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A Phase Transition Model for the Speed-Accuracy Trade-Off

Han van der Maas. Eric-Jan Wagenmakers. Ingmar Visser. A Phase Transition Model for the Speed-Accuracy Trade-Off. Gilles Dutilh. University of Amsterdam, Department of Psychology Psychological Methods Group. Outline of this Talk. Speed-Accuracy Trade-Off Experimental focus

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A Phase Transition Model for the Speed-Accuracy Trade-Off

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  1. Han van der Maas Eric-Jan Wagenmakers Ingmar Visser A Phase Transition Model for the Speed-Accuracy Trade-Off Gilles Dutilh University of Amsterdam, Department of Psychology Psychological Methods Group

  2. Outline of this Talk • Speed-Accuracy Trade-Off • Experimental focus • the Phase Transition Model • Experiment and Data • Conclusions

  3. Speed-Accuracy Trade-Off • Participants can speed up • at the cost of accuracy. • Participants can improve their accuracy • at the cost of speed • Most models of the SAT implicitly assume a continuous trade-off function.

  4. Bimodality Counts RT Scope of this study • Most studies have focused on higher regions of accuracy. • - Now: what happens when we push participants to, e.g., perform at 75% correct

  5. Scope of this study • Bimodality implies two separate modes of processing: • accurate responding • fast guessing • Our main study explores dynamics of the transitions between these modes.

  6. Experiment • Aim: • Use reward function to push participants from • highly accurate behavior • to • very fast behavior • and back and forth. • Lexical Decision Task • Line Length Discrimination

  7. Experiment 900 700 Pay-off for Accuracy RT 500 300 100 1 Correct 0 0 20 40 60 80 trial

  8. Phase Transition Model • We want a model that describes the dynamics of these two modes. • In physics and biology, it is common to model dynamical systems like these using Catastrophe Theory.

  9. Phase Transition Model Cusp Catastrophe State Temperature -4°C Bimodality Hysteresis 0°C Pressure

  10. State Accurate Mode Payoff for Accuracy Guess Mode Stakes Phase Transition Model Hysteresis

  11. Experiment • Predictions • Participants adopt one of the modes, depending on pay-off for accuracy • - Switches between modes display hysteresis.

  12. Experiment • Predictions • Participants adopt one of the modes, depending on pay-off for accuracy • - Switches between modes display hysteresis.

  13. Hysteresis Experiment Results

  14. Hysteresis Experiment • Results • Clear hysteresis effect for at least some of the participants. • Hidden Markov Analyses confirm these results uniformly.

  15. Discussion • To Conclude • At intermediate pressure on speed and accuracy, behavior is Bimodal. • The transitions from guessing to accurate responding displayed Hysteresis. • Speed-accuracy trade-off is a catastrophe for at least some participants. • Future work: incorporate existing RT-models in a phase transition framework.

  16. The end Thank You

  17. Hysteresis Experiment Results

  18. Experiment

  19. Experiment RTotal = Raccuracy + RSpeed RAccuracy ~ PAccuracy * Accuracy RSpeed ~ PSpeed * Speed PAccuracy + PSpeed = constant

  20. R(RT) = Prt * (RTacc - RT)/(RTacc - RTguess) R(acc) = f(acc) * Pacc F(acc) = 1 (if acc = 1) -1 (if acc = 0) R(total) = R(RT) + R(acc)

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