(posted 3/16/06)
Reading assignment: Chapter 11

Normative vs. Descriptive

1. ___________ theory = best or rational way to reason; gold standard
2. Biases = ______________________________
• Provides clue about psychological processes
• Indicates area where improvement is needed
3. ___________ theory = psychological theory about how people actually reason.
• A good theory doesn't just catalogue biases, it explains why they occur (and how to correct them).

• Deductive reasoning
• Conclusions are _______________
• Inductive reasoning
• Conclusions are _______________

Inductive Reasoning

• ___________ conclusions
• Revising beliefs based on ___________
• Example:
• If Joe committed the robbery, then he has 15 television sets, a crowbar, and no alibi.
• Joe has 15 television sets, a crowbar, and no alibi.
• Therefore . . .

• Youre worried you might have a rare disease.
• 1% of the population has this disease.
• There is a diagnostic test for the disease that has these properties:
• If the disease is present, 98% of the time the test will be positive [____________ rate]
• If the disease is absent, 1% of the time the test will be positive [______________ rate].
• Your test result is positive.
• How likely is that you have the disease?
• More likely than it was before, but how much more?

Some terms

• ___________ Probability = probability of disease after you get the test result. Depends on 3 things:
• ___________ Probability = probability of disease before you knew the test result.
• New Evidence
• __________ rate = likelihood of getting positive test result if disease is present.
• __________ rate = likelihood of getting positive test result if disease is absent.

• p(H/E) = p(H)p(E/H) / (p(H)p(E/H) + p(~H)p(E/~H))
• Prior probability
• Hit rate (aka sensitivity)
• False alarm rate (1 – specificity)

 

• Bayes’ theorem is a __________ theory of __________ reasoning.
•     Applies to belief-updating tasks.

 

• How does the prior probability affect the posterior probability?
• What if the disease affected 50% of people (rather than 1%)?

______________ Neglect

• A cab company was involved in a hit and run accident at night.  Two cab companies, the Green and the Blue, operate in the city.  You are given the following data:
• 85% of the cabs in the city are Green, 15% are Blue
• A witness identified the cab as Blue.  The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time (e.g., p(say blue/really blue) = 0.80).
• What is the probability that the cab involved in the accident was Blue rather than Green?

Base Rate Neglect

• Most people give estimates higher than ________%.
• Accident caused by blue cab is representative of the witness testimony.

Neglects the low base rate of blue cabs.

Examples of Bayes' Theorem Applications

• Any case where current belief is updated by new evidence
• Medical diagnosis
• Detective gathering crime evidence
• Scientist testing a hypothesis
• Mechanic troubleshooting a car

Forming an impression on a blind date

• The probability of breast cancer is 1% for a woman at age 40.  If a woman has breast cancer, the probability is 80% that she will have a positve mammogram.  If a woman does not have breast cancer, the probability is 9.6% that she will also have a positive mammogram.

A 40-year-old woman has a positive mammogram.  What is the probability that she has breast cancer?

• 10 of 1000 women at age 40 have breast cancer.  8 of these 10 women with breast cancer will get a positive mammogram.  Of the 990 women without breast cancer, 95 will also get a positive mammogram.
• Of women who get positive mammograms, how many have breast cancer?

Why is frequency version easier?

• Gigerenzer argues that cognitive system is set up to expect certain inputs
• Frequencies are more ______________________ valid
• Cognitive system has the ___________________ concept, but not good at doing the math, given resources available.
Therefore, develop heuristics that deal with frequencies, and store information that way.

Deductive Reasoning

• ______________ conclusions
• Conclusions follow __________________
• Example:
• No anteaters are beauticians
• All beauticians are celebrities
• Therefore, ___________________________

 

• Logic = a ________ theory of ______________ reasoning
• normative model of valid arguments
• Shows how to reach deterministic conclusions from premises or facts already known to be true.
• _____________ because if the premises are true then the conclusion is definately true (not just probably true).
• What is a _______ argument?
• One is which is there no way for the premises to be true and the conclusion to be false.
• How is this different from a true conclusion?

