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Piéron’s Law holds in conditions of response conflict

Tom Stafford, Kevin N. Gurney & Leanne Ingram

Department of Psychology, University of Sheffield

t.stafford@shef.ac.uk

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CogSci 2009, Amsterdam, 2nd of August

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Image thanks to Roger Carpenter

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Stages to decision making? (1)‏

  • ‘‘Most research on AFM shows consistent and robust evidence in favor of seven successive processing stages in traditional choice reactions” (Sanders, 1990)‏
  • “information is transmitted discretely between perceptual and response stages of processing” (Woodman et al, 2008)‏

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Sanders, A. F. (1990). Issues and trends in the debate on discrete vs continuous

processing of information. Acta Psychologica, 74 (2-3), 123-167.

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Woodman, G. F., Kang, M. S., Thompson, K., & Schall, J. D. (2008). The effect of visual search efficiency on response preparation: neurophysiological evidence for discrete flow. Psychological Science, 19(2), 128-136.

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Stages to decision making? (2)‏

  • PDP framework (Rumelhart et al, 1986) explicitly rejects stage models, in favour of continuous processing (McClelland, 1979)‏
  • Most successful model of RTs is single stage, Ratcliff's diffusion model‏

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Rumelhart, D., McClelland, J. & the PDP Research Group (Eds.), Parallel distributed processing: Explorations in the microstructure of cognition. Cambridge, MA: MIT Press.

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McClelland, J. (1979). On the time-relations of mental processes: An examination of systems of processes in cascade. Psychological Review, 86, 287-330.

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The diffusion model of decision making

Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85(2), 59-108.

Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks. Neural computation, 20(4), 873-922.

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Decision making

  • ‘decision making’ research has focused on perceptual decisions (e.g. Gold & Shadlen, 2007)‏
  • Diffusion model has been shown to be optimal (Bogacz et al, 2006)‏
  • Optimal processing seems to require integration of factors influencing a decision into a single variable (e.g. Ratcliff, 2001?)‏

Bogacz, R., Brown, E., Moehlis, J., Holmes, P., & Cohen, J. D. (2006). The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks. Psychological Review, 113 (4), 700-65.

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Gold, J. I., & Shadlen, M. N. (2007). The neural basis of decision making. Annual Review of Neuroscience, 30, 535-574

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Ratcliff, R. (2001). Putting noise into neurophysiological models of simple decision making. Nature Neuroscience, 4 (4), 336-336.

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  • Task: to inspect RTs in a more complex‏ choice task, something that is not just a perceptual decision
  • ...a decision which involves two factors, which provide evidence that (we might assume) is represented at different stages
  • Are reaction times affected additively by these two factors?
  • Can existing single stage models account for the pattern of results?

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The Stroop Task

Name the colour

Control SHOE

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The Stroop Task

Name the colour

Control SHOE

Congruent GREEN

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The Stroop Task

Name the colour

Control SHOE

Congruent GREEN

Conflict BLUE

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The stimulus intensity – reaction time function

aka ‘Piéron’s Law’

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RT = R0 + kI-β

Pieron, H. (1952). The sensations; their functions, processes and mechanisms: Their Functions, Processes, and Mechanisms. Yale University Press.

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  • Pieron's Law found for white light, pure tones, taste...(Luce, 1986)‏
  • ...and in simple choice decisions (Pins & Bonnet, 1996)‏
    • “luminance processing and any further processing due to the specific requirements of the psychophysical task combine additively”

Rumelhart, D., McClelland, J. & the PDP Research Group (Eds.), Parallel distributed processing: Explorations in the microstructure of cognition. Cambridge, MA: MIT Press.

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Luce, R. D. (1986). Response times: Their role in inferring elementary mental organization. Oxford University Press

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Pins, D., & Bonnet, C. (1996). On the relation between stimulus intensity and processing time: Piéron's law and choice reaction time. Perception and Psychophysics, 58(3), 390-400

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Piéron’s Law inherent in any rise-to-threshold decision process

Stafford, T., & Gurney, K. N. (2004). The role of response mechanisms in determining reaction time performance: Pieron’s law revisited. Psychonomic Bulletin & Review, 11(6), 975-987.

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Expt 1:

A Stroop task with varying levels of colour saturation

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If saturation and response conflict information are integrated then the different Stroop conditions should differ by different amounts at each level of saturation

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Interactive

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Additive

Interactive

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Expt 1 Results, i

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Colour saturation (%)‏

Reaction Time (ms)‏

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Expt 1 Results, ii

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Expt 2:

A Stroop task with varying levels of colour saturation,

with word and colour elements of the stimulus separated in space

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Expt 2 Results, i

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Colour saturation (%)‏

Reaction Time (ms)‏

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Expt 2 Results, ii

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Cohen et al’s (1990) model of Stroop processing

Cohen, J. D., Dunbar, K., & McClelland, J. L. (1990). On the control of automatic processes - a parallel distributed-processing account of the stroop effect. Psychological Review, 97 (3), 332-361.

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S

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Stimulus

Stimulus-Response

Translation

RT

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Stimulus

Stimulus-Response

Translation

RT

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S

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Stimulus

Stimulus-Response

Translation

RT

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Simulation Results, i

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Simulation Results, ii

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Conclusions (1/2)‏

  • Stimulus intensity and response conflict appear additive in a colour-saturation variant of the Stroop task
  • ...but existing continuous-processing single-stage models of the Stroop task are adequate to account for this result
  • We must be careful before inferring discrete stages from additive RT data

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Conclusions (2/2)‏

  • Also, Piéron’s Law holds for colour saturation…
  • ….in a complex choice task

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Stafford, T., Gurney, K.N. & Ingram, L. (2009). Piéron’s Law holds in conditions of response conflict. In N.A. Taatgen & H. van Rijn (Eds.), Proceedings of the 31th Annual Conference of the Cognitive Science Society. Cognitive Science Society.

We thank Sarah Fox for help running the experiments, David Lawrence & David Yates for reading drafts and Marius Usher and Eddy Davelaar for useful discussion of the material.

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CogSci 2009, Amsterdam, 2nd of August

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Locked

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independent

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Single stage, independent inputs

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Two stage, locked

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Two stages, locked inputs

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Two stage, independent

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Two stages, independent inputs

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Expt 2, Separated stroop