lecture 13- judgements and probabilities Flashcards
(30 cards)
what is a judgement?
calculating likelihood of events using incomplete information
(different from ‘decision’- actively choosing one from a number of possible actions)
what is a hit (sensitivity)?
positive result if you have disease
what is a miss?
negative result if you have disease
what is a correct rejection (specificity)?
negative result if you don’t have disease
what is a flase alarm?
positive result if you don’t have disease
what is the base rate?
prevalence
what is Bayes theorem?
probability of an event, based on current information AND prior beliefs
what is Bayes’ rule?
posterior = likelihood x prior
posterior = probability of hypothesis (have disease) given data (test result)
likelihood = probability of data given hypothesis
prior = probability of hypothesis being correct
what is the odds version of Bayes’ rule?
for comparing two hypotheses ->
posterior odds = likelihood ratio x prior odds
posterior odds = ratio of probability for hypothesis 1 vs hypothesis 2 given the data
likelihood ratio = ratio for probability for data given hypothesis
prior odds = ratio probability of one hypothesis over another before seeing data
these ratios: one divided by the other (p/d)
what is the different between prior odds and posterior odds?
prior odds- likelihood of hypothesis (having disease) before data (positive test result)
posterior odds- likelihood of hypothesis after data
as in more likely to have numerator of fraction in likelihood ratio
what study did Kahneman & Tversky (1973) carry out about base rate neglect?
- p’s given situation of group of 100 people, condition 1 = 70 lawyers 30 engineers, condition 2 = 30 lawyers 70 engineers
- p’s given description of man ‘jack’ in situation and his hobbies and asked whether engineer or lawyer (within population of group 1 or group 2)
- 90% p’s said more likely engineer, regardless of whether more likely engineer/lawyer in 70/30 split
what study did Cascells et al. (1978) carry out about neglecting base rate?
- faculty and advanced students at harvard medical school
- “If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming that you know nothing about the person’s symptoms or signs?”
- actual answer is ~2%, but 45% participants said 95% (more likely to be false positive than actual detection)
- so neglected base rate!
what study did Kahneman & Tversky (1983) carry out on conjunction fallacy?
- “Linda is 31 years old, single, outspoken & very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations”
- asked whether linda was (1) a bank teller or (2) a bank teller in the feminist movement?
- many chose 2 despite 1 being inclusive of statement 2
- conjunction fallacy- mistaken assumption that probability of conjunction of two events > probability of one of them
what is the alternative possibility about the conjunction fallacy study?
- maybe we value precision/specificity- i.e balance between probability of being correct, and specificity of answer?
- we may ignore redundant information in answers- i.e, given ‘bank teller’ in both answers- must be true, so we focus on extra information
how are we somewhat optimal in our judgement?
- including information about causal structure improves performance
- presenting in frequentist terms improves performance
- personal relevance of problem improves performance
what is the representativeness heuristic?
assume object/individual belongs to specific category because it is representative
what is the availability heuristic?
- frequencies of events estimated by ease of memory retrieval
- e.g estimate probability of contracting disease based on number of people you know with disease
what Lichenstein (1978) find about the availability heuristic?
- p’s estimated the likelihoods of causes of death
- the causes of death normally publicised were estimated to have a higher probability than those non-publicised (e.g murder was rated more likely than suicide)
what factors did Pachur et al. (2012) conclude drive the availability heuristic?
- direct experiences
- emotional response
- media coverage
what study did Oppenheimer (2004) carry out that had findings opposing the availability heuristic?
- effect can be reversed
- which surname is more common? p’s given one famous, one non-famous
- p’s often choose non-famous, despite ‘availability’ of famous surname
- however, this could be because the availability of famous name was reduced as only retrieving instances related to specific individual vs. all individuals with a non-famous surname?
what are the problems with heuristics?
- vaguely defined
- doesn’t define when specific heuristics are used
- not necessarily biased processing, but because of poor information
- list of heuristics doesn’t equate to a theory
what is the dual-process theory (Kahneman)?
- judgements are based on two distinct systems
1. system 1- fast, automatic, effortless, implicit
2. system 2- slow, serial, effortful, controlled - conforms to intuitive sense of fast solution vs. slow effortful solution
- system 1 used often (in heuristics- NOT OPTIMAL-prone to errors)
what is meant when we say we are ‘cognitive misers’
we can use system 2 to produce correct answer, but often use system 1 because it is easier/less effort
what is not clear about the dual-process theory?
- system 2 can also lead to errors- not clear when
- is there evidence for a distinction between the two system?
- both systems are relatively ill-defined
