Judgement

Question 1

What theories do subjective probability judgements form part of?

Answer 1

Subjective Expected Utility theories of normative decision-making

Question 2

People make judgements on the basis of…

Answer 2

…heuristics

Question 3

What are heuristics?

Answer 3

Mental rules of thumb, shortcuts
Don’t always work
Help us to get to a reasonable estimate of the likelihood of something happening

Question 4

What is the availability heuristic?

Answer 4

Judging probability by ease with which things come to mind

Question 5

What are the pros of the availability heuristic?

Answer 5

• frequency of events happening is a good tally for how often things come to mind

Question 6

Frequency isn’t the only thing that can affect the availability of info. What can this lead to?

Answer 6

Biased judgements

Question 7

Which research highlights the limitations of the availability heuristic?

Answer 7

Tversky & Kahneman (1974) – asked students “does ‘r’ appear more in 1st/3rd position?” –> most pps said 1st position because it is easier to recall words from memory by their 1st letter than their 3rd letter

Slovic, Fischhoff & Lichtenstein (1979) – pps were given a list of causes of death & had to estimate the frequencies of each cause –> pps overestimated ones that were heavily reported in newspapers (murder, fires) & underestimated ones that were rarely reported (emphysema, stomach cancer)

Question 8

Why is Slovic, Fischhoff & Lichtenstein’s (1979) study good?

Answer 8

It uses source material - we know the correct answers (of the causes of death) & can compare them to pps’ answers

Question 9

What is the representativeness heuristic?

Answer 9

An assessment of the degree of correspondence between an instance & a category

Question 10

What helps to drive our likelihood judgement?

Answer 10

How much a set of circumstances looks like another set that has been previously experienced

Question 11

What are limitations of the representativeness heuristic?

Answer 11

X other things can influence representativeness – it doesn’t always work, is tied to stereotypes

X it doesn’t rely on all the info out there, only a small sub-set –> this can affect our judgements

X can lead to the conjunction fallacy

Question 12

What is the conjunction fallacy?

Answer 12

When we assume that specific conditions are more probable than a single general one

The conjunction of 2 events can’t be more probable that either of its constituent events

Question 13

Which researcher/s studied the conjunction fallacy?

Answer 13

Tversky & Kahneman (1983) - the Linda problem

Question 14

What did Tversky & Kahneman’s (1983) study involve?

Answer 14

Pps were shown a description about ‘Linda’…
“Linda is 31 years old, single, outspoken & very bright. She majored in philosophy. As a student, she was deeply concerned about issues of discrimination & social justice, & also participated in anti-nuclear demonstrations. Put these statements about Linda in order of probability…”
a) Linda is active in the feminist movement
b) Linda is a bank teller
c) Linda is a bank teller & active in the feminist movement

Question 15

What did Tversky & Kahneman (1983) find?

Answer 15

Pps rated Linda as a feminist quite highly, a bank teller quite low, & a feminist + bank teller in the middle
This breaks the rules of probability because feminist bank tellers are a sub-set of ‘bank tellers’ – it must be more probable that she is a bank teller than a feminist bank teller

Question 16

What is ‘anchoring’?

Answer 16

A cognitive bias

When we rely too heavily on the first piece of info we are given (the ‘anchor’) when making decisions

Question 17

What researchers studied anchoring? (x2)

Answer 17

Tversky & Kahneman (1974)

Lichtenstein et al. (1978)

Question 18

What did Tversky & Kahneman’s (1974) study involve?

Answer 18

Pps had to estimate the answer to sums under time pressure, either…

a) 1x2x3x4x5x6x7x8
b) 8x7x6x5x4x3x2x1

Question 19

What did Tversky & Kahneman (1974) find?

Answer 19

Mean estimates:
Group a) = 512
Group b) 2,250

Pps anchored on the first values they were given & didn’t adjust their estimates appropriately

Question 20

What did Lichtenstein et al.’s (1978) study involve?

Answer 20

Pps estimated the frequencies of 40 causes of death; they were given an answer, either…

a) 50,000 deaths by motor vehicle accidents
b) 1,000 deaths by electrocution

Question 21

What did Lichtenstein et al. (1978) find?

Answer 21

Group a)’s estimates were higher - they had adjusted down from the high value they were given

Group b) had adjusted upwards, starting with lower frequency estimates

Question 22

What are Bayesian reasoning problems?

Answer 22

Reasoning problems that we solve using base theorem

Involves updating probabilities on the basis of additional info

Question 23

What can Bayesian reasoning be influenced by?

Answer 23

Representativeness

Question 24

What is the base rate fallacy?

Answer 24

If we are presented with base rate info (generic info) & specific info, we tend to ignore the base rate info & focus on the specific info

Question 25

Kahneman & Tversky (1973) told pps that there were 30 engineers & 70 lawyers in a sample. Pps were given a personality description of a person and asked what the probability of the person being an engineer was.
What did pps do?

Answer 25

The description was stereotypical of an engineer.

Pps focused on the stereotypical/specific info & not on the base rate info (the actual number of engineers in the sample)

–> said that there was a higher chance of the description being about an engineer

Question 26

Kahneman & Tversky (1973) found that even if pps were given a neutral description (30/70)…

Answer 26

…pps still tended to say there was a 50% chance of the description being about an engineer (ignored the base rate info)

Question 27

What type of info do we tend to get over-influenced by?

Answer 27

Stereotypical info

Info that gets representativeness

Question 28

What is an example of a ‘probability format’ problem?

Answer 28

“The probability of breast cancer is 1% for women at age 40 who have routine screenings. If she has breast cancer, there is an 80% probability that she will get a positive mammography. If she doesn’t have breast cancer, there is a 9.6% probability that she will get a positive mammography. A woman in this age group had a positive mammography in routine screening, what is the probability that she actually has breast cancer?”

