Midterm and Final exam review sheets
Midterm and Final exam review sheets 115
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This 25 page Study Guide was uploaded by Joseph Wolf on Sunday January 31, 2016. The Study Guide belongs to 115 at University at Buffalo taught by James Beebe in Fall 2015. Since its upload, it has received 36 views. For similar materials see Critical Thinking in PHIL-Philosophy at University at Buffalo.
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PHI 115 Exam I Study Sheet Fall 2015 Richard Feldman, Reason and Argument , chs. 1 & 2 Understand how harmony between belief and evidence make for rationality. Understand the most common kinds of disharmony that occur between belief and evidence. Understand how what it is rational for me to believe can be different from what it is rational for you to believe. Know the following terms: Truth value A proposition can’t describe the world correctly and also describe it incorrectly. It must either be true or false. Proposition (statement) Specific thought or idea that a declarative sentence token expresses. Fallibilism A belief can be rational even though it is actually false. Conclusive evidence evidence that is so strong that it can never lead to false beliefs. Premise The reasons that are supposed to support the conclusion. Conclusion The claim that the argument is intended to establish. Argument The combining of reasons and points in such a way to convince others. Reconstructing the argument The process of interpreting and clarifying an argument. Evaluating the argument The process of figuring out if the author has succeeded in establishing the point they are trying to establish. Argument analysis Process that consists of reconstruction and evaluation. Rhetorical power The ability to convince others. Rational strength How strong an argument is. If it provides a good reason to believe its conclusion it has a lot of rational strength, even if it does not convince people. Literacy merit how original, interesting, and well written it is. Argument stoppers Quick responses that have the effect of cutting off discussion and preventing careful analysis. Rational thinkers people who try to understand the information they receive and form conclusions based on that information. Ability to distinguish genuine arguments from other things Ability to understand and interpret arguments Ability to evaluate arguments Willingness to have an open mind Willingness to change ones mind Willingness to form beliefs even when matters are uncertain. Correspondence principle A declarative sentence is true just in case it corresponds to the facts as they actually are. A declarative sentence is false just in case it fails to correspond to the facts as they actually are. Sentence Tokens specific utterances or inscriptions such as marks on paper, Sentence Types Pattern that tokens follow. They are kinds, or types, of sentence. Context Situation that the sentence is used within. One truth value principle Every proposition has exactly one truth value. It is either true or false, but not both. Belief principle Whenever a person considers any proposition, that person must believe the proposition, disbelieve the proposition, or suspend judgment about the proposition. A person cannot at any time have more than one of these attitudes toward one proposition. Evidence All the information we have concerning a proposition. Principle of rational belief If a person’s evidence concerning a proposition supports that proposition, then it is rational for the person to believe the proposition. If the person’s evidence goes against the proposition, then it is rational for the person to disbelieve the proposition. And if the person’s evidence is neutral, then it is rational for the person to suspend judgment. Principle of proportional belief It is rational to proportion the strength of ones belief to the strength of one’s evidence. The strong ones evidence for a proposition is, the stronger ones belief in it should be. Three reasons for irrational belief Motivational Errors Misevaluation of evidence Not considering the total evidence Total evidence All the evidence must support a proposition. Theories Know what Feldman’s “one truth value principle” is. Every proposition has exactly one truth value. It is either true or false, but not both. Know what Feldman’s Belief Principle is. Whenever a person considers any proposition, that person must believe the proposition, disbelieve the proposition, or suspend judgment about the proposition. A person cannot at any time have more than one of these attitudes toward one proposition. If someone puts forward an argument for a particular conclusion, understand the various ways a critical thinker has of responding to that argument. They can believe it They cannot believe it They can suspend judgment. (I think these are correct. I am not certain.) Understand the difference between evaluating the truth of the premises of an argument and evaluating the logical