Piéron’s Law holds in conditions of response conflict Tom Stafford, Kevin N. Gurney & Leanne Ingram Department of Psychology, University of Sheffield [email protected].

Piéron’s Law holds in conditions of response conflictTom Stafford, Kevin N. Gurney & Leanne IngramDepartment of Psychology, University of [email protected]

CogSci 2009, Amsterdam, 2nd of August

Image thanks to Roger Carpenter

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)

30/07/09 © The University of Sheffield

3

Sanders, A. F. (1990). Issues and trends in the debate on discrete vs continuousprocessing of information. Acta Psychologica, 74 (2-3), 123-167.

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.

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

30/07/09 © The University of Sheffield

4

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

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

30/07/09 © The University of Sheffield

5

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.

30/07/09 © The University of Sheffield

6

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.

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

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

• 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?

The Stroop Task

Name the colour

Control SHOE

30/07/09 © The University of Sheffield

8

The Stroop Task

Name the colour

Control SHOE

Congruent GREEN

30/07/09 © The University of Sheffield

9

The Stroop Task

Name the colour

Control SHOE

Congruent GREEN

Conflict BLUE30/07/09 © The University of Sheffield

10

30/07/09 © The University of Sheffield

11

The stimulus intensity – reaction time function

aka ‘Piéron’s Law’

RT = R0 + kI-β

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

• 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.

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

30/07/09 © The University of Sheffield

13

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.

30/07/09 © The University of Sheffield

14

Expt 1:A Stroop task with varying levels of colour saturation

30/07/09 © The University of Sheffield

15

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

Interactive

AdditiveInteractive

Expt 1 Results, i

30/07/09 © The University of Sheffield

18

Colour saturation (%)

React

ion T

ime (

ms)

Expt 1 Results, ii

30/07/09 © The University of Sheffield

19

30/07/09 © The University of Sheffield

20

Expt 2:A Stroop task with varying levels of colour saturation,with word and colour elements of the stimulus separated in space

Expt 2 Results, i

30/07/09 © The University of Sheffield

21

Colour saturation (%)

React

ion T

ime (

ms)

Expt 2 Results, ii

30/07/09 © The University of Sheffield

22

30/07/09 © The University of Sheffield

23

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.

30/07/09 © The University of Sheffield

24

S

S

Stimulus

Stimulus-Response

Translation RT

30/07/09 © The University of Sheffield

25

Stimulus

Stimulus-Response

Translation RT

S

S

30/07/09 © The University of Sheffield

26

S

Stimulus

Stimulus-Response

Translation RT

S

30/07/09 © The University of Sheffield

27

Simulation Results, i

30/07/09 © The University of Sheffield

28

Simulation Results, ii

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

30/07/09 © The University of Sheffield

29

Conclusions (2/2)

• Also, Piéron’s Law holds for colour saturation…

• ….in a complex choice task

30/07/09 © The University of Sheffield

30

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.

CogSci 2009, Amsterdam, 2nd of August

Locked

S

S

independent

S

1

Single stage, independent inputs

Two stage, locked

1S

1S

Two stages, locked inputs

Two stage, independent

1S

11

Two stages, independent inputs

Expt 2, Separated stroop