Noise and Weber's law: The discrimination of brightness and other dimensions.

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Abstract

The model of the threshold given by signal detection theory is used as a basis for explaining the form of the Weber function. For this purpose three sources of noise are considered: spontaneous background noise, the irreducible physical variability of the stimulus, and variation in the response of the neural pathways simultaneously excited by the administration of a stimulus. It is postulated that the last will show positive correlation, i.e., that the central effects of the different elements which are simultaneously activated by a stimulus will vary from trial to trial in a similar, rather than in independent fashion. If this is accepted, a law for the Weber function can be derived which gives, for visual brightness discrimination, a square root relation at low stimulus intensities with a continuous transition to a linear law at high intensities, and which can be applied to explain some features of visual spatial and temporal summation. The model also allows Weber's law to be derived for other sensory dimensions. Weber's law states that A/// = k, where k is a constant, / is a given stimulus intensity, and A/ is the just noticeable difference in that intensity, according to some criterion (e.g., that it is detected on 50% of trials when it is added to /). But the Weber functions (the relations between A7 and /) which are determined experimentally for the different modalities are not well described by Weber's law. The law holds, to an approximation , for the midranges of many stimulus dimensions, but for low values of /, and sometimes for high values, the Weber fraction A///, tends to increase. The linear generalization of Weber's law, given by adding a constant, /„, to /, usually