Question 29

How do pps normally respond to this probability format problem?

Answer 29

“The probability of breast cancer is 1% for women at age 40 who have routine screenings. If she has breast cancer, there is an 80% probability that she will get a positive mammography. If she doesn’t have breast cancer, there is a 9.6% probability that she will get a positive mammography. A woman in this age group had a positive mammography in routine screening, what is the probability that she actually has breast cancer?”

Most common answer = 70-80%

Normative Bayesian answer = 7.8%

Question 30

Why do pps respond like this?

Answer 30

“The probability of breast cancer is 1% for women at age 40 who have routine screenings. If she has breast cancer, there is an 80% probability that she will get a positive mammography. If she doesn’t have breast cancer, there is a 9.6% probability that she will get a positive mammography. A woman in this age group had a positive mammography in routine screening, what is the probability that she actually has breast cancer?”

Pps focus on the hit rate (80%) at the expense of the base rate info (1%)

Question 31

Misunderstandings are common in naive pps, expert pps are not as susceptible. True/false?

Answer 31

False

Misunderstandings are common in both naïve pps & experts (e.g. medical students, Casscells et al., 1978)

Question 32

How can we improve Bayesian reasoning?

Answer 32

We can change the way we present info - use a frequency format instead to improve understanding of probabilities (Gigerenzer & Hoffrage, 1995)

Question 33

Give an example of a frequency format problem.

Answer 33

“10/1,000 women at age 40 who have routine screenings have breast cancer. 8/10 women with breast cancer will get a positive mammography. 95/990 women without breast cancer will also get positive mammography. In a sample of women at age 40 who got a positive mammography in routine screening, how many do you actually expect to have breast cancer?”

Question 34

Why is the frequency format easier to understand than the probability format?

Answer 34

“10/1,000 women at age 40 who have routine screenings have breast cancer. 8/10 women with breast cancer will get a positive mammography. 95/990 women without breast cancer will also get positive mammography. In a sample of women at age 40 who got a positive mammography in routine screening, how many do you actually expect to have breast cancer?”

We can see the number of women with & without cancer = easier to see the total sums

Most get the answer correct = 8/103 women

Question 35

Cosmides & Tooby (1996) claim that frequency format is easier because…

Answer 35

…natural frequencies are more alike the kind of info we get in our daily environment & that we have evolved alongside compared to single event probabilities (which are a relatively new invention)

Question 36

Probability info is not always bad & frequency info is not always good.

Who said this?

Answer 36

Girotto & Gonzalez (2001)

Question 37

Probability info is not always bad.

Give an example of a ‘chances format’ problem.

Answer 37

“Chances of breast cancer in women age 40 who have routine screenings are 10 chances in 1,000. 8 of the 10 chances of having breast cancer are associated with a positive mammography. 95 of the remaining 990 chances of not having breast cancer are associated with a positive mammography. A woman is tested now. Out of a total of 1,000 chances, she will have ___ chances of a positive mammography, of which ___ chances will be associated with having breast cancer.”

Question 38

What are ‘chances’?

Answer 38

Chances are single-event probabilities that can be broken down like frequencies

They are well-structured

Question 39

Frequency info isn’t always good.

What problems might make frequency format problems impossible to solve? (x2)

Answer 39

1. Defective frequency

2. Multiple sample

Question 40

Give an example of a defective frequency problem.

Answer 40

“5/100 applicants on the list were accepted. 3/5 applicants who were accepted passed the oral test. 88/95 applicants who were rejected didn’t pass oral test. Among 100 applicants who passed the oral test, the proportion that get accepted are ___ out of ___.”

• we don’t have enough frequency info to create a tree diagram/answer the question
• people may think they understand the problem but they can’t answer it

Question 41

Give an example of a problem with multiple samples.

Answer 41

“5/100 applicants were accepted. 80/100 applicants who passed oral test were accepted. 20/100 applicants who were rejected also passed oral test. Among 100 applicants who pass oral test, the proportion that get accepted are ___ out of ___.”

• applicants are drawn from different samples so would be put onto separate tree diagrams that you can’t put together to answer the question

Question 42

How might we improve Bayesian frequency?

Answer 42

• it is the structure, not the format, that helps us answer questions
• this also applies to other types of statistical reasoning tasks (e.g. cumulative risk problems)
• if you give people training on tree diagrams, they are better at answering the questions

Question 43

How do we make judgements about probabilities?

Answer 43

Johnson-Laird et al. (1999) - it may relate to how we consider the alternatives

Question 44

What experiment did Johnson-Laird et al. (1999) do on naive probability?

Answer 44

They told pps “there is a box in which there is a black marble/red marble/both. In the box there is a black marble with or without another marble: probability = __%”

–> pps tended to say 67% or 2/3 probability

Question 45

What is a limitation of Johnson-Laird et al.’s (1999) study?

Answer 45

The problem is ill-specified (there is no info about probabilities) – in the absence of info, we assume that all possible alternatives are equiprobable

Question 46

What does ‘all possible alternatives are equiprobable’ mean?

Answer 46

All alternatives are just as likely

Question 47

How do we answer Johnson-Laird et al.’s (1999) question?

Answer 47

We think about the different states of affairs that could have been the case on the basis of the description – 3 possibilities: 
Mental models: 	
1) Black
2)		Red
3) Black	Red

In 2 ^ there is a black marble in the box so we say that there is 2/3 probability that there will be a black marble

We total up the proportion of situations that come to mind in which that event happens –> as we do this, things like availability will have an influence (e.g. if we can readily think of states of affairs where black marbles happen in the world, we will rate those as more likely)