Test 2 - Questions with Commentary
Test 1 - Questions with Commentary
Quiz 6
1. For Patrick, handing out badges and posters in support of your favored political candidate is a form of propaganda.
True. He includes these as examples in his list of ways that one can function as a source of information for propaganda purposes, on p. 30.
2. Patrick believes that having an “informational monopoly” is essential for successful propaganda campaigns today.
False. See page 39.
“An informational monopoly might be nice from the vantage point of the propagandist, but is not essential or practical, especially in these days of general literacy and near-universal media access where many channels and sources compete. Complete monopoly may not even be possible in politically open societies, or not worth the effort, so one must think in terms of the practical. A qualified monopoly or dominant presence in prestige media is sufficient.”
3. Patrick does not view censorship as a form of propaganda.
False. He explicitly includes censorship is a form of propaganda via exclusion of information sources.
4. For Patrick, propaganda is an essential administrative function of any bureaucracy.
True. See the opening paragraphs of the section titled “Bureaucracy and Informational Control”.
5. One of the reasons why the ‘inverted pyramid style’ became such a common writing format in journalism is because it made it possible to cut stories to fit the available page space while still maintaining a coherent story.
True. See p. 43.
True. He includes these as examples in his list of ways that one can function as a source of information for propaganda purposes, on p. 30.
2. Patrick believes that having an “informational monopoly” is essential for successful propaganda campaigns today.
False. See page 39.
“An informational monopoly might be nice from the vantage point of the propagandist, but is not essential or practical, especially in these days of general literacy and near-universal media access where many channels and sources compete. Complete monopoly may not even be possible in politically open societies, or not worth the effort, so one must think in terms of the practical. A qualified monopoly or dominant presence in prestige media is sufficient.”
3. Patrick does not view censorship as a form of propaganda.
False. He explicitly includes censorship is a form of propaganda via exclusion of information sources.
4. For Patrick, propaganda is an essential administrative function of any bureaucracy.
True. See the opening paragraphs of the section titled “Bureaucracy and Informational Control”.
5. One of the reasons why the ‘inverted pyramid style’ became such a common writing format in journalism is because it made it possible to cut stories to fit the available page space while still maintaining a coherent story.
True. See p. 43.
Quiz 5
1. Patrick dates the first “wave” of propaganda back to the Greeks.
False. He dates the first wave of propaganda to early 17th century, specifically with the Pope Gregory XV's "Congregatio de Propaganda Fide", which translates as "Congregation for the Propagation of the Faith".
The original usage of the term "propaganda" was in a religious context, referring to church/Jesuit missionary work during the counter-reformation, the church's organized attempt to suppress heresy and impose a uniform interpretation of scripture and church teachings.
Patrick dates the first wave of propaganda to this event because it is the first large-scale propaganda effort that had an accompanying bureaucracy, and he associates true propaganda with bureaucratic organization.
2. Early on in the war (WWI) the British cut the transatlantic cable linking Germany to the United States.
True. Why did they do this? So that they could control the flow of information from Europe to the United States. The British wanted to persuade the Americans to enter the war. So they organized a campaign of demonizing Germany and casting it as a threat to democracy and Christianity, and sending prepared news reports to political officials in the US government. They wanted to ensure that news directly from Germany didn't undermine these efforts to recruit the Americans to the war effort.
3. The job of the Committee on Public Information (CPI) was to produce anti-Jewish propaganda materials for the German public.
False. The CPI was established in the United States Congress after the decision was made to support the British in WWI. The function of this organization was to raise support for the war effort among the American populace. Patrick describes the CPI as "American's first propaganda ministry".
The CPI employed a variety of propaganda tactics, including staging photographs, writing press releases, preventing pictures of the millions of dead soldiers from being published in American newspapers, promoting the notion that the war was a "battle to save Christian civilization", etc.
4. Edward Bernays coined the term “public relations”, and used the terms “propaganda” and “public relations” interchangeably.
True. Bernays worked for the CPI during WWI. After the war ended and the duties of the CPI curtailed by Congress, Bernays turned his propaganda skills toward the commercial industries. He coined the term "public relations", and described the goal of PR as the "engineering of consent".