strength of the argument; know how these two things can vary independently. An argument can have false premises yet still be true yielding a low logical strength. An argument can also have a false conclusion, yet have true premises again yielding a low logical strength. The only time an argument has a lot of logical strength is when the premises and the conclusion are in line. Understand how there is an analogy between (i) one’s evidence and what one believes on the basis of that evidence and (ii) premises and conclusions. Ones evidence and what one believes is the basic principle of premises and conclusions. Evidence can be seen a sort of premise, and the person belief can be seen as a conclusion. There has to be a lot of evidence in order for someone to believe something, just like there has to be logical premises in order for there to be a truthful conclusion. Timothy D. Wilson, Strangers to Ourselves , chs. 1 & 2 Terms associated with unconscious/ nonconscious Automatic Implicit Preattentive Procedural Freud’s Unconscious Preconscious o Multitude of thoughts that are simply not the focus of their current attention, such as the name of their seventh grade math teacher. o Could only be made conscious by directing attention to it. o Vast storehouse of primitive thought that is kept out of consciousness because it is a source of psychic pain. Argued that our primitive urges do not reach consciousness because they are unacceptable to our more rational, conscious selves and to society at large. According to the modern perspective, Freud’s view was far too limited. The mind operates most efficiently by relegating a large amount of high level, sophistaced thinking to the unconscious. The adaptive unconscious sizes up the world, warns people of danger, sets goals, and initiates action. The modern view states that the reason unconscious mental processes exist is due to the fact that people cannot directly examine how many parts of their mind work. Cartesian dualism “mind body problem”. Descartes said the mind is not part of physical laws, and he restricted the mind to consciousness. This thought eliminates all nonconscious thought. This is known as the Cartesian catastrophe. Parents of the theory on adaptive unconscious Hamilton, Laycock, Carpenter. Low order mental processes occur outside of awareness Divided attention Automaticity of thought Implications of nonconscious processing for prejudice Lack of awareness for ones own feelings A nonconscious self Wilson Unconscious mental processes that are inaccessible to consciousness but that influence judgments, feelings, or behavior. Edouard Claparede guy who had a pin in his hand and shook the hand of an amnesiac. Selective attention The nonconscious filter that examines the information reaching our senses and decides what to admit to consciousness. Bargh and Pietromonaco study words flashed on a screen, then they rate how hostile someone is. Know the main differences between the Freudian unconscious and Wilson’s adaptive unconscious. Freud states that the unconscious can be looked at by getting rid of barriers. Wilson states that while sometimes that may be true, most of the unconscious is not accessible. And even if we could access it, we probably wouldn’t be able to understand it. Need more information here Be able to explain the phenomenon of misattribution of arousal. Some guys link power with sex. They don’t know of this link, and thus when they mean to be powerful they come off sexual. These links may explain a lot of sexual harassment. Understand how the implicit association test works and what it purports to measure. The Implicit Association Test (IAT) measures attitudes and beliefs that people may be unwilling or unable to report. It measures the strength of associations between concepts (e.g., black people, gay people) and evaluations (e.g., good, bad) or stereotypes (e.g., athletic, clumsy). Know the difference between implicit and explicit memories (cf. passage on amnesia). Explicit memory is memory that has been labored to learn. It can be intentionally recalled. Implict memory is memory that was not intentionally learned. It occurred almost subliminally. This is the kind of memory people have when they cant remember things, such as where the bathroom is. Understand how the Donald story was used by Srull & Wyer. People were flashed words while looking at a screen. They were not aware of these words which were harsh. They later judged a person’s actions. The people who received harsh words judged the man to be mean, whereas other people judged him neutrally. Understand how Wilson’s view of the mind differs from Rene Descartes’. Descartes thought that there was no unconscious. The conscious mind is the only thing that humans had. Wilson disagrees with this completely. Wilson states that the unconscious does almost all the work, and without it we would be left useless. Understand the phenomena of confabulation. Often happens with amnesiacs. They don’t know why they don’t want