Combining Information: Probability Summation and Probability Averaging in Detection and Discrimination

Detection may improve if a stimulus offers 2 cues rather than 1. This is sometimes attributed to probability summation of independent detections, which provides an especially simple model for sensory information combination. However, this model assumes a strong bias toward the positive response, which is not appropriate for discrimination. The probability summation model is here extended to apply to discrimination and to allow different degrees of summation, ranging from complete through partial to probability averaging, and the use of this model is illustrated for the method of constant stimuli. It allows performance based on independent decisions to be distinguished from performance (e.g., integration) that is better than summation can explain. Models for the discrimination of complex stimuli may provide a tool for studying the development of expertise in areas where this involves a perceptual component, such as clinical judgment. The detection and discrimination of stimuli is the main subject matter of psychophysics , and study of these processes has given researchers a sophisticated understanding of them. Unfortunately, the benefit of applying this knowledge to areas of research or application other than psychophysics has not been fully realized. This article examines and extends a simple model of how information is combined when one detects or discriminates stimuli that are defined by more than one sensory component or feature. The application of these ideas to a wider range of problems is also considered. A laboratory detection task may require a subject to decide, for example, whether a faint sound was presented. A discrimination task may require the participant to judge whether a given line is longer or shorter than a 5-in (12.7 cm) standard. In each case the task is made difficult because of noise. This noise may be external, such as a background of white noise, or it may arise internally, from the variability of the response of the sensory organ and the nervous system to the stimulus input.

[1]  B. Wandell,et al.  Reaction times to weak test lights , 1984, Vision Research.

[2]  M. Pirenne,et al.  Binocular and Uniocular Threshold of Vision , 1943, Nature.

[3]  Richard E. Pastore,et al.  Common-Factor Model of Categorical Perception. , 1977 .

[4]  Svem Magnussen,et al.  High-Fidelity Perceptual Long-Term Memory , 1994 .

[5]  R. Dawes.  Judgment under uncertainty: The robust beauty of improper linear models in decision making , 1979 .

[6]  R M Mulligan,et al.  Multimodal signal detection: Independent decisions vs. integration , 1980, Perception & psychophysics.

[7]  A. B. Kristofferson,et al.  DETECTABILITY OF TARGETS CONSISTING OF MULTIPLE SMALL POINTS OF LIGHT , 1958 .

[8]  K. M. Dallenbach,et al.  "Facial Vision": The Perception of Obstacles by the Blind , 1944 .

[9]  B. Rogers,et al.  The Interaction of Binocular Disparity and Motion Parallax in the Computation of Depth , 1996, Vision Research.

[10]  Brian A. Wandell,et al.  A model of a single visual channel's response to weak test lights , 1984, Vision Research.

[11]  Paul E. Meehl,et al.  Clinical vs. Statistical Prediction. , 1955 .

[12]  L MATIN,et al.  Binocular summation at the absolute threshold of peripheral vision. , 1962, Journal of the Optical Society of America.

[13]  M. Treisman,et al.  Generation of random sequences by human subjects: Cognitive operations or psychological process? , 1987 .

[14]  H. McGurk,et al.  Hearing lips and seeing voices , 1976, Nature.

[15]  R. Dawes.  Experience and validity of clinical judgment: The illusory correlation. , 1989 .

[16]  Martin Lages,et al.  Spatial frequency discrimination: Visual long-term memory or criterion setting? , 1998, Vision Research.

[17]  G. S. Brindley,et al.  Shorter Articles and Notes two more Visual Theorems , 1960 .

[18]  Neil A. Macmillan,et al.  Detection Theory: A User's Guide , 1991 .

[19]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[20]  J. S. Wiggins,et al.  Clinical and statistical prediction: Where are we and where do we go from here? , 1981 .

[21]  Same-different texture discrimination in pigeons: testing competing models of discrimination and stimulus integration. , 1997, Journal of experimental psychology. Animal behavior processes.

[22]  A. D. D. Groot.  Thought and Choice in Chess , 1978 .

[23]  D. M. Green,et al.  Multiple Observations of Signals in Noise , 1959 .

[24]  L. Thurstone.  A law of comparative judgment. , 1994 .

[25]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .

[26]  M. Treisman.  There Are Two Types of Psychometric Function: A Theory of Cue Combination in the Processing of Complex Stimuli With Implications for Categorical Perception , 1999 .

[27]  A. Watson.  Probability summation over time , 1979, Vision Research.

[28]  J P Thomas,et al.  Simultaneous discrimination of the spatial frequency and contrast of periodic stimuli. , 1993, Journal of the Optical Society of America. A, Optics and image science.

[29]  Michel Treisman,et al.  THE EFFECT OF ONE STIMULUS ON THE THRESHOLD FOR ANOTHER: AN APPLICATION OF SIGNAL DETECTABILITY THEORY1 , 1964 .

[30]  P. Gribble,et al.  Temporal constraints on the McGurk effect , 1996, Perception & psychophysics.

[31]  M. Funnell,et al.  Hemispheric contributions to the integration of visual and auditory information in speech perception , 1994, Perception & psychophysics.

[32]  N. Perrin,et al.  Varieties of perceptual independence. , 1986, Psychological review.

[33]  K. Green,et al.  Cross-modal discrepancies in coarticulation and the integration of speech information: the McGurk effect with mismatched vowels. , 1995, Journal of experimental psychology. Human perception and performance.

[34]  R. Duncan Luce,et al.  Parallel psychometric functions from a set of independent detectors , 1975 .

[35]  N. Graham.  Visual detection of aperiodic spatial stimuli by probability summation among narrowband channels , 1977, Vision Research.

[36]  G. Brindley.  The physiology of the retina and visual pathways , 1962 .

[37]  M. Treisman,et al.  Relation between signal detectability theory and the traditional procedures for measuring sensory thresholds: Estimating d' from results given by the method of constant simuli. , 1966 .

[38]  R L Stubblefield,et al.  Behavioral sciences and the law. , 1966, The American journal of orthopsychiatry.

[39]  Herbert A. Simon,et al.  The Roles of Recognition Processes and Look-Ahead Search in Time-Constrained Expert Problem Solving: Evidence From Grand-Master-Level Chess , 1996 .

[40]  D G Pelli,et al.  Uncertainty explains many aspects of visual contrast detection and discrimination. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[41]  M. Funnell,et al.  Audiovisual integration in perception of real words , 1992, Perception & psychophysics.

[42]  The effect of the shape of the stimulus on spatial summation at the fovea , 1975, Vision Research.

[43]  L. Weed.  New connections between medical knowledge and patient care , 1997, BMJ.