Among his many successes was a campaign on behalf of American Tobacco Company to get more single young women to smoke in public. He staged a photo-opportunity at the New York City Easter Parade by hiring a group of models to pose as young women's rights advocates, and on cue he had them light up cigarettes in front of media photographers. The newspapers reported the event as news and the images lead to a dramatic increase in smoking by women in public.
5. According to Patrick, after WWII, propaganda became part of the social norm of mass society.
True. This is what he means by the "ubiquity" of propaganda in the modern age. "Ubiquitous" means it's found everywhere.
False. He dates the first wave of propaganda to early 17th century, specifically with the Pope Gregory XV's "Congregatio de Propaganda Fide", which translates as "Congregation for the Propagation of the Faith".
The original usage of the term "propaganda" was in a religious context, referring to church/Jesuit missionary work during the counter-reformation, the church's organized attempt to suppress heresy and impose a uniform interpretation of scripture and church teachings.
Patrick dates the first wave of propaganda to this event because it is the first large-scale propaganda effort that had an accompanying bureaucracy, and he associates true propaganda with bureaucratic organization.
2. Early on in the war (WWI) the British cut the transatlantic cable linking Germany to the United States.
True. Why did they do this? So that they could control the flow of information from Europe to the United States. The British wanted to persuade the Americans to enter the war. So they organized a campaign of demonizing Germany and casting it as a threat to democracy and Christianity, and sending prepared news reports to political officials in the US government. They wanted to ensure that news directly from Germany didn't undermine these efforts to recruit the Americans to the war effort.
3. The job of the Committee on Public Information (CPI) was to produce anti-Jewish propaganda materials for the German public.
False. The CPI was established in the United States Congress after the decision was made to support the British in WWI. The function of this organization was to raise support for the war effort among the American populace. Patrick describes the CPI as "American's first propaganda ministry".
The CPI employed a variety of propaganda tactics, including staging photographs, writing press releases, preventing pictures of the millions of dead soldiers from being published in American newspapers, promoting the notion that the war was a "battle to save Christian civilization", etc.
4. Edward Bernays coined the term “public relations”, and used the terms “propaganda” and “public relations” interchangeably.
True. Bernays worked for the CPI during WWI. After the war ended and the duties of the CPI curtailed by Congress, Bernays turned his propaganda skills toward the commercial industries. He coined the term "public relations", and described the goal of PR as the "engineering of consent".
Among his many successes was a campaign on behalf of American Tobacco Company to get more single young women to smoke in public. He staged a photo-opportunity at the New York City Easter Parade by hiring a group of models to pose as young women's rights advocates, and on cue he had them light up cigarettes in front of media photographers. The newspapers reported the event as news and the images lead to a dramatic increase in smoking by women in public.
5. According to Patrick, after WWII, propaganda became part of the social norm of mass society.
True. This is what he means by the "ubiquity" of propaganda in the modern age. "Ubiquitous" means it's found everywhere.
Quiz 4: Robert Cialdini, The Science of Influence
1. People are more likely to give change for a parking meter to a complete stranger if the requester wears a uniform rather than casual clothes.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
2. Putting a card in a hotel room that says “75 percent of people staying in this room reuse their towel” lead to a 33 percent increase in towel reuse.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
3. Two groups of people in similar neighborhoods (call them Group A and Group B) were asked if they would agree to put a large “drive safely” sign on their front law, in support of a driving safety campaign. Four times as many people in Group A agreed to put the signs on their lawns, as in Group B. The difference? Ten days earlier, the people in Group A and been approached and agreed to put a small “drive safely” postcard in their window.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
4. When a waiter offers a customer a mint while handing them the bill, customers tend to give a higher tip than if no mint was offered.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
5. When British passengers learned that the supersonic Concorde plane was no longer going to be used for twice-daily flights from London to New York, ticket sales for these flights increased dramatically the next day.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
2. Putting a card in a hotel room that says “75 percent of people staying in this room reuse their towel” lead to a 33 percent increase in towel reuse.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
3. Two groups of people in similar neighborhoods (call them Group A and Group B) were asked if they would agree to put a large “drive safely” sign on their front law, in support of a driving safety campaign. Four times as many people in Group A agreed to put the signs on their lawns, as in Group B. The difference? Ten days earlier, the people in Group A and been approached and agreed to put a small “drive safely” postcard in their window.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
4. When a waiter offers a customer a mint while handing them the bill, customers tend to give a higher tip than if no mint was offered.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
5. When British passengers learned that the supersonic Concorde plane was no longer going to be used for twice-daily flights from London to New York, ticket sales for these flights increased dramatically the next day.
