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Test #3 Review #4 - Lecture#22 Two types of reasoning tasks...

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Lecture #22 Two types of reasoning tasks o Deductive/deterministic—tasks in which there is a deterministic answer (solving puzzle, or logic problem o Inductive/probabilistic—there is more than one answer, each with an associated probability of being correct Two theories of reasoning—the ways that people reason o Normative—how people should reason o Descriptive—how people actually reason Normative inductive reasoning—the way that people should think when solving an inductive problem o Base rate—proportion of people overall that have the condition Combining with hit rate and false alarm rate is what gives you an idea of the likelihood that the person actually has disease o Mammogram example—how doctors determine whether or not a woman actually has breast cancer after seeing her mammogram results Probability (positive mammogram/breast cancer)=.8 Probability (breast cancer/positive mammogram)=.07 95% of doctors confuse these two; they fail to take into account the overall low probability that people have breast cancer; this is a descriptive method o Bayes theorem—a way of combining the hit rate and the false alarm rate with the base rate information to come up with the normative conclusion about the likelihood that some hypothesis is true given some evidence. P(H/E)=P(E/H)*P(H) / P(E/H)*P(H) + P(E/not H)*P(not H) P(disease given positive test)=P(hit)*P(disease) / P(hit)*P(disease) + P(false alarm)*P(no disease) The number of people with the disease who show a positive test divided by the total number of people who show a positive test This theorem takes three pieces of information into account Base rate—overall probability that someone has the disease Hit rate—probability of a positive test given that someone has disease False alarm rate—the probability of the positive test given that person doesn’t have disease Descriptive theory—what people actually do as opposed to normative o People make errors in two ways o Don’t properly consider current evidence Poker chip example 2 bags of poker chips mix of red and blue Bag 1 is 70/30, bag 2 is 30/70 If person choose1 bag, what is probability that it is predominantly red bag = .5 o This is a very simple probability problem
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If we choose one chip and chip is red, what is the probability that it is from the predominantly red bag o This gives us enough information to use Bayes Theroem The right answer is .7 Many people answer .6 because they pay too much attention to the base rate, not enough weight to current evidence o Don’t properly consider the base rate Chip problem Bag A has 10 blue, 20 red; bag B has 20 blue 10 red You are told that the probability of choosing from bag A is .8 Draw 3 chips from bag (with replacement and get 2 blues and 1 red People are asked what the probability is that they chose from bag A Most people say higher probability of bag B Base rate is ignored; people are looking at 3 chips and 2
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