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Understanding Decision Making Under Uncertainty: Thresholds and Signal Detection Theory

This overview explores how we make decisions regarding uncertain events, focusing on key concepts from psychophysics. It delves into absolute and difference thresholds, Weber’s Law, Fechner’s Law, and the just-noticeable difference (jnd). The text explains signal detection and decision theory, highlighting response biases, payoffs, and expectations. It contrasts liberal and conservative decision-making strategies and provides empirical methods for determining individual detection thresholds. This comprehensive examination is essential for understanding the cognitive processes behind perception in uncertain environments.

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Understanding Decision Making Under Uncertainty: Thresholds and Signal Detection Theory

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  1. How do we make decisions about uncertain events? • Psychophysics • Absolute and Difference Thresholds • Weber’s Law and Fechner’s Law • The concept of the jnd (just-noticeable difference) • Signal detection and Decision Theory • Response bias: payoffs and expectations • Liberal vs. conservative strategies

  2. Physical Stimulus Perception

  3. 100 90 80 70 60 50 40 30 20 10 0 Step function Ogive % presentations detected Idealized Actual 0 6 8 10 12 14 Intensity of stimulus The absolute threshold of detection:idealized and actual

  4. 100 90 80 70 60 50 40 30 20 10 0 % presentations detected 0 6 8 10 12 14 Intensity of stimulus How to obtain empirically an individual’s absolute detection threshold:

  5. “Is the stimulus there?” (yes, no) standard stimulus comparison stimulus “Is the comparison stimulus “stronger” than the standard stimulus?” (yes, no) Finding the Absolute threshold: Finding the Difference threshold:

  6. 100 90 80 70 60 50 40 30 20 10 0 % differences detected 10 11 12 13 14 15 Intensity of comparison stimulus How to obtain empirically an individual’s difference threshold: (standard stimulus) Difference threshold = I = 12.7 – 10 = 2.7 stimulus units

  7. I c I c I or I I (difference threshold) I (Intensity of Stimulus) Weber’s Law:

  8. Fechner’s Law: S = k log I S8 S7 S6 S5 S4 S (Sensation Units or JND’s) S3 S2 I I I S1 S0 0 20 40 60 80 100 I (Intensity of the stimulus)

  9. Stimulus present Stimulus absent Responds “yes” Responds “no” A single Signal Detection trial Reality: Hit False Alarm Decision: Miss Correct rejection

  10. Stimulus present Stimulus absent $2 -$2 Responds “yes” 70% 40% $0 $0 Responds “no” 30% 60% Session 17: Payoff matrix is $2 for hit and -$2 for false alarm Reality: Hit False Alarm Decision: Miss Correct rejection

  11. Stimulus present Stimulus absent $2 $0 Responds “yes” 100% 100% $0 $0 Responds “no” 0% 0% Session 22: Payoff matrix is $2 for hit and $0 for false alarm Reality: Hit False Alarm Decision: Miss Correct rejection

  12. Stimulus present Stimulus absent $0 -$2 Responds “yes” 0 0 $0 $0 Responds “no” 100% 100% Session 18: Payoff matrix is 0 for hit and -$2 for false alarm Reality: Hit False Alarm Decision: Miss Correct rejection

  13. Experimental Conditions (Payoff schedule) Hypothetical results (Hit, F.A.) % hits %F.A. 1. ($0, -$2 ) 0% 0% 2. ($1, -$2) 40% 10% 3. ($2, -$2) 70% 40% 4. ($2, -$1) 90% 70% 5. ($2, $0) 100% 100% Summary of sample results:

  14. 1. 0% 0% 0% 2. 25% 40% 10% 3. 50% 70% 40% 4. 75% 90% 70% 5. 100% 100% 100% Summary of sample results: Experimental Conditions (Expectation of signal) Hypothetical Results % hits %F.A. % of trials observer thinks signal is present

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