1. 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 CogSci 2009, Amsterdam, 2 nd of August

2. Image thanks to Roger Carpenter

3. 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 continuous processing 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.

4. 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.

5. 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.

6. 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.

7. 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?

8. The Stroop Task Name the colour ControlSHOE 30/07/09© The University of Sheffield 8

9. The Stroop Task Name the colour ControlSHOE CongruentGREEN 30/07/09© The University of Sheffield 9

10. The Stroop Task Name the colour ControlSHOE CongruentGREEN ConflictBLUE 30/07/09© The University of Sheffield 10

11. 30/07/09© The University of Sheffield 11 The stimulus intensity – reaction time function aka ‘Piéron’s Law’ RT = R 0 + kI -β Pieron, H. (1952). The sensations; their functions, processes and mechanisms: Their Functions, Processes, and Mechanisms. Yale University Press.

12. 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

13. 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.

14. 30/07/09© The University of Sheffield 14 Expt 1: A Stroop task with varying levels of colour saturation

15. 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

16. Interactive

17. Additive Interactive

18. Expt 1 Results, i 30/07/09© The University of Sheffield 18 Colour saturation (%)‏ Reaction Time (ms)‏

19. Expt 1 Results, ii 30/07/09© The University of Sheffield 19

20. 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

21. Expt 2 Results, i 30/07/09© The University of Sheffield 21 Colour saturation (%)‏ Reaction Time (ms)‏

22. Expt 2 Results, ii 30/07/09© The University of Sheffield 22

23. 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.

24. 30/07/09© The University of Sheffield 24 S S Stimulus Stimulus-Response Translation RT

25. 30/07/09© The University of Sheffield 25 Stimulus Stimulus-Response Translation RT S S

26. 30/07/09© The University of Sheffield 26 S Stimulus Stimulus-Response Translation RT S

27. 30/07/09© The University of Sheffield 27 Simulation Results, i

28. 30/07/09© The University of Sheffield 28 Simulation Results, ii

29. 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

30. Conclusions (2/2)‏ Also, Piéron’s Law holds for colour saturation… ….in a complex choice task 30/07/09© The University of Sheffield 30

31. 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, 2 nd of August

32. Locked S S

33. independent S 1

34. Single stage, independent inputs

35. Two stage, locked 1 S 1 S

36. Two stages, locked inputs

37. Two stage, independent 1 S 1 1

38. Two stages, independent inputs

39. Expt 2, Separated stroop