(1) reciprocity
(2) scarcity
(3) authority
(4) consistency
(5) liking
(6) consensus
Quiz 3
1. Here’s a typical Bayes’ rule question:
One symptom of meningitis is a stiff neck. Let’s assume that one in 50,000 people have meningitis. Now assume that at any given time, 1 in 20 people have stiff necks. Assume also that only 50% of people who have meningitis get a stiff neck.
If a patient complains of a stiff neck, what is the likelihood that they have meningitis?
People tend to think the probability is much higher than it is in reality. One way of diagnosing their error is to say that they’ve commited the fallacy of “ignoring the base rate”.
Question: What number above represents the base rate that, if you were to ignore it, would make you guilty of the base rate fallacy?
Answer: 1 in 50,000
This is the base rate of meningitis in the population. It’s a very small percentage. This is the rate that you SHOULD anchor your estimate to. If we ignore the base rate when estimating the probability of having meningitis, that’s a mistake.
2. Damian is a high school senior. He is 6’ 7” tall and weighs 215 lbs.
Here is a list of high school sports:
If I was asked to rank order these sports by the likelihood that Damian plays them, would it be an error to rank basketball at the top of the list?
(Assume there are no significant differences in the proportion of students who participate in each of these sports.)
Yes, it’s an error. No, it’s not an error.
Answer: In this case there are no base rate differences, so we can’t be guilty of “ignoring the base rate” in our probability estimation.
So we’re only left with the information we infer from how close Damian is to the stereotype -- Damian looks more like a basketball player than any other kind of athlete. Is it a mistake to infer that he’s more likely a basketball player?
No. This inference is more likely to be true than if you just guessed by chance.
Kahneman makes it clear that judgments of probability based on representativeness can be more accurate than judging by chance. Stereotypes often contain elements of truth.
We’d be guilty of an error if we had information about the base rates (say, only 15 students in the school play basketball, but over 40 play football ...), and ignored this information in our estimate.
[Note: We discussed in class that Damian’s profile may well fit certain stereotypes for football players. In which case, it would be reasonable to have basketball and football both at the top of the list.]
In each of the remaining questions, what you're asked to do is select the interpretation of probability that is being used or is most appropriate in understanding what is being asserted.
3. “Ty Cobb has the highest career batting average in baseball history (0.3664)”.
(a) relative frequency interpretation
(b) subjective interpretation
(c) propensity interpretation
Answer: (a) relative frequency
Batting averages are calculated directly from the number of base hits divided by the total number of at-bats. It’s a straightforward relative frequency calculation.
4. “The probability that the coin will land heads on the next coin toss is 50%. This probability is a property of this physical coin in my hand, right now.”
(a) relative frequency interpretation
(b) subjective interpretation
(c) propensity interpretation
Answer: (c) propensity interpretation
The propensity interpretation identifies the probability of a coin toss with the physical features of the coin that are causally responsible for its relative frequency behavior.
Note the differences:
relative frequency interpretation: P(H) = long run relative frequency of heads
propensity interpretation: P(H) = a measure of the causal features of the coin that are responsible for the long run frequency of heads (this is the coin’s propensity to land hands)
On the relative frequency interpretation it makes no sense to say that THIS COIN has a probability 0.5 to land heads on the next coin toss. All you can say is that the relative frequency of heads would approach 50% in the limit as you tossed the coin over and over. This is what probability means on the relative frequency interpretation.
The relative frequency interpretation has many useful applications, but it has a hard time making sense of so-called “single-case” probabilities, where we’re asked to estimate the probability of a singular event.
