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EXPLORING the HOT HAND PHENOMENON a Thesis Submitted DETECTING STRUCTURE IN ACTIVITY SEQUENCES: EXPLORING THE HOT HAND PHENOMENON A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science By TALERI HAMMACK B.S., University of Idaho, 2012 2015 Wright State University WRIGHT STATE UNIVERSITY GRADUATE SCHOOL August 20, 2015 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Taleri Hammack ENTITLED Detecting Structure in Activity Sequences: Exploring the Hot Hand Phenomenon BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Masters of Science . ____________________________ John Flach, Ph.D. Thesis Director ___________________________ Scott Watamaniuk, Ph.D. Graduate Program Director ___________________________ Debra Steele-Johnson, Ph.D. Chair, Department of Psychology Committee on Final Examination _________________________________ John Flach, Ph.D. _________________________________ Kevin Bennett, Ph.D. _________________________________ Joseph Houpt, Ph.D. _________________________________ Robert E. W. Fyffe, Ph.D. Vice President for Research and Dean of the Graduate School ABSTRACT Hammack, Taleri Lynn. M.S. Human Factors and Industrial/Organizational Psychology, Department of Psychology, Wright State University, 2015. Detecting Structure in Activity Sequences: Exploring the Hot Hand Phenomenon. Can humans discriminate whether strings of events (e.g., shooting success in basketball) were generated by a random or constrained process (e.g., hot and cold streaks)? Conventional wisdom suggests that humans are not good at this discrimination. Following from Cooper, Hammack, Lemasters, and Flach (2014), a series of Monte Carlo simulations and an empirical experiment examined the abilities of both humans and statistical tests (Wald-Wolfowitz Runs Test and 1/f) to detect specific constraints that are representative of plausible factors that might influence the performance of athletes (e.g., learning, non-stationary task constraints). Using a performance/success dependent learning constraint that was calibrated to reflect shooting percentages representative of shooting in NBA games, we found that the conventional null hypothesis tests were unable to detect this constraint as being significantly different from random. Interestingly however, the analysis of human performance showed that people were able to make this discrimination reliably better than chance. Hence, people may also be able to detect patterned/constrained processes in a real-world setting (e.g., streaks in basketball performance), thus supporting the belief in the hot hand. iii TABLE OF CONTENTS Page 1. INTRODUCTION ....................................................................................................... 1 1.1. Heuristic: Bias or Smart Mechanism ................................................................... 1 1.2. Hot Hand: Fallacy or Adaptive Strategy .............................................................. 3 1.2.1. Is Performance Streaky ................................................................................. 3 1.2.2. Can People Discriminate Streaky from Random Sequences ........................ 5 1.2.3. Does Context Matter ..................................................................................... 6 1.3. Structure of Current Research .............................................................................. 6 2. MONTE CARLO SIMULATIONS ............................................................................ 8 2.1. Simulation Method ............................................................................................... 8 2.1.1. Quadrant 1 ..................................................................................................... 9 2.1.2. Quadrant 2 ..................................................................................................... 9 2.1.3. Quadrant 3 ..................................................................................................... 9 2.1.4. Quadrant 4 ................................................................................................... 10 2.2. Simulation Analysis ........................................................................................... 10 2.3. Simulation Results ............................................................................................. 11 3. MONTE CARLO SIMULATIONS OF A PERFORMANCE DEPENDENT LEARNING CURVE........................................................................................................ 17 3.1. Introduction ........................................................................................................ 17 3.2. Simulation Method ............................................................................................. 18 3.3. Simulation Analysis ........................................................................................... 19 3.4. Simulation Results ............................................................................................. 21 4. EMPIRICAL STUDY METHOD ............................................................................. 24 4.1. Introduction ........................................................................................................ 24 4.2. Participants ......................................................................................................... 24 4.3. Equipment .......................................................................................................... 25 iv TABLE OF CONTENTS (Continued) Page 4.4. Procedure ............................................................................................................ 25 4.5. Design ................................................................................................................ 26 4.6. Independent Variables ........................................................................................ 27 4.7. Dependent Variables .......................................................................................... 27 5. EMPIRICAL RESULTS ........................................................................................... 29 5.1. Measuring Sensitivity (d’) .................................................................................. 29 5.2. Response Bias c.................................................................................................. 30 5.3. Individual Participants ....................................................................................... 32 5.3.1. Participant Strategies .................................................................................. 34 6. EMPIRICAL RESULTS RECODED ....................................................................... 36 6.1. Recoding Method ............................................................................................... 36 6.2. Recoded Results ................................................................................................. 36 6.2.1. Recoded Measure of Sensitivity (d’) .......................................................... 37 6.2.2. Recoded Response Bias c ........................................................................... 38 6.2.3. Individual Participants after Recoding........................................................ 39 7. ARCHIVAL NBA DATA METHOD ....................................................................... 43 8. ARCHIVAL NBA DATA RESULTS ....................................................................... 44 9. DISCUSSION ............................................................................................................ 45 9.1. Monte Carlo Simulations ................................................................................... 45 9.2. Empirical Experiment ........................................................................................ 46 9.3. Archival NBA Data ............................................................................................ 49 10. SUMMARY AND CONCLUSIONS .................................................................... 51 10.1. Specific Implications Relative to Gilovich, Vallone, and Tversky (1985) ........ 51 10.2. Specific Implications Relative to the Hot Hand ................................................. 51 10.2.1. Pattern Perception: Fallacy or Adaptive Strategy? ..................................... 52 10.3. General Implications Relative to Human Decision Making .............................. 55 10.3.1. Heuristics: Bias or Smart Mechanism? ....................................................... 55 10.3.2. Abduction and Ecological Rationality ........................................................ 55 v TABLE OF CONTENTS (Continued) Page APPENDICES A. Empirical Experiment Interface ............................................................................... 57 B. Participant Instructions ............................................................................................. 58 C. Participant Debriefing .............................................................................................. 59 REFERENCES ................................................................................................................. 61 vi LIST OF FIGURES Figure Page 1. Four types of processes……………………………………………………………..…8 2. Spectral plot for a condition in Quadrant 1…………………………………………..14 3. Spectral plot for a condition in Quadrant 2……………………………….………….14 4. Spectral plot for a condition in Quadrant 3……………………………….………….15 5. Spectral plot for a condition in Quadrant 3……………………………….………….15 6. Spectral plot for a condition
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