A statistical decision model for sensory discrimination which predicts Weber’s law and other sensory laws: Some results of a computer simulation

Abstract

I. The Model"Weber's law stands as a milestone in psychological research. It is one of the first psychological laws worthy of the name, and it may prove to be of far greater and more general significance than the differential threshold problems that provided its initial formulation. In effect, it establishes a lawofpsychological relativity: subjective discriminations are not bound to absolute characteristics of stimuli but to relations between them." (Berelson & Steiner, 1964). This claim illustrates a conunon error among psychologists: the over-evaluation of "laws," whose discovery is taken as an end in itself for psychology. We need to substitute for this nineteenth century fallacy the appreciation that the observation of a behavioral regularity is not the conclusion to a psychological investigation, but a question inviting one; a "law" can only be said to be satisfactorily understood when we have a model of how the subject functions from which the observed behavior follows as a logical consequence. No grandiloquent generalization can substitute for this. The present paper arises from an attempt to examine whether we are yet in a position to devise such a model to account for Weber's law and some related findings (Treisman, 1964a); to examine the implications of the model devised it was simulated on a digital computer.The model as presented is intended to apply only to the simplest detection situation: determination of the increment or absolute threshold for a flash superimposed on a background of the same area or larger. Extra assumptions will be needed to extend it to more complex situations, such as determination of the CFF, Perception & Psychophysics, 1966, Vol. 1 but it will be better to add these assumptions when the basic model has been evaluated. It has been applied to visual thresholds since we know more about the absorption of energy by the receptors for vision than for other senses, but in principle it is capable of being adapted to any sense.The main assumptions on which the model rests are: (i) There is a statistical relation between the nominal intensity of a stimulus and its effect on the retinal receptors. The variation from trial to trial in the number of quanta absorbed from a light-flash of constant nominal intensity is described by a Poisson distribution. (ii) There is a statistical relation between the effect on the sense organ and the nervous message received centrally. Thus if the same number of quanta were absorbed by the receptors on more than one trial, sensory noise would nevertheless cause the number of nerve impulses arriving at the point where the threshold is determined to vary. (iii) The variation due to this sensory noise is, to somedegree,positivelycorrelated. (iv) A statistical decision procedure determines the response made.For the most part, these assumptions are not new. The last three could be adapted to apply to any sensory system, and would then account for the occurrence of Weber's law (Treisman, 1964a). A number of lesser assumptions are included in the model to give ...

Visual detection of signals in the presence of continuous and pulsed backqrounds

“…In an attempt to unify stimulus-and organism-oriented approaches to visual detection, Treisman (1966) has proposed a neurophysiological model that takes into account the statistics of light and the variability of neural messages in sensory channels. The Treisman model can be extended to the 2ATFC-continuous-and pulsedmasker situations.…”

Binocular brightness combinations: Additive and nonadditive aspects

“…We do prefer power-form functions, because experimental and theoretical studies point to this kind of transducer function. Treisman (1966Treisman ( , 1970 and Thiissen and Vendrik (19':71) propose power-form transducer functions on theoretical grounds. In a completely different kind of approach, Luce and Green (1972) prefer power functions above logarithmic functions in a study on a neural timing model for the psychophysics of intensity.…”

The effects of duration, area, and background intensity on the visual intensity difference threshold given by the forced-choice procedure: Derivations from a statistical decision model for sensory discrimination

“…But if we allow that variability may arise in the nervous pathways as well as in the physical stimulus, it becomes evident that the prediction of a square root law from the quantum variability of light must rest on one of the following assumptions: (1) The discriminatory response is determined at the receptor level, immediately on the absorption of quanta-but there is ample evidence, reviewed by Treisman (1966), that the behavioral threshold is more centrally determined. (2) The absorption of a quantum or quanta triggers a sequence of neural events that result in "messages" being transmitted to the central locus at which the discriminatory response is determined, the magnitude of the total message indicating the size of the stimulus; the variability or "noise" in this central transmission is negligible, so that the variation of the central message from trial to trial reflects only the Poisson variability of the stimulus.…”

“…Treisman (1966) applied it to what may be called the "detection procedures," i.e., those procedures in which the opportunity for an increment occurs once in each trial and the S may detect or fail to detect it. Here we shall apply the model to the "forced-choice procedures" (FCP) in which the increment may occur at two or more alternative locations and the S must decide which one contained it.…”

“…Unfortunately our knowledge of the visual pathways is insufficient for us to use physiological observations to characterize definitively all sources of biological noise. However, Treisman (1964aTreisman ( , 1966 has considered a simplified schema of Fig. 1.…”