On the propensity interpretation you can say that THIS COIN has a probability 0.5 to land heads on the next coin toss, since what you’re referring to when you say this is the propensity of the coin to land heads, and this is supposed to be a feature of the coin itself, not a hypothetical sequence of coin tosses.
5. “What are the odds that Jesus actually rose from the dead?”
(a) relative frequency interpretation
(b) subjective interpretation
(c) propensity interpretation
Answer: (b) subjective interpretation
The subjective interpretation of probability identifies probabilities with degrees of belief, or degrees of confidence in a belief.
The most natural way to interpret this question is that it’s asking how strongly one believes that Jesus actually rose from the dead.
Think of the alternatives. If we were using the relative frequency interpretation we’d be asking -- what? What fraction of all deaths are followed by resurrections? What fraction of times that Jesus dies, does he rise from the dead? No ...
If we were using the propensity interpretation we’d be asking about the physical properties of Jesus that would be causally responsible for his disposition to rise from the dead. But that’s not what we’re asking either...
So the subjective interpretation is the best choice to make sense of this question.
One symptom of meningitis is a stiff neck. Let’s assume that one in 50,000 people have meningitis. Now assume that at any given time, 1 in 20 people have stiff necks. Assume also that only 50% of people who have meningitis get a stiff neck.
If a patient complains of a stiff neck, what is the likelihood that they have meningitis?
People tend to think the probability is much higher than it is in reality. One way of diagnosing their error is to say that they’ve commited the fallacy of “ignoring the base rate”.
Question: What number above represents the base rate that, if you were to ignore it, would make you guilty of the base rate fallacy?
Answer: 1 in 50,000
This is the base rate of meningitis in the population. It’s a very small percentage. This is the rate that you SHOULD anchor your estimate to. If we ignore the base rate when estimating the probability of having meningitis, that’s a mistake.
2. Damian is a high school senior. He is 6’ 7” tall and weighs 215 lbs.
Here is a list of high school sports:
- soccer
- football
- basketball
- softball
- rugby
- gymnastics
If I was asked to rank order these sports by the likelihood that Damian plays them, would it be an error to rank basketball at the top of the list?
(Assume there are no significant differences in the proportion of students who participate in each of these sports.)
Yes, it’s an error. No, it’s not an error.
Answer: In this case there are no base rate differences, so we can’t be guilty of “ignoring the base rate” in our probability estimation.
So we’re only left with the information we infer from how close Damian is to the stereotype -- Damian looks more like a basketball player than any other kind of athlete. Is it a mistake to infer that he’s more likely a basketball player?
No. This inference is more likely to be true than if you just guessed by chance.
Kahneman makes it clear that judgments of probability based on representativeness can be more accurate than judging by chance. Stereotypes often contain elements of truth.
We’d be guilty of an error if we had information about the base rates (say, only 15 students in the school play basketball, but over 40 play football ...), and ignored this information in our estimate.
[Note: We discussed in class that Damian’s profile may well fit certain stereotypes for football players. In which case, it would be reasonable to have basketball and football both at the top of the list.]
In each of the remaining questions, what you're asked to do is select the interpretation of probability that is being used or is most appropriate in understanding what is being asserted.
3. “Ty Cobb has the highest career batting average in baseball history (0.3664)”.
(a) relative frequency interpretation
(b) subjective interpretation
(c) propensity interpretation
Answer: (a) relative frequency
Batting averages are calculated directly from the number of base hits divided by the total number of at-bats. It’s a straightforward relative frequency calculation.
4. “The probability that the coin will land heads on the next coin toss is 50%. This probability is a property of this physical coin in my hand, right now.”
(a) relative frequency interpretation
(b) subjective interpretation
(c) propensity interpretation
Answer: (c) propensity interpretation
The propensity interpretation identifies the probability of a coin toss with the physical features of the coin that are causally responsible for its relative frequency behavior.
