On the possible relations between discriminability and apparent magnitude

Abstract

Some psychophysicists seek a unified theory in which the scaling of apparent sensory magnitude and the discrimination of differences in intensity can be encompassed. When contextual factors arc held constant, there is a positive correlation over many sensory continua between the exponent of the power function for sensory scaling and the inverse of the Weber fraction. Variations in neural efficiency also show a similar correlation with apparent magnitude and discrimination. The role of other factors (such as contrast, adaptation and size scaling) remains unclear. Both Weber and Fechner considered aspects of these issues. Weber held that, for the same physical stimulus intensity, apparent magnitude and discriminatory ability increased with neural efficiency. Fechner held that changes in apparent magnitude had no effect on discrimination: a stable differential threshold was predicted by the Parallel Law (Weber's Law applied to internal sensations). Evidence is considered for the tactile sense and weight perception, and for visual size. The relation between apparent heaviness and weight discrimination is complex, varying with the state of adaptation and with neural efficiency. There is some evidence that both tactile and visual apparent size increase with a finer underlying neural structure; but it is unclear whether other types of increase in apparent size lead to increased spatial acuity, or to differences in the Weber fraction for line length. The variety of values of apparent magnitude and discrimination, and the lack of a monotonic relation between them, makes it unlikely that all known relationships could be encompassed in a unified psychophysical theory.

The nature of correlation perception in scatterplots

“…But those that are possible in theory do not seem likely in practice: perceived correlation corresponds neither to the orientation of the regression line (Experiment 3; Lane et al, 1985) nor to the ratio of the major and minor axes of the dot cloud (Cleveland et al, 1982; although see Boynton, 2000). Furthermore, the perceived magnitude of most physical properties (including area or distance) is generally described best by a power function of its physical magnitude (see e.g., Billock & Tsou, 2011; Ross, 1997), not a logarithmic function of the kind found here.An even more important consideration perhaps is the invariance of correlation perception to different kinds of graphical representation. Large dots in a scatterplot, for example, make the dot cloud blobby and give it a larger outer boundary.…”

“…Again letting u = 1 - b est r , this becomes g = ln( u )/(ln(1 - b est )). This is an instance of Fechner ’ s Law , which has been proposed for the relation between the perceived and physical magnitudes of various properties (see Ross, 1997). In addition, Rensink and Baldridge (2010) found that b disc = b est , connecting discrimination and estimation in a systematic way.…”

Application of Psychophysical Techniques to Haptic Research

“…The second area is focused on the measurement of sensory attributes such as the perceived intensity of suprathreshold stimuli or the ability to identify or categorize stimuli. A persistent theme throughout the history of psychophysics is that there must be a relation between these two aspects of perception, that is the discrimination of differences in intensity must be related in some way to how the apparent magnitude of stimuli is scaled, an endeavor that is characterized as the search for a unifying psychophysical law [17], [18], [19].…”

The material-weight illusion revisited

“…S. Steven's (1961) power law. We propose to use the exponent as a coarse measure of the system's ability to differentiate along the continuum of mass (for further discussion, see, e.g., Ross, 1997). For any pair of masses, lower slopes signify smaller differences in perceived weight.…”