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STAGES OF INDUCTIVE REASONING

STAGES OF INDUCTIVE REASONING. list current evidence P1: Jane smiles at me in class P2: Jane asked if we could study together form hypotheses: possible conclusions that see implied by the evidence Ci: ? Jane needs help in the class Cj: ? Jane wants to see me socially

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STAGES OF INDUCTIVE REASONING

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  1. STAGES OF INDUCTIVE REASONING • list current evidence • P1: Jane smiles at me in class • P2: Jane asked if we could study together • form hypotheses: possible conclusions that see implied by the evidence • Ci: ? Jane needs help in the class • Cj: ? Jane wants to see me socially • evaluate probability that each hypothesis is true • Ci: .30 Cj: .80 • search for new evidence • P3: Bob says that Jane failed the first exam • revise probabilities in light of new evidence • Ci: .30 .75 Cj: .80 .30

  2. OBSTACLES TO “INDUCTIVE RATIONALITY” • ignore potential hypotheses • ignore potential evidence • misinterpret evidence • err in estimates of hypotheses’ probabilities • bias in searching for new evidence • ignore prior probabilities when new evidence is considered

  3. HEURISTICS OF INDUCTIVE REASONINGKahneman & Tversky, 1972 • AVAILABILITY • ease of generating instances (sample) from memory • death from diabetes or accident? • words with “k” in first or third position? • estimates of quantities “anchor” our judgments about possible error • ease of imagining outcomes (“simulation”) can be biased by actual outcomes (hindsight bias) • REPRESENTATIVENESS • “typical” events and outcomes are judged more likely than others • HHHHTTTT or THHTHTTH? • is Linda a bank teller and feminist?

  4. task: given several arguments for and against a current issue (e.g., universal health care), “vote” on issue 2 strong arguments for program 4 weak arguments against program AVAILABILITY AND DECISION MAKING (Alba, 1992) vote occurs. . immediate 2 days % voting for program: 68% __% 42

  5. Eats Doesn’t eat spinach spinach Can barpress own weight15 9 Can’t barpress own weight 5 __ positive instances may be more available in memory than negative “instances” AVAILABILITY AND ILLUSORY CORRELATIONS 3

  6. ESTIMATING EVERYDAY RISKS • being killed by lightning • 1 in 2 million • being killed by husband or lover • 1 in 800,000 • emergency treatment for injury from sink or toilet • 1 in 7,500 • dying in childbirth • 1 in 12,000 Paling, 1994

  7. Considering Sample Size • Two hospitals in town • One has mean of 45 births / day • One has mean of 15 births / day • Both count days with >60% males. Which is more likely? • Large hospital has more • Small hospital has more • About equal of such days • Correct answer: small hospitalWhy?

  8. RELIANCE ON REPRESENTATIVENESS • ignoring small sample size • the smaller the sample, the less representative it will be • how to make sample size salient • ignoring the laws of probability • conjunction of two events can’t be more likely than either event alone • p(A&B) = p(A) x p(B), both < 1.00 • ignoring prior probabilities • Bayes’ Theorem: combines old prior probabilities and “strength” of new evidence to obtain new odds

  9. SAMPLE SIZE AND REPRESENTATIVENESSNisbett et al., 1983 • on imagined trip to Oceana, you find samples of: • natives, all of whom are obese • a new species, shreeble birds, all of whom are red • a new element, Floridium, all rocks of which are conductive • task: Given samples of size N, estimate the percent of the whole population with that trait:

  10. The conjunction fallacy Linda is 31 yrs old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. Linda … • Is a teacher in elementary school • Works in a bookstore and takes yoga classes • Is active in the feminist movement • Is a psychiatric social worker • Is a member of the League of Women Voters • Is a bank teller • Is an insurance salesperson • Is a bank teller and is active in the feminist movement

  11. IGNORING THE “BASE RATE” Management job interview scenario: Pool of applicants includes 70% law background 30% engineering background “Tom R. is 30 yrs. old, married, no children, intelligent and motivated, well liked by his colleagues” How likely is it that Tom R. is a lawyer, and not an engineer? Actual:p = .70 (why?) Obtained:p = .52

  12. Inductive Reasoning and “Circumstantial Evidence” • CIRCUMSTANTIAL EVIDENCE • Circumstantial evidence is a fact that can be used to infer another fact. • Indirect evidence that implies something occurred but doesn't directly prove it • proof of one or more facts from which one can find another fact • proof of a chain of facts and circumstances indicating that the person is either guilty or not guilty. • E.g., If a man accused of embezzling money from his company had made several big-ticket purchases in cash around the time of the alleged embezzlement, that would be circumstantial evidence that he had stolen the money.