Note the differences:
relative frequency interpretation: P(H) = long run relative frequency of heads
propensity interpretation: P(H) = a measure of the causal features of the coin that are responsible for the long run frequency of heads (this is the coin’s propensity to land hands)
On the relative frequency interpretation it makes no sense to say that THIS COIN has a probability 0.5 to land heads on the next coin toss. All you can say is that the relative frequency of heads would approach 50% in the limit as you tossed the coin over and over. This is what probability means on the relative frequency interpretation.
The relative frequency interpretation has many useful applications, but it has a hard time making sense of so-called “single-case” probabilities, where we’re asked to estimate the probability of a singular event.
On the propensity interpretation you can say that THIS COIN has a probability 0.5 to land heads on the next coin toss, since what you’re referring to when you say this is the propensity of the coin to land heads, and this is supposed to be a feature of the coin itself, not a hypothetical sequence of coin tosses.
5. “What are the odds that Jesus actually rose from the dead?”
(a) relative frequency interpretation
(b) subjective interpretation
(c) propensity interpretation
Answer: (b) subjective interpretation
The subjective interpretation of probability identifies probabilities with degrees of belief, or degrees of confidence in a belief.
The most natural way to interpret this question is that it’s asking how strongly one believes that Jesus actually rose from the dead.
Think of the alternatives. If we were using the relative frequency interpretation we’d be asking -- what? What fraction of all deaths are followed by resurrections? What fraction of times that Jesus dies, does he rise from the dead? No ...
If we were using the propensity interpretation we’d be asking about the physical properties of Jesus that would be causally responsible for his disposition to rise from the dead. But that’s not what we’re asking either...
So the subjective interpretation is the best choice to make sense of this question.
Quiz 2
1. The surgical air strike on Syria goes badly. According to military intelligence, approximately 900 civilians were unintentionally killed in the strike. The President’s advisor recommends releasing a statement to the public that estimates the number of civilian casualties at around 200.
Which cognitive bias is the advisor trying to exploit with this recommendation?
1. anchoring bias
2. availability bias
3. affect bias
This is the anchoring bias, or the anchoring effect. The idea is that the public's estimate of the real number of casualties will be anchored to the first number they're exposed to. So if that number is low their estimate will be anchored low. From a PR standpoint this is preferable to having someone in the media speculate that the number is very high, and having the public's estimate be anchored high.
2. Subjects in Group A are asked to list six instances in which they have acted assertively. They are then asked to estimate their own level of assertiveness.
Subjects in Group B are asked to list twelve instances in which they have acted assertively. The are then asked to estimate their own level of assertiveness.
Which is true?
1. Subjects in Group A tend to view themselves as more assertive than subjects in Group B.
2. Subjects in Group B tend to view themselves as more assertive than subjects in Group A.
3. There is no difference in self-reports of assertiveness between the two groups.
Answer: (1), subjects in Group A tend to view themselves as more assertive. Why? Because the subjects in Group B have a harder time coming up with twelve instances (they're "less available" to memory). This is surprising, so they look for an explanation. The default explanation is maybe they're not as assertive as they thought they were. So they report lower self-ratings of assertiveness than the subjects in Group A. This is an example of the availability heuristic.
3. When people have a positive emotional response to a technology, they tend to judge it as offering large benefits and imposing little risks.
True False
True. This is an example of the “affect bias” (in fact, it’s practically a definition of the affect bias).
4. When people are given arguments for the potential benefits of a technology, they judge the technology to be less risky (even though they have been given no new information about risks).
True False
True. Again, the affect bias. It works the other way too. If you inform people about the risks of a technology they tend to judge the benefits as less, even though the benefits may be unchanged. Also, if you simply improve the emotional association a person has with a technology (give it a "positive affect") that will cause them to increase their judgment of the benefits and reduce their judgment of the risks.
5. Paul Slovic, a pioneer on research on emotion, availability and risk assessment, argues that the public has a richer conception of risks than experts do.
True False
True. The idea is that experts tend to assess risk based on a small number of quantifiable indices, like "expected number of fatalities". But ordinary people tend to assess risk along a larger number of dimensions, such as the newness of the technology, the threat that the technology might present to future generations, the dread that the technology inspires on a gut level, the uncertainty associated with the risk, whether exposure to the risk is voluntary or involuntary, and so on. Slovic thinks that it's foolish for risk analysis experts to ignore the specific ways that the public perceives risk, even if they are prone to biases in risk assessment.
