Biomedical Engineering Reference
In-Depth Information
the principle as the Power Law, which has since been confirmed by many experimenters
in many experiments performed in many sense modalities. Next to the Weber Law that
withstood the test of time for almost two centuries, it is the best-documented general
relationship of psychophysics. Because it may be considered as the answer to Fechner's
fundamental question of the relationship between the 'spiritual' and the 'material,' to
use Fechner's language, Stevens regarded the Power Law as the Psychophysical Law. In
his monograph, the view is accepted that the Power Law is the most fundamental law
of psychophysics, and he designates it as the First Law of Psychophysics. Nevertheless,
additional laws are possible and may have considerable usefulness [34].
10.4.2 Law of Asymptotic Linearity
Before the Power Law was firmly established, methods of measuring psychological quan-
tities had to be developed. The original method introduced by Stevens to measure loudness
and brightness, which he called 'magnitude estimation,' proved partially misguided and
produced the correct results only by fortuitous happenstance. Stevens and his coworkers
soon discovered that the exact functions relating to the psychological magnitudes of the
underlying stimulus magnitudes depended upon the designated reference standards. As
it transpired, the 'best' power functions were obtained when the observers were allowed
to choose the standards themselves. This discovery suggested that the observers did not
strictly obey the rules of ratio scaling, which allows for entirely arbitrary reference stan-
dards, but, to some degree, attached absolute values to numbers. A more systematic
investigation of the effects of reference standards was performed by J. Zwislocki and
Rhona P. Hellman [35, 36]. The investigation led to the conclusion that experimental
observers do not use numbers in a relative way, depending on chosen units, but rather in
an absolute way. In other words, probably because of the way they are used in everyday
life and the way children use them when learning, they acquire absolute subjective values.
For example, children learn numbers by counting objects such as pebbles or pencils, so
coupling numbers to perceived objects occurs early in life and complies with numeric
rules in which numbers have absolute recurring values. When asked to assign numbers
to subjective impressions of line length or to loudness, adults and children produced the
same absolute functions within the range of the numerals they knew. If numbers acquire
absolute subjective values, ME becomes a matching operation. The subjective values of
numbers are matched to the subjective values of whatever variable is being scaled. Because
Stevens' method of ME appeared to produce biased results due to asymmetry, he intro-
duced a complementary method in which numbers were given by the experimenter, and
the observers had to find matching sensation magnitudes that they produced by manip-
ulating appropriate instrumental controls. He called this method 'MP'. In the methods
of scaling subjective magnitudes developed by Zwislocki and Hellman, the numbers are
assumed to have absolute subjective values. Consequently, they call what started as ME,
'absolute magnitude estimation' (AME), and what started as MP, 'absolute magnitude
production' (AMP). The designations conserve Stevens' tradition but are not completely
accurate because both are regarded as matching operations. The methods have opened a
wide world of subjective magnitudes to measurement in spite of objections by staunch
opponents who do not believe that they constitute legitimate measurements. However, the
mutually consistent results tend to cast doubt on these objections. Sensation magnitudes
