When less equals more: Probability summation without sensitivity improvement

Journal of Experimental Psychology: Human Perception and Performance

Volumn 40, Issue 5, 2014, Pages 2091-2100

  Schwarz, Wolf ^a   Miller, Jeff O ^b  

^a UNIVERSITY OF POTSDAM   (Germany)

^b UNIVERSITY OF OTAGO   (New Zealand)

Author keywords

2AFC; Compound detection or discrimination; Probability summation; Psychometric functions; Redundancy gain; ROC curve

Indexed keywords

ADOLESCENT; ADULT; FEMALE; HUMAN; MALE; PERCEPTIVE DISCRIMINATION; PHYSIOLOGY; PROBABILITY; PROCEDURES; PSYCHOMOTOR PERFORMANCE; PSYCHOPHYSICS; RECEIVER OPERATING CHARACTERISTIC; STATISTICAL ANALYSIS; YOUNG ADULT;

ADOLESCENT; ADULT; DATA INTERPRETATION, STATISTICAL; FEMALE; HUMANS; MALE; PROBABILITY; PSYCHOMOTOR PERFORMANCE; PSYCHOPHYSICS; ROC CURVE; SIGNAL DETECTION, PSYCHOLOGICAL; YOUNG ADULT;

EID: 84925704208     PISSN: 00961523     EISSN: 19391277     Source Type: Journal    
DOI: 10.1037/a0037548     Document Type: Article

References (70)