[Note: I gave everyone the mark for this question on the quiz, in response to the concerns about ambiguity in the notion of "richness" in the question.]
Which cognitive bias is the advisor trying to exploit with this recommendation?
1. anchoring bias
2. availability bias
3. affect bias
This is the anchoring bias, or the anchoring effect. The idea is that the public's estimate of the real number of casualties will be anchored to the first number they're exposed to. So if that number is low their estimate will be anchored low. From a PR standpoint this is preferable to having someone in the media speculate that the number is very high, and having the public's estimate be anchored high.
2. Subjects in Group A are asked to list six instances in which they have acted assertively. They are then asked to estimate their own level of assertiveness.
Subjects in Group B are asked to list twelve instances in which they have acted assertively. The are then asked to estimate their own level of assertiveness.
Which is true?
1. Subjects in Group A tend to view themselves as more assertive than subjects in Group B.
2. Subjects in Group B tend to view themselves as more assertive than subjects in Group A.
3. There is no difference in self-reports of assertiveness between the two groups.
Answer: (1), subjects in Group A tend to view themselves as more assertive. Why? Because the subjects in Group B have a harder time coming up with twelve instances (they're "less available" to memory). This is surprising, so they look for an explanation. The default explanation is maybe they're not as assertive as they thought they were. So they report lower self-ratings of assertiveness than the subjects in Group A. This is an example of the availability heuristic.
3. When people have a positive emotional response to a technology, they tend to judge it as offering large benefits and imposing little risks.
True False
True. This is an example of the “affect bias” (in fact, it’s practically a definition of the affect bias).
4. When people are given arguments for the potential benefits of a technology, they judge the technology to be less risky (even though they have been given no new information about risks).
True False
True. Again, the affect bias. It works the other way too. If you inform people about the risks of a technology they tend to judge the benefits as less, even though the benefits may be unchanged. Also, if you simply improve the emotional association a person has with a technology (give it a "positive affect") that will cause them to increase their judgment of the benefits and reduce their judgment of the risks.
5. Paul Slovic, a pioneer on research on emotion, availability and risk assessment, argues that the public has a richer conception of risks than experts do.
True False
True. The idea is that experts tend to assess risk based on a small number of quantifiable indices, like "expected number of fatalities". But ordinary people tend to assess risk along a larger number of dimensions, such as the newness of the technology, the threat that the technology might present to future generations, the dread that the technology inspires on a gut level, the uncertainty associated with the risk, whether exposure to the risk is voluntary or involuntary, and so on. Slovic thinks that it's foolish for risk analysis experts to ignore the specific ways that the public perceives risk, even if they are prone to biases in risk assessment.
[Note: I gave everyone the mark for this question on the quiz, in response to the concerns about ambiguity in the notion of "richness" in the question.]
Quiz 1 (Law of Small Numbers)
1. A hospital has six births, in sequence (B for boy, G for girl). Which of these sequences of births is more probable?
1. BBBGGG
2. GGGGGG
3. BGBBGB
[Note: this question is taken directly from the reading, p. 115]
The answer is that all three sequences are equally probable. Our intuition would suggest that 3 is the most probable, followed by 1, followed by 2. But that’s a mistake.
We can use this example to introduce some elementary probability concepts.
The probability of any given birth being a boy or a girl is roughly 50% (or equivalently, 1/2, or 0.5). The important fact about births is that are statistically INDEPENDENT of the history of previous births. There’s no way that the birth of a boy in ward C down the hall can influence the probability that the baby in ward D will be a boy or a girl.
For statistically independent events A and B, the probability of BOTH A and B occurring is just this:
P(A and B) = P(A) x P(B)
This is the standard rule for calculating the probability of a two independent events occurring together, from probability theory. It sometimes called the "conjunction rule", and sometimes called the "multiplication rule".
So, you just multiply the individual probabilities together.
In our examples, P(Boy) = 0.5 and P(Girl) = 0.5.