to shake someones hand, but they know they don’t want to. Due to this they create a story to explain their reasoning. The story is often vague and doesn’t explain why. Know what cognitive load and the Stroop Task are. Cognitive load is when you put a lot of pressure on the conscious, such as remembering 7 numbers. Productivity and accuracy fail when this happens. The stroop task is when you have color names, but the name doesn’t represent the color. This test is hard for most people. Understand how the misattribution of arousal, the implicit association test, the Donald story, cognitive load, and the Stroop Task all provide evidence for the adaptive unconscious (a.k.a., System 1). Daniel Kahneman, Thinking, Fast and Slow , chs. 3 & 5 Flow Effortless attending, A state of effortless concentration so deep that they lose their sense of time, of themselves, of their problems. Idea thought by Mihaly Csikszentmihaly. Effects of being cognitively busy More likely to be selfish, use sexist language, make superficial judgments. Ego depletion if you have to force yourself to do something, you are less willing or less able to exert selfcontrol when the next challenge arises. Know the attributes of System 1 and System 2, their strengths and weaknesses, when it is best to use system1 vs. system2. System 1 o impulsive and intuitive o Quick o Easier o Produces feelings of familiarity o Cognitive ease System 2 o controls thoughts and behaviors o Lazy o Supervises o capable of reasoning, and it is cautious o Slower o Harder o Relies on the impression of system 1 o Cognitive strain Understand the autopilot vs. manual control metaphor for the difference between System 1 and System 2 processing. Think of a plane. The planes autopilot is system one monitoring things and making sure things are alright. The pilot is system 2. He decides the big decisions, decides how to act, and so on. System 1 is autopilot System 2 is manual control. Know how critical thinking relates to System 1 and System 2. System 1 has almost no critical thinking. System 1 simply relays information. System 2 is responsible for critical thinking. Understand what cognitive ease is, what contributes to it, and what is consequences are. Things are going well, no threats or major news. Contributions o Repeated experience o Clear display o Primed idea o Good Mood This causes o Us to feel good, think things are true, make things feel effortless, and make things feel familiar. o More intuitive, more creative Cognitive strain Vigilant and suspicious Invest more effort Feel less comfortable Make fewer errors Less intuitive Less creative Mobilizes system 2 Know what the mere exposure effect is. The link between the repetition of an arbitrary stimulus and the mild affection that people eventually have for it. A Dual Processing (i.e., System 1 vs. System 2) approach to Fallacies Appeal to money any argument that assumes that someone or something is better simply because they are wealthier or more expensive. Appeal to common practice The Appeal to Common Practice is a fallacy with the following structure: X is a common action. Therefore X is correct/moral/justified/reasonable, etc. Appeal to popular belief a fallacious argument that concludes that a proposition is true because many or most people believe it: "If many believe so, it is so." Appeal to wishful thinking the formation of beliefs and making decisions according to what might be pleasing to imagine instead of by appealing to evidence, rationality, or reality Appeal to ridicule an informal fallacy which presents an opponent's argument as absurd, ridiculous, or in any way humorous, to the specific end of a foregone conclusion that the argument lacks any substance which would merit consideration. How are these often more appealing to and work most effectively on System 1. Understand how there could still be good System 2 reasons for reasoning in accord with these fallacies. None of these fallacies require critical thinking a crucial component to system 2. They all rely on either gut feelings or logic that is easy to assume. This makes these fallacies a prime target of system 1. With that said, sometimes these appeals can be used in conjunction with system 2. For example A 20,000 dollar car is almost always better than a 1 thousand dollar car due to differences in material cost, labor cost, research and development, and so on. Alan Graham, Statistics: A Complete Introduction , ch. 7 Know the following terms: Population Everything. For example all the people in the US. Sampling frame The list of the items from which the sample is to be chosen. For example people aged 2550. Sample The representative subset of the sampling frame which is chose as failry as possible to represent the entire population. Typically a lowercase n refers to the number of items in the sample. For example Rich 2550 year olds. Random sample A sample in which every item in the population has an equal chance of being chosen. Sampling with replacement putting an item