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# Base-Rate Respect (Barbey & Sloman, 2007)

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Base-Rate Respect (Barbey & Sloman, 2007)

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### Base-Rate Respect (Barbey & Sloman, 2007)

1. 1. Barbey & Sloman
2. 2.
3. 3. Category instances (outside view, expectbetter performance ): “Here is a new sample ofpatients who have obtained a positive test resultin routine screening. How many of these patientsdo you expect to actually have the disease? __out of __.”Category properties (inside view): “Pierre has apositive reaction to the test.” [then computeprobability estimate]
4. 4.  Single-event:  “A 40-year-old woman who participates in routine screening has 10 out of 1,000 chances to have breast cancer.” Frequencies:  “A proportion of 0.01 of women at age 40 who participate in routine screening have breast cancer.”
5. 5. Swiss Army Natural Natural Non-evo. Nested sets andKnife frequency frequency natural freq. dual processes algorithm heuristic heuristicImpenetrable NOT impenetr. NOT impenetr. NOT impenetr. NOT impenetr.Encapsulated Encapsulated Not encapsulat. Not encapsulat. Not encapsulat.One module Simplified form Heuristic to Simplified Bayes’ General purposerepresents of Bayes’ compute Bayes’ calculation, no reasoningnatural theorem: rule from natural need for natural processes (Sys. Ifrequencies calculate number frequencies, sampling and II) - of cases where “fast and frugal” “associative and#1: natural hypothesis and Sampling rule-based”frequency info observations method thateasy to store occur (“the “one way or Bayesian#2: preserves Ratio”) another” people inference fromsample size can use rule-based(10/1,000) systemInaccessible to No explicit No explicit High degree ofconscious control consideration of consideration of cog control base rates base ratesEvo Evo Evo Non-evo Non-evo “The mind is a frequency monitoring device”
6. 6.  Bayesian inference comes from rule-based system Errors from cognitive heuristics come from associative processes Base-rate neglect comes from “associative responding” and facilitation comes when people use rules to make inferences
7. 7.
8. 8. 10 out of 10,000 women have breast cancerStructure: representation of category instances demonstrates set structure (10 have, 9,990 don’t, but also everyone either has or does not have)Nested sets theory
9. 9.  First and second frameworks can really be collapsed into one, identical to #3 (Brase) Non-evolutionary natural frequency heuristic is non- evolutionary….
10. 10. Swiss Army Natural Natural Non-evo. Nested sets andKnife frequency frequency natural freq. dual processes algorithm heuristic heuristicImpenetrable NOT impenetr. NOT impenetr. NOT impenetr. NOT impenetr.Encapsulated Encapsulated Not encapsulat. Not encapsulat. Not encapsulat.One module Simplified form Heuristic to Simplified Bayes’ General purposerepresents of Bayes’ compute Bayes’ calculation, no reasoningnatural theorem: rule from natural need for natural processes (Sys. Ifrequencies calculate number frequencies, sampling and II) - of cases where “fast and frugal” “associative and#1: natural hypothesis and Sampling rule-based”frequency info observations method thateasy to store “one way or#2: preserves Really,(“the same occur the Nonsense another” people Bayesian Ratio”) inference fromsample size can use rule-based(10/1,000) systemInaccessible to No explicit No explicit High degree ofconscious control consideration of consideration of cog control base rates base ratesEvo Evo Evo Non-evo Non-evo
11. 11. Predictive factors: Degree of cognitive control in probability judgment  More control = Bayesian inference in more contexts Cognitive operations that underlie estimates of probability (only *more control* theories)  Evolutionary & non-evolutionary frequency heuristics depend on structural features of question  Nested set does not depend on natural frequencies, and instead predicts Bayesian inference when problem structure is transparent (because it triggers these elementary set operations)
12. 12.  Academic selectivity of university Monetary incentive“The former observation is consistent with theview that Bayesian inference depends on domaingeneral cognitive processes to the degree thatintelligence is domain general. The lattersuggests that Bayesian inference is strategic, andnot supported by automatic (e.g., modularized)reasoning processes.”BUT: Money decreases performance on cog tasks…
13. 13. Diagrammatic Representations! 48% got it
14. 14. Idea: Bayesian inference with natural frequencyestimates depends on accurate encoding ofautobiographical events.Really: If people are bad at remembering events(e.g., # beers had past week), then we can’t beBayesian with natural frequency estimates.Result: Our autobiographical memories are really,really, really, really bad, so we “don’t have thatcapacity.”
15. 15.  What about hypotheses that are not mutually exclusive and exhaustive (MECE)? (“I eat cookies AND I eat them with milk”) What about non-independent events? (“sweaty palms is symptomatic in 640 out of 800 patients have a disease, and 160 out of 200 patients without the disease”  80% have symptom in both cases)
16. 16. Partitioned data + prompt to use samplecategory = best chance of proper calculation Understand question See underlying nested set structure by partitioning data into subsets (to do elementary set operations) Select pieces of evidence needed for solution
17. 17. 1) Effects of intelligence and motivation supportthe idea of domain general (vs. automatic,modular) processes, supporting the nested setshypothesis
18. 18. 2) Use of category instances and divide solutioninto two parts of ratio facilitate properjudgment, facilitation depends on cues to the setstructure (vs. natural frequencies)
19. 19. 3) Frequency judgments come from fragmentedand incomplete inferential strategies
20. 20. 4) People don’t accurately weigh and combinepriors, and use irrelevant info in calculations
21. 21. 5) Nested set representations improve correctcalculation rates
22. 22. 1. Effects of intelligence and motivation support the idea of domain general (vs. automatic, modular) processes, supporting the nested sets hypothesis2. Since use of category instances and divide solution into two parts of ratio facilitate proper judgment, facilitation depends on cues to the set structure (vs. natural frequencies)3. Frequency judgments come from fragmented and incomplete inferential strategies4. People don’t accurately weigh and combine priors, and use irrelevant info in calculations5. Nested set representations improve correct calculation rates
23. 23.  “Cognitive algorithms, Bayesian or otherwise, cannot be divorced from the information on which they operate and how that information is represented.” (Gaissmaier, et al.) Mind is prepared to interpret “ecologically structured information” (Gigerenzer & Hoffrage) Perceptual system uses info through capacities for pattern recognition (G & H) Require computational models of cognitive processes to evaluate ecological rationality (G & H)
24. 24.  Do people need to be able to explicitly solve Bayesian problems to do them automatically? “Without formal training they will have no access to the rules of Bayesian inference and can therefore only attempt to use general- purpose analytic reasoning procedures which involve constructing and manipulating mental models to represent the problem information” (Evans & Elqayam)  does this explain the education effect?
25. 25. Frequencies (whole numbers) is better than rates (percentages)due to configuration of human brain in therepresentation of sets and numbers(Butterworth)Automatic neural process of extracting numbersfrom visible objects (Butter.)
26. 26.  “We can find no evidence in the target article for the authors’ assertion that base-rate neglect is due to associative processing” (Evans & Elqayam)  Problem is really the failure to integrate base rate and diagnostic info and weigh them equally  B&S say: use System 2 = perfect! Response: basically, breast cancer is associated with a mammogram (?)
27. 27.  What about people revising their judgment in light of new information? (Girotto & Gonzales) Confusion of whether observed frequencies are actually statements of expected or observed probabilistic (“8 out of 10 women with breast cancer will get a positive mammography”) (Girotto & Gonzales) Heuristics can be good (Gaissmaier, Straubinger, Funder)