So P(BBBGGG) = P(B) x P(B) x P(B) x P(G) x P(G) x P(G)
= 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5
= 0.016 (approximately)
So you’ll expect this particular sequence to occur about 16 times in every 1000 sequences of six births.
Now, the key to the question is to realize that you’ll get the same answer for ANY sequence of six births. So the probability of getting (GGGGGG) or (BGBBGB) is the same as the probability of getting (BBBGGG).
Why does BGBBGB strike us as the most probable sequence? Because we have a conception of randomness that is associated with the concept of HAVING NO STRUCTURE OR PATTERN. But randomness CAN, and DOES, generate structure and pattern. But these structures and patterns have a statistical origin, not a causal origin.
Quoting Kahneman, “We are pattern seekers, believers in a coherent world, in which regularities (such as a sequence of six girls) appear not by accident but as a result of mechanical causality or of someone’s intention. We do not expect to see regularity produced by a random process, and when we detect what appears to be a rule, we quickly reject the idea that the process is truly random.” (p. 115)
2. Circle the best answer.
A. Studies showed that the incidence of kidney cancer is LOWEST in counties that are rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West.
B. Studies showed that the incidence of kidney cancer is HIGHEST in counties that are rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West.
C. Both A and B are true.
(C), both are true.
How is this possible? Because smaller sample sizes (in this case, “sparsely populated” counties) will exhibit larger fluctuations from the expected value, both higher and lower.
It is just like tossing sequences of coins and recording how many heads or tails you get. Over 100 tosses you expect the number of heads to converge to 50%. But over, say, FOUR tosses it’s quite common to get four heads in a row, or four tails in a row.
So this result is due entirely to chance, an effect of small sampling sizes.
3. Studies of thousands of shots in basketball confirmed the existence of the “hot hand”, i.e. players go through periods where the probability of them sinking a shot is higher than at other times, resulting in longer sequences of successful shots.
False. Studies have FALSIFIED the “hot hand” hypothesis. What the studies have shown is that the distribution of unbroken hits or misses (having a “hot hand” or being “in a slump”) of individual players is precisely what you’d expect from chance variation around the player’s long term shooting average.
So let’s say that Tom’s long term shooting average is 0.45. Over the long run, he hits about 45 baskets for every 100 shots he takes.
When Tom sinks ten shots in a row he thinks he’s “hot”. In other words, he thinks that the probability of him sinking any given shot (while he’s hot) is HIGHER than 0.45.
This is the illusion of the “hot hand”. There’s no evidence that these successful sequences of shots are due to anything but chance variation around the player’s long term shooting average.
But don’t tell Tom that.
4. Circle the best answer.
A. Surveys indicate that the best performing schools tend to be the smallest schools
B. Surveys indicate that the worst performing schools tend to be the smallest schools.
C. Both A and B are true.
(C), both A and B are true. This is the same situation as in question 1. What’s notable about this example is the Gates Foundation spent almost 2 billion dollars creating new schools and modifying schools under the assumption that smaller school sizes beget better academic performance. No one asked the question whether the survey results might be an effect of the small sample sizes.
5. Kahneman believes that our vulnerability to what he calls the “law of small numbers” is due in part to the fact that we pay more attention to the content of messages than to information about their reliability. As a result we end up with a view of the world around us that is simpler and more coherent than the data justify.
True. See pp. 118, it’s the first part of the closing paragraph in the chapter.
The second part of this closing paragraph important too:
“Statistics produce many observations that appear to beg for causal explanations but do not lend themselves to such explanations. Many facts of the world are due to chance, including accidents of sampling. Causal explanations of chance events are inevitably wrong.”
1. BBBGGG
2. GGGGGG
3. BGBBGB
[Note: this question is taken directly from the reading, p. 115]
The answer is that all three sequences are equally probable. Our intuition would suggest that 3 is the most probable, followed by 1, followed by 2. But that’s a mistake.
We can use this example to introduce some elementary probability concepts.
The probability of any given birth being a boy or a girl is roughly 50% (or equivalently, 1/2, or 0.5). The important fact about births is that are statistically INDEPENDENT of the history of previous births. There’s no way that the birth of a boy in ward C down the hall can influence the probability that the baby in ward D will be a boy or a girl.
