PSY 341 Lecture Notes - Lecture 18: Modus Ponens
5/1/18
Ignoring Sample Size and Representativeness
• Law of Large #: larger sample are more representative
• Small samples not likely to be representative of true probabilities
•Even if someone doesn’t know about statistics, they are less likely to believe in a false *laws of small #, of
• they are knowledgeable about a domain (eg. Obstetrics Nurse)
Representativeness and Base Rate Neglect
• We often have 2 kinds of information available for decision making
• Diagnostic info
• Descriptive information that suggests category membership
• A type of representativeness / similarity judgment
• Base Rate Info: likelihood of membership in a category (probability)
• People often rely on heuristics and ignore base rate info and/or real probabilities and instead rely solely on
diagnostic info
What is the rationale way to use diagnostic and base rate info
• We should apply the Normative Model for Inductive Reasoning
• Probability / Statistical Theory
• For Base Rate + Diagnostic info, normative model is:
• Baye Theorem: Probability estimate that takes base rates and estimates for diagnostic information
into account
• Concrete example to determine whether people make decisions about the likelihood of events that are
consonant with statistical theory.
Same Problem: Frequency Format
•Frequency computation easier to compute than probability computation
• Doctors overestimate likelihoods when give probabilities, but less likely to do so when given frequencies.
Are people bad at statistical reasoning?
• Frequency vs Probability Demonstration suggests: Not always!
• Clearly algorithms that differ in computational complexity can yield mathematically equivalent solutions
• What influences the algorithm we select?
•How problem is Framed is important
•Different formats evoke different mental operations
• Some frames lead us to use algorithms that are computationally more complex -> may make us
look worse as reasoners than we really are
1. Frequency vs probabilities
2. Roman vs Arabic numerals (V x LV)multiple additions vs multiplication
3. Physics: equivalent formulations of same law
4. Conceptual / definitional vs computational formulae in statistics
Successful Statistical Reasoning
• What are the factors that control quality of judgments?
• Data Format (Evolutionary Perspective): biologically adapted to consider/ notice frequencies and not
probabilities
• Whether format triggers Statistical Knowledge
•People may understand statistical principles but fail to apply them, especially if there is a heuristic
handy
• May not recognize when they are relevant
• Ignoring base rates or sample sizes
•Conjunction fallacies
Statistical Knowledge and Training
• Statistical Training can improve use of statistical reasoning and its transfer to other domains
Inductive Reasoning Optimizing vs Statisficing
• Picture that emerges: We often fall short of the optimal, normative models in reasoning, judgement, and
design making
• We often rely on heuristics, but using them comes at a cost:
•Heuristics can lead to errors
• But without them we have tremendous difficulty living our lives
• Violating normative models may nor always be such a bad thing
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Document Summary
Law of large #: larger sample are more representative. Small samples not likely to be representative of true probabilities. Even if someone doesn"t know about statistics, they are less likely to believe in a false *laws of small #, of they are knowledgeable about a domain (eg. obstetrics nurse) Representativeness and base rate neglect: we often have 2 kinds of information available for decision making. Base rate info: likelihood of membership in a category (probability) People often rely on heuristics and ignore base rate info and/or real probabilities and instead rely solely on diagnostic info. What is the rationale way to use diagnostic and base rate info: we should apply the normative model for inductive reasoning. For base rate + diagnostic info, normative model is: Baye theorem: probability estimate that takes base rates and estimates for diagnostic information into account. Concrete example to determine whether people make decisions about the likelihood of events that are consonant with statistical theory.