1. Bamber, D. (1975). The area above the ordinal dominance graph and the area below the receiver operating characteristic graph. Journal of Mathematical Psychology, 12, 387-415.
2. Bentvelzen, A., Leung, J.,&Alais, D. (2009). Discriminating audiovisual speed: Optimal integration of speed defaults to probability summation when component reliabilities diverge. Perception, 38, 966-987.
3. Benzschawel, T.,&Cohn, T. E. (1985). Detection and recognition of visual targets. Journal of the Optical Society of America, A, 2, 1543-1550.
4. Blake, R.,&Fox, R. (1973). The psychophysical inquiry into binocular summation. Perception&Psychophysics, 14, 161-185.
5. Blake, R., Sloane, M.,&Fox, R. (1981). Further developments in binocular summation. Perception&Psychophysics, 30, 266-276.
6. Blurton, S. P., Greenlee, M. W.,&Gondan, M. (2014). Multisensory processing of redundant information in go/nogo and choice responses. Accepted for publication in Attention, Perception&Psychophysics, 76, 1212-1233.
7. Braddick, O. (1972). Binocular interaction and signal detection theory. Vision Research, 12, 1435-1437.
8. Breitmeyer, B.,&Ögmen, H. (2006). Visual masking (2nd ed.). New York: Oxford University Press.
9. Burmester, A.,&Wallis, G. (2011). Flexible resource allocation for the detection of changing visual features. Perception, 40, 299-316.
10. Collier, G. (1954). Probability of response and intertrial association as functions of monocular ad binocular stimulation. Journal of Experimental Psychology, 47, 75-83.
11. Di Stefano, M., Kusmic, C.,&Musumeci, D. (1987). Binocular interactions measured by choice reaction times in pigeons. Behavioural Brain Research, 25, 161-165.
12. Duncan, J. (1980). The locus of interference in the perception of simultaneous stimuli. Psychological Review, 87, 272-300.
13. Duncan, J., Ward, R.,&Shapiro, K. (1994). Direct measurement of attentional dwell time in human vision. Nature, 369, 313-315.
14. Eckstein, M. P., Thomas, J. P., Palmer, J.,&Shimozaki, S. S. (2000). A signal detection model predicts the effects of set size on visual search accuracy for feature, conjunction, triple conjunction, and disjunction displays. Perception&Psychophysics, 62, 425-451.
15. Foley, J.,&Schwarz, W. (1998). Spatial attention: Effect of position uncertainty and number of distractor patterns on the threshold vs. contrast (TvC) function for contrast discrimination. Journal of the Optical Society of America, A, 15, 1036-1047.
16. Gescheider, G. A., Guclu, B., Sexton, J. L., Karalunas, S.,&Fontana, A. (2005). Spatial summation in the tactile sensory system: Probability summation and neural integration. Somatosensory and Motor Research, 22, 255-268.
17. Ghose, K.,&Maunsell, J. H. R. (2012). A strong constraint to the joint processing of pairs of cortical signals. Journal of Neuroscience, 32, 15922-15933.
18. Graham, N. V. S. (1989). Visual pattern analyzers. New York, NY: Oxford University Press.
19. Graham, N., Robson, J. G.,&Nachmias, J. (1978). Grating summation in fovea and periphery. Vision Research, 18, 815-825.
20. Hanley, J. A.,&McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143, 29-36.
21. Heil, P. (2004). First-spike latency of auditory neurons revisited. Current Opinion in Neurobiology, 14, 461-467.
22. Heil, P., Verhey, J. L.,&Zoefel, B. (2013). Modelling detection thresholds for sounds repeated at different delays. Hearing Research, 296, 83-95.
23. Howard, I. P.,&Rogers, B. J. (1995). Binocular vision and stereopsis. New York, NY: Oxford University Press.
24. Kihara, K.,&Takeda, Y. (2010). Time course of the integration of spatial frequency-based information in natural scenes. Vision Research, 50, 2158-2162.
25. King-Smith, P. E.,&Kulikowski, J. J. (1975). The detection of gratings by independent activation of line detectors. Journal of Physiology, 247, 237-271.
26. Koriat, A. (2012). When are two heads better than one and why? Science, 336, 360-362.
27. Kulikowski, J. J. (2003). Neural basis of fundamental filters in vision. In: G. T. Buracas, O. Ruksenas, G. M. Boynton,&T. D. Albright (Eds.), Modulation of neuronal responses: Implications for active vision, ch. 1 (pp. 3-68). Amsterdam, The Netherlands: IOS Press.
28. Laming, D. (2013). Probability summation - a critique. Journal of the Optical Society of America, A, 30, 300-315.
29. Liston, D. B.,&Stone, L. S. (2013). Saccadic brightness decisions do not use a difference model. Journal of Vision, 13, 1-10.
30. Luce, R. D. (1986). Response times: Their role inferring elementary mental organization. New York, NY: Oxford University Press.
31. Macmillan, N. A.,&Creelman, C. D. (2005). Detection theory: A user's guide (2nd ed.). Mahwah, NJ: Erlbaum.
32. Marks, L. E., Veldhuizen, M. G., Shepard, T. G.,&Shavit, A. Y. (2012). Detecting gustatory-olfactory flavor mixtures: Models of probability summation. Chemical Senses, 37, 263-277.
33. Meddis, R.,&Lecluyse, W. (2011). The psychophysics of absolute threshold and signal duration: A probabilistic approach. Journal of the Acoustical Society of America, 129, 3151-3165.
34. Meese, T. S.,&Summers, R. J. (2009). Neuronal convergence in early contrast vision: Binocular summation is followed by response nonlinearity and area summation. Journal of Vision, 9, 1-16.
35. Meese, T. S.,&Williams, C. B. (2000). Probability summation for multiple patches of luminance modulation. Vision Research, 40, 2101-2113.