For statistically independent events A and B, the probability of BOTH A and B occurring is just this:
P(A and B) = P(A) x P(B)
This is the standard rule for calculating the probability of a two independent events occurring together, from probability theory. It sometimes called the "conjunction rule", and sometimes called the "multiplication rule".
So, you just multiply the individual probabilities together.
In our examples, P(Boy) = 0.5 and P(Girl) = 0.5.
So P(BBBGGG) = P(B) x P(B) x P(B) x P(G) x P(G) x P(G)
= 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5
= 0.016 (approximately)
So you’ll expect this particular sequence to occur about 16 times in every 1000 sequences of six births.
Now, the key to the question is to realize that you’ll get the same answer for ANY sequence of six births. So the probability of getting (GGGGGG) or (BGBBGB) is the same as the probability of getting (BBBGGG).
Why does BGBBGB strike us as the most probable sequence? Because we have a conception of randomness that is associated with the concept of HAVING NO STRUCTURE OR PATTERN. But randomness CAN, and DOES, generate structure and pattern. But these structures and patterns have a statistical origin, not a causal origin.
Quoting Kahneman, “We are pattern seekers, believers in a coherent world, in which regularities (such as a sequence of six girls) appear not by accident but as a result of mechanical causality or of someone’s intention. We do not expect to see regularity produced by a random process, and when we detect what appears to be a rule, we quickly reject the idea that the process is truly random.” (p. 115)
2. Circle the best answer.
A. Studies showed that the incidence of kidney cancer is LOWEST in counties that are rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West.
B. Studies showed that the incidence of kidney cancer is HIGHEST in counties that are rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West.
C. Both A and B are true.
(C), both are true.
How is this possible? Because smaller sample sizes (in this case, “sparsely populated” counties) will exhibit larger fluctuations from the expected value, both higher and lower.
It is just like tossing sequences of coins and recording how many heads or tails you get. Over 100 tosses you expect the number of heads to converge to 50%. But over, say, FOUR tosses it’s quite common to get four heads in a row, or four tails in a row.
So this result is due entirely to chance, an effect of small sampling sizes.
3. Studies of thousands of shots in basketball confirmed the existence of the “hot hand”, i.e. players go through periods where the probability of them sinking a shot is higher than at other times, resulting in longer sequences of successful shots.
False. Studies have FALSIFIED the “hot hand” hypothesis. What the studies have shown is that the distribution of unbroken hits or misses (having a “hot hand” or being “in a slump”) of individual players is precisely what you’d expect from chance variation around the player’s long term shooting average.
So let’s say that Tom’s long term shooting average is 0.45. Over the long run, he hits about 45 baskets for every 100 shots he takes.
When Tom sinks ten shots in a row he thinks he’s “hot”. In other words, he thinks that the probability of him sinking any given shot (while he’s hot) is HIGHER than 0.45.
This is the illusion of the “hot hand”. There’s no evidence that these successful sequences of shots are due to anything but chance variation around the player’s long term shooting average.
But don’t tell Tom that.
4. Circle the best answer.
A. Surveys indicate that the best performing schools tend to be the smallest schools
B. Surveys indicate that the worst performing schools tend to be the smallest schools.
C. Both A and B are true.
(C), both A and B are true. This is the same situation as in question 1. What’s notable about this example is the Gates Foundation spent almost 2 billion dollars creating new schools and modifying schools under the assumption that smaller school sizes beget better academic performance. No one asked the question whether the survey results might be an effect of the small sample sizes.
5. Kahneman believes that our vulnerability to what he calls the “law of small numbers” is due in part to the fact that we pay more attention to the content of messages than to information about their reliability. As a result we end up with a view of the world around us that is simpler and more coherent than the data justify.
True. See pp. 118, it’s the first part of the closing paragraph in the chapter.
The second part of this closing paragraph important too:
“Statistics produce many observations that appear to beg for causal explanations but do not lend themselves to such explanations. Many facts of the world are due to chance, including accidents of sampling. Causal explanations of chance events are inevitably wrong.”