back into the sampling frame after it has been selected. Without replacement not putting the item back Mean the average of the numbers Median the number that is halfway into the set Mode The value that appears most often in a set of data Sampling errorAll sampling is inherently prone to error. Confidence interval the percentage showing how confident a sample is. Selfselection bias any situation in which individuals select themselves into a group, causing a biased sample with nonprobability sampling. Sampling bias an issue where a sample is collected in such a way that some members of the intended population are less likely to be included than others Social desirability bias The tendency of survey respondents to answer questions in a manner that will be viewed favorably by others. Stereotype threat a situational predicament in which people are or feel themselves to be at risk of confirming negative stereotypes about their social group. Law of large numbers A principle of probability and statistics which states that as a sample size grows, its mean will get closer and closer to the average of the whole population Systematic sampling a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equalprobability method. In this approach, progression through the list is treated circularly, with a return to the top once the end of the list is passed. Stratified sampling a probability sampling technique wherein the researcher divides the entire population into different subgroups or strata, then randomly selects the final subjects proportionally from the different strata. Cluster sampling a sampling technique used when "natural" but relatively homogeneous groupings are evident in a statistical population. It is often used in marketing research. In this technique, the total population is divided into these groups (or clusters) and a simple random sample of the groups is selected. Census a situation in which the entire population is sampled. Understand how skewed distributions can affect the relation between means and medians. Understand the importance of obtaining the right kinds of samples for drawing conclusions about statistical data and some common ways that samples are incorrectly obtained. Understand how measurements (e.g., polls, test scores) vary randomly around a central point. If I toss a fair coin 10 times, and I repeat this action of tossing the coin 10 times, know what percentage of the time I should expect to get exactly 5 heads. Regression to the mean data that is extremely higher or lower than the mean will likely be closer to the mean if it is measured a second time The regression fallacy Failing to recognize the regression to the man. Some common mistakes that people make when they do not recognize the existence or importance of regression to the mean. Assuming that a player will continue to play well, despite the law of regression to the mean. Leonard Mlodinow, The Drunkard’s Walk , chs. 1, 7 & 9 Know what the law of large numbers is (also discussed in Mlodinow, ch. 1). A principle of probability and statistics which states that as a sample size grows, its mean will get closer and closer to the average of the whole population Sample standard deviation numerical measure of variation in data points. Know what the standard deviation measures and why it is useful. Understand how many data points fall within +/ 1 and +/ 2 standard deviations of the mean. Standard deviation measures how close data points are to the mean. 1 Standard dev 68 percent 2 devs 95 percent Understand what a normal distribution is and know some examples of nonnormal distributions discussed in class. A normal distribution is a bell curve Non normal o Partisanship in the senate Understand the controversy over Larry Summers’ remarks about differences in the standard deviations of men’s and women’s abilities in math and science. He states that men are “better” in the upper echelons of ability when it comes to math and science. He broadened the male deviation, which makes more males on the top and on the bottom when compared to women. He is essentially saying the same thing he was trying to defend against. Understand how patterns will inevitably appear in large sets of data, even if they are not always meaningful. Understand the point of the following stories: Kahneman’s and the flight instructor Flight instructors yelled at cadets when they did poorly Praised them when they did well Their performance has nothing to do with the way the instructor acted It’s all about regression to the mean Roger Maris vs. Mickey Mantle Babe Ruth’s record Thomas Gilovich, How We Know What Isn’t So , ch. 2 & Mlodinow, The Drunkard’s Walk , ch. 9 Understand the respects in which a short run pattern or frequency may or may not reflect the long run pattern or frequency. When things are say 50/50, they can have streaks of all X or O. This is different than the actual 50/50. Understand the criticisms that Tom Gilovich makes of common ways of thinking about the hot hand phenomenon and