a different psychophysical function, in the form of a power function, in which the
perceived intensity (S) is a constant (k) times the physical intensity or concentration (I) to the power
of n.
A psychophysical function according to Stevens’ law – linear on a log-log plot. The exponent n
determines whether the psychophysical function is accelerating of decelerating on a linear-linear
plot: an exponent value larger than 1 yields accelerating psychophysical functions, while exponent
values smaller than 1 yields decelerating psychophysical functions.
, This is a linear-linear plot. Normally, according to Stevens’ law, the psychophysical function is linear
on a log-log plot.
Stevens’ power law is often considered to supersede the laws of Weber and Fechner – they do not
function for very low intensities. Stevens’ law is based on a logarithmic relationship between stimulus
and sensation and describes a wider range of sensory comparisons down to zero intensity.
The effect of scaling on the psychophysical function
In practice in sensory research, the shape of the psychophysical function depends on the type of scale
that is used. In general, magnitude estimation scales yield psychophysical functions according to the
power law, which is in line with Stevens’ law. Magnitude estimation assumes that people are able to
judge ratios of perceived intensity.
Category scales and visual analogue scales yield psychophysical functions which are in line with
Fechner’s law – based n the assumption that people are able to rate differences in perceived
intensity.
Summary
To sum up, different scaling methods yield different shapes of psychophysical functions. In general,
JND scales, obtained through indirect scaling, converge with psychophysical functions obtained with
visual analogue scales or category scales. Those psychophysical functions follow Fechner's law.
Threshold
E-module - Threshold
After the e-modules, the student is expected to:
Understand and explain different concepts and definitions of thresholds
Understand, explain, and apply different methods of measuring thresholds
Understand, apply and interpret different psychophysical functions in relation to thresholds
E-module – Thresholds: the laws of Weber, Fechner and Stevens
A psychophysical function describes the relationship between the psychophysical function and
perceived intensity of a sensory stimulus.
Weber’s law
This law states that the amount of a physical stimulus which is needed to increase to be ‘just
perceivably different’ is a constant linear ratio.
Delta intensity/intensity = constant (k) over the range of possible concentrations
A definition of the Weber fraction is the ‘Just-Noticeable-Difference’ (JND) = the difference between
two stimuli that can be detected or perceived in 50% of the cases.
For both glucose and fructose, Weber's Fraction is between 0.10 and 0.15 (or 10-15%). This means
that when you have a solution with 10 grams of glucose per 100 grams, an increase in concentration
of ~10%, to 11 grams glucose per 100 grams, is just perceivably more sweet. Similarly, with 30 grams
per 100 grams, you would need an increase of 3 grams (10%, or a fraction of 0.10), to 33 grams per
100 grams, for it to be just perceivably more sweet.
Fechner’s law
Fechner’s law is built upon Weber’s law and states that the subjective sensation is proportional to the
logarithm of the stimulus intensity.
,By adding up JNDs, you can construct a psychophysical function between physical stimulus intensity
(or concentration) and perceived sensory intensity. If you do that, the perceived intensity (S) is a
linear function of the logarithm of the concentration (𝐼).
!Note that the concentrations on the x-axis for Fechner’s law are plotted on a logarithmic scale.
The psychophysical function according to Fechner’s law is linear in a semi-log plot (a plot that has one
logarithmic axis).
Stevens’ law
Stevens’ power law – method of magnitude estimation. People could easily rate the intensity of one
stimulus in proportion to the intensity of another stimulus.
An example of a magnitude estimation instruction is: 'Please taste this solution. This standard
solution has a standard intensity of 10. Now, please assign the intensities of the other stimuli that you
are going to taste in proportion to the standard stimulus. If the presented stimulus is twice as sweet
as the standard stimulus, then you assign the value of 20. If it is half as sweet, then assign the value
of 5.'
This yields a different psychophysical function, in the form of a power function, in which the
perceived intensity (S) is a constant (k) times the physical intensity or concentration (I) to the power
of n.
A psychophysical function according to Stevens’ law – linear on a log-log plot. The exponent n
determines whether the psychophysical function is accelerating of decelerating on a linear-linear
plot: an exponent value larger than 1 yields accelerating psychophysical functions, while exponent
values smaller than 1 yields decelerating psychophysical functions.
, This is a linear-linear plot. Normally, according to Stevens’ law, the psychophysical function is linear
on a log-log plot.
Stevens’ power law is often considered to supersede the laws of Weber and Fechner – they do not
function for very low intensities. Stevens’ law is based on a logarithmic relationship between stimulus
and sensation and describes a wider range of sensory comparisons down to zero intensity.
The effect of scaling on the psychophysical function
In practice in sensory research, the shape of the psychophysical function depends on the type of scale
that is used. In general, magnitude estimation scales yield psychophysical functions according to the
power law, which is in line with Stevens’ law. Magnitude estimation assumes that people are able to
judge ratios of perceived intensity.
Category scales and visual analogue scales yield psychophysical functions which are in line with
Fechner’s law – based n the assumption that people are able to rate differences in perceived
intensity.
Summary
To sum up, different scaling methods yield different shapes of psychophysical functions. In general,
JND scales, obtained through indirect scaling, converge with psychophysical functions obtained with
visual analogue scales or category scales. Those psychophysical functions follow Fechner's law.
