several measurements of the threshold value of the stimulus are averaged
to arrive at an accurate estimation of the absolute threshold. When a
stimulus above absolute threshold is applied to the sense organ, the
intensity of this stimulus must be increased or decreased by some critical
amount before a person is able to report any change in sensation. The
difference threshold (DL for the German Differenz Limen) was defined as the
amount of change in a stimulus (Δϕ) required to produce a just noticeable
difference (jnd) in the sensation. If the intensity of the stimulus is 10 units,
and the stimulus must be increased to 12 units to produce a just noticeable
increment in the sensation, then the difference threshold would be 2 units.

Sensation intensity is only one of several ways in which sensations can
differ, and DL's have also been measured for other dimensions of sensation.
It is generally agreed that sensations can differ on at least four basic
dimensions--intensity, quality, extension, and duration. The dimension of
quality refers to the fact that sensations may be different in kind. The
different sensory modalities have unique kinds of sensations; for example,
seeing is an entirely different kind of experience than hearing. Within
sensory modalities, sensations also vary in quality. A sound becomes
higher or lower in pitch as the vibration frequency of the stimulus is
changed. Variations of the wavelength of light are accompanied by changes
in hue. A cutaneous sensation may be felt as pain, warmth, cold, or simply
a pressure. If the underlying stimulus dimensions for a sensation are
known, the difference thresholds can be measured to find the changes in
these dimensions necessary to produce just noticeable changes in the
sensation. For example, in auditory pitch discrimination the DL for changes
in frequency has been measured. In color discrimination the DL for the
perception of changes in the wavelength of light has been measured. Since
sensations can vary along the dimension of extension, the DL can be
measured for variation in spatial aspects of physical stimuli, such as size,
location, and separation. And, finally, since sensations last for varying
periods of time, the DL for stimulus duration has been of interest to
psychophysicists.

Much work in psychophysics has consisted of investigating how the
absolute and difference thresholds change as some aspect of the stimulus
(wavelength, frequency, adaptation time, intensity level, etc.) is system-
atically varied. The resulting relations are called stimulus critical value
functions, since they describe how the threshold (critical stimulus value)
changes as a function of other aspects of the stimulus.

One of the first stimulus critical value functions to be investigated was
the relation between the difference threshold for intensity and the intensity
level of a stimulus. If, for example, the difference threshold is 2 units

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