  13. E.g., X is suing his wife, Y, for a divorce, claiming she is having an affair with Z. Z's fingerprints are found on a book in X and Y's bedroom. A judge or jury may infer that Z was in the bedroom. The fingerprints are circumstantial evidence of Z's presence in the bedroom. Circumstantial evidence is usually not as good as direct evidence (an eyewitness saw Z in the bedroom) because it is easy to make the wrong inference - Y may have loaned Z the book and then carried it back to the bedroom herself after getting it back. • The law makes no distinction between the weight given to either direct or circumstantial evidence • “Circumstantial evidence is generally admissible in court unless the connection between the fact and the inference is too weak to be of help in deciding the case. Many convictions for various crimes have rested largely on circumstantial evidence.”[‘Lectric Law Library] • “The case against him is purely circumstantial.” • “Theories can’t be proven, only disproven; therefore, one theory is as good as another.” • “Evolution is just a theory, not a fact.”

  14. We end with a comment on the status of evolution-as fact, "just a theory," or something in between. In the physical sciences there are many observations or facts that have given rise to generalizations: two of these are the law of conservation of matter and the law of definite proportions (which states that when two or more elements combine to form a compound they do so in definite proportions by weight). The statements of facts and their convenient generalization to laws are expressed in terms of macroscopically observable and weighable quantities. The overarching explanation for these laws is achieved in atomic theory, which is expressed in terms of invisible atoms and molecules. No one thinks that atomic theory is "just a theory," for it possesses extraordinary explanatory power and provides the context in which many of the conveniences of our civilization depend. Thus we proceed from many observations or facts to their generalization in terms of laws, both levels macroscopic, to a theory expressed in terms of invisible entities. • If we now apply this scheme to biology, we see that the concept of evolution is at the law level, as it summarizes the results of a large number of observations or facts about organisms. The analogous theory is natural selection or other means by which evolution is achieved. Unknown nearly 150 years ago to Darwin, explanations of macroscopic evolution in terms of microscopic genes and molecular sequences of nucleic bases in DNA are known to us. Placing the concept of evolution at the law level clarifies its status; it is not a theory. [Bruce & Francis Martin, Skeptical Enquirer, Nov. 2003]cf. William A. Dembski: "The Design Inference: Eliminating chance through small probabilities," Cambridge University Press, (1998) 

  15. CHOOSING ALTERNATIVE ACTIONS UNDER UNCERTAINTY consider the costs & benefits of various combinations of actions and outcomes: Action: take umbrella? OutcomeProb.NOYES RAIN .40 - 10[-4.0]+ 5 [+2] SUNNY .60 + 2 [+1.2]- 2 [-1.2] expected outcome:- 2.8+0.8 what to choose? Utility theory says pick action that gives best “average” or expected outcome. for each action, expected outcome = sum of [probs x outcomes]

  16. FRAMING CHOICES FOR GAINS OR LOSSES task: choose disease control program. If no intervention, 600 will die. Program A Program B prob. of . .(low risk)(high risk) none saved 0.00 0.67 200 saved 1.00 0.00 600 saved 0.00 0.33 “persons saved” frame: __% choose A “persons killed” frame: __% choose A (Kahneman & Tversky, 1982) 72 22

  17. COGNITIVE PSYCHOLOGYCourse Goals In EXP 3604, you will learn about... • THE COGNITIVE APPROACH • how to think about cognition like acognitive psychologist • THE METHODS OF THAT APPROACH • understanding the interplay between theoretical and experimental tools • THE NATURE AND LIMITS OF COGNITION • how we do those things we do(e.g., perceive, attend, recall, think…) • TIPS AND TECHNIQUES FOR ENHANCING COGNITION • methods of improving your skills inlearning, remembering and thinking … and revive that childlike sense of awe

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