36. Miller, J. O. (1982). Divided attention: Evidence for coactivation with redundant signals. Cognitive Psychology, 14, 247-279.
37. Morris, A. P., Liu, C. C., Cropper, S. J., Forte, J. D., Krekelberg, B., & Mattingley, J. B. (2010). Summation of visual motion across eye movements reflects a nonspatial decision mechanism. Journal of Neuroscience, 30, 9821-9830.
38. Mulligan, R. M.,&Shaw, M. L. (1980). Multimodal signal detection: Independent decision vs. integration. Perception&Psychophysics, 28, 471-478.
39. Nachmias, J. (1981). On the psychometric function for contrast detection. Vision Research, 21, 215-223.
40. Nolte, L. W.,&Jaarsma, D. (1967). More on the detection of one of M orthogonal signals. Journal of the Acoustical Society of America, 41, 497-505.
41. Otto, T. U., Dassy, B.,&Mamassian, P. (2013). Principles of multisensory behavior. Journal of Neuroscience, 33, 7463-7474.
42. Palmer, J., Verghese, P.,&Pavel, M. (2000). The psychophysics of visual search. Vision Research, 40, 1227-1261.
43. Pashler, H. E. (1998). The psychology of attention. Cambridge, MA: MIT Press.
44. Peckham, R. H.,&Hart, W. M. (1959). Subthreshold retinal integration shown in low contrast flicker measurements. Science, 130, 1256-1258.
45. Peckham, R. H.,&Hart, W. M. (1960). Binocular summation of subliminal repetitive visual stimulation. American Journal of Ophtalmology, 49, 1121-1126.
46. Pirenne, M. H. (1943). Binocular and uniocular thresholds for vision. Nature, 152, 698-699.
47. Prins, N. (2008). Texture modulation detection by probability summation among orientation-selective and isotropic mechanisms. Vision Research, 48, 2751-2766.
48. Prinzmetal, B.,&Gettleman, L. (1993). Vertical-horizontal illusion: One eye is better than two. Perception&Psychophysics, 53, 81-88.
49. Raab, D. H. (1962). Statistical facilitation of simple reaction times. Transactions of the New York Academy of Sciences, 24, 574-590.
50. Sachs, M. B., Nachmias, J.,&Robson, J. G. (1971). Spatial-frequency channels in human vision. Journal of the Optical Society of America, 61, 1176-1186.
51. Schwarz, W. (1992). Do two eyes really see more than one? Journal of Mathematical Psychology, 36, 269-277.
52. Schwarz, W. (1994). Diffusion, superposition, and the redundant-targets effect. Journal of Mathematical Psychology, 38, 504-520.
53. Shaw, M. L. (1982). Attending to multiple sources of information. I. The integration of information in decision making. Cognitive Psychology, 14, 353-409.
54. Shimozaki, S. S., Schoonveld, W. A.,&Eckstein, M. P. (2012). A unified Bayesian observer analysis for set size and cueing effects on perceptual decisions and saccades. Journal of Vision, 12, 1-26.
55. Shiu, L.,&Pashler, H. (1992). Improvement in line orientation discrimination is retinally local but dependent on cognitive set. Perception & Psychophysics, 52, 582-588.
56. Spence, C., Baddeley, R., Zampini, M., James, R.,&Shore, D. I. (2003). Multisensory temporal order judgments: When two locations are better than one. Perception&Psychophysics, 65, 318-328.
57. Srinivasan, M. V. (1999). When one eye is better than two. Nature, 399, 305-306.
58. Swensson, R. G., King, J. L.,&Gur, D. (2001). A constrained formulation for the receiver operating characteristic (ROC) curve based on probability summation. Medical Physics, 28, 1597-1609.
59. Tolhurst, D. J. (1975). Reaction times in the detection of gratings by human observers: A probabilistic mechanism. Vision Research, 15, 1143-1149.
60. Tyler, C. W.,&Chen, C. C. (2000). Signal detection theory in the 2AFC paradigm: Attention, channel uncertainty and probability summation. Vision Research, 40, 3121-3144.
61. van Mierlo, C. M., Brenner, E.,&Smeets, J. B. J. (2011). Better performance with two eyes than with one in stereo-blind subjects' judgments of motion in depth. Vision Research, 51, 1249-1253.
62. Verghese, P. (2001). Visual search and attention: A signal detection theory approach. Neuron, 31, 523-535.
63. Wandell, B.,&Luce, R. D. (1978). Pooling peripheral information: Averages versus extreme values. Journal of Mathematical Psychology, 17, 220-235.
64. Watson, A. B. (1979). Probability summation over time. Vision Research, 19, 515-522.
65. Westendorf, D.,&Blake, R. (1988). Binocular reaction times to contrast increments. Vision Research, 28, 355-359.
66. Wilk, M. B.,&Gnanadesikan, R. (1968). Probability plotting methods for the analysis of data. Biometrika, 55, 1-17.
67. Wuerger, S. M., Hofbauer, M.,&Meyer, G. F. (2003). The integration of auditory and visual motion signals at threshold. Perception&Psychophysics, 65, 1188-1196.
68. Yellott, J. I., Jr. (1977). The relationship between Luce's choice axiom, Thurstone's theory of comparative judgment, and the double exponential distribution. Journal of Mathematical Psychology, 15, 109-144.
69. Zenger, B.,&Fahle, R. (1997). Missed targets are more frequent than false alarms: A Model for error rates in visual search. Journal of Experimental Psychology: Human Perception and Performance, 23, 1783-1791.
70. Zohar, O., Shackleton, T. M., Nelken, I., Palmer, A. R.,&Shamir, M. (2011). First spike latency code for interaural phase difference discrimination in the guinea pig inferior colliculus. Journal of Neuroscience, 31, 9192-9204.