• _____ but not _____:
• If it is snowing, class is canceled
• It is snowing.
• Class is canceled
• _____ but not _____:
• If the horses had been to the waterhole, we would see their tracks.
• We see their tracks
• They have been to the waterhole

Wason's 4 card selection task

• If there is a vowel on one side of the card, then there is an even number on the other (p -> q)

Are people solving this using logic?
      • If so, they should be following the rules of logic.

Valid Conclusions

 modus _______ (MP)
•  p  -> q
•  p
•  q
 modus ________ (MT)
•  p -> q
•  ~q
•  p

 Denying the _________ (DA)
•  p  -> q
•  ~p
•  ~q
 ________ the Consequent (AC)
•  p -> q
•  q
•  p

• ________ (conditional if)
– p -> q
– If p then q
• _________ (biconditional if)
– p <-> q
– If and only if p then q
– ________

In 4 card selection task they
• Turn over the “____” card [correct]
• Do not turn over the “____” card [correct]
• Turn over the “____” card [incorrect]
• Fail to turn over the “_____” card [incorrect]

Mistake “if” as __________________
• Clarifying instructions do improve performance.
• But is this were the whole story, why don’t Ss turn over ___________?

_______________
• Pick the cards named in the rule.
• Supported by the fact that if the rule is
– If the card has a vowel on one side then it does not have an ________ number on the other side
– People pick “vowel” (p) and ________ (q)
– Which is correct in this case
 

An easier problem

• If person is drinking beer, then person must be 21 or older

• Can’t be logic because:
– Make errors on Modus Tollens
– Effect of _________
• (Logic says only the structure of the argument matters, not the ___________)
• Could be ____________?
– People remember actual beer-drinking instances

Can't be memory cueing

• Can’t be remembering actual beer drinking episodes
• Because performance is just as good for ___________ contents.
• What do these two examples have in common?

• __________ schema

– If action A is taken, precondition P must be satisfied
– If action A is not taken, precondition P __________ satisfied.
– If precondition P is satisfied, action A can be taken
– If precondition P is not satisfied, action A ________ be taken.
• People use these schemas (not logic)
• Can solve even unfamiliar problems that fit this schema
• without actually understanding the ________.
• suggests special role for _________ reasoning
• get people to follow ____
• detect ______________

• If the reactor is intact, then it is safe.
• If the reactor is safe, then no graphite is outside it.
• The reactor is intact and some graphite is outside it.

Models Theory(P.N. Johnson-Laird)

• Reasoners try to envisage what is possible, given the premises + own knowledge
• Each possibilities is represented in a separate _________.
• Problems that require constructing ________ are harder than those that require __________
• A mental model has the same structure as the possibility it represents.
• Principle of _______:  represent what is true; do not represent what is false.

Example

• On the blackboard there is either a circle, or a triangle, or both.
• Circle
•                   Triangle
• Circle         Triangle
• Does this follow:  It is possible that there is both a circle and a triangle.

• Reasoners evaluate consistency of a set of propositions by searching for a ______________
• If find such a model, conclude the propositions are ___________.
• If fail to find such a model, conclude the propositions are _________

• If there isn’t an apple then there is a banana.
• If there is a banana then there is a cherry.
• There isn’t an apple and there is a cherry.

• There is an apple or there is a banana.
• There isn’t a banana or there is a cherry.
• There isn’t an apple and there is a cherry.

• A problem that requires consideration of 2 models is more _______ than one that requires consideration of 1 model.
• Subjects are more accurate in the ______ problems.

• There is an apple or there is a banana
• If there is not an apple then there is a banana
• These two statements are logically equivalent.
• But they don’t trigger the same first model.
• This equivalence can be exploited to create logically equivalent groups of statements that can be evaluated:
• By examining the first model only
• Only by examining multiple models
• There are more errors in the multiple model condition.

• Model Theory predicts that people will make errors in certain situations.
• Because of the principle of ________
• Models represent what is _____; don’t explicitly represent what is _______.

• The tray is portable or else not both beautiful and heavy.
• The tray is portable and not beautiful.
• The 2nd statement appears consistent with the ______ model.  But this is because the first model does not explicitly represent not (not both beautiful & heavy) –- in other words, _______________