“Think Like You Don’t Know:” A Form of Belief Bias in Judgments of Bayesian Rationality Richard Anderson Department of Psychology Bowling Green State University Bowling Green, Ohio 1 INTRODUCTION 2 INTEGRATING DISPARATE PROBLEM DOMAINS Belief Bias in Syllogistic Reasoning: Our belief that a particular conclusion is true or false, affects how valid the argument seems. "If it were true that all fish are animals, and if it were true that all animals have wings, then it would also be true that all fish have wings." Bayesian Inference: "If the presence or absence of Disease A produces Symptom S with the probability, p, or q, respectively, and if Disease A has a prior probability, or Base Rate, R: If the symptom is present, what is the probability that Disease A is also present?" Signal Detection Modeling: If Categories I and II partially overlap on Dimension E, how does the pattern of correct and erroneous classifications reveal the magnitude of category overlap and the location criterion, on E, for classification? Metacognition: Broadly: Thinking about thinking. More specifically: thinking about Bayesian rationality. 3 A Few Links in the Research Chain 1. Belief Bias in Syllogistic Reasoning: If a syllogism's conclusion is believable (i.e., is apparently true), that makes it seem like the conclusion is valid (i.e., makes it appear to follow logically from the premises (Evans, Handley, & Harper, 2001). ... 4 A Few Links in the Research Chain 1. Belief Bias in Syllogistic Reasoning: If a syllogism's conclusion is believable (i.e., is apparently true), that makes it seem like the conclusion is valid (i.e., makes it appear to follow logically from the premises (Evans, Handley, & Harper, 2001). 2. Belief Bias, not in Syllogistic Reasoning, and not in Bayesian reasoning, but in Judgments of Sample Size Adequacy: When a sample is used to make a statistical inference: The sample size seems less adequate if the value of the sample statistic happens to be unrepresentative of the known population parameter (Anderson & Hartzler, 2013). ... 5 A Few Links in the Research Chain 1. Belief Bias in Syllogistic Reasoning: If a syllogism's conclusion is believable (i.e., is apparently true), that makes it seem like the conclusion is valid (i.e., makes it appear to follow logically from the premises (Evans, Handley, & Harper, 2001). 2. Belief Bias, not in Syllogistic Reasoning, and not in Bayesian reasoning, but in Judgments of Sample Size Adequacy: When a sample is used to make a statistical inference, the sample size seems less adequate when the decision-maker believes the inference to be false (Anderson & Hartzler, 2013). 3. The Present Study: Belief Bias in Judgments about Bayesian Rationality Anderson, Leventhal, Fasko, Basehore, Billman, Zhang, Gamsby, Branch, & Patrick (manuscript in preparation). A Form of Belief Bias in Judgments of Bayesian Rationality. 6 METHOD Trial 1 of 32. Note that the UNDERLINED text may CHANGE on each trial. A DOCTOR KNOWS THAT . . . 95% of pregnant women are pregnant with ONLY ONE fetus, and 5% are pregnant with TWINS. There is a TEST that indicates whether one or two fetuses are present. The test is accurate 70% of the time for women who are pregnant with only one fetus. The test is accurate 70% of the time for women who are pregnant with twins. ACTUAL STATUS . . . A particular woman is actually pregnant with TWINS. TEST RESULT . . . . . . Her test result indicates she is pregnant with TWINS. CONCLUSION . . . . . . The doctor cannot have direct knowledge of the pregnancy's actual status. But using only the percentages and test results described above, the doctor concludes that the woman is probably pregnant with ONLY ONE FETUS. Regardless of whether the doctor's conclusion turned out to be correct or incorrect, did the doctor draw the most reasonable conclusion given the test result? Yes. It was the most reasonable conclusion. No. It wasn't the most reasonable conclusion. How certain are you that the Yes or No answer you just gave is the correct answer? Not at all certain Slightly certain Moderately certain Very certain (Reality consistency pertained to whether the diagnosis matched the actual status.) 8 RESULTS & DISCUSSION Error bars indicate 95% confidence intervals. N = 98. 9 RESULTS & DISCUSSION Error bars indicate 95% confidence intervals. N = 98. 10 11 RESULTS & DISCUSSION 12 A Conceptual Cognitive Model 13 INTEGRATING DISPARATE PROBLEM DOMAINS Belief Bias in Syllogistic Reasoning: Our belief that a particular conclusion is true or false, affects how valid the argument seems. "If it were true that all fish are animals, and if it were true that all animals have wings, then it would also be true that all fish have wings." Bayesian Inference: "If the presence or absence of Disease A produces Symptom S with the probability, p, or q, respectively, and if Disease A has a prior probability, or Base Rate, R: If the symptom is present, what is the probability that Disease A is also present?" Signal Detection Modeling: If Categories I and II partially overlap on Dimension E, how does the pattern of correct and erroneous classifications reveal the magnitude of category overlap and the location criterion, on E, for classification? Metacognition: Broadly: Thinking about thinking. More specifically: thinking about Bayesian rationality. 14 A Form of Belief Bias in Judgments of Bayesian Rationality Richard Anderson Department of Psychology Bowling Green State University Bowling Green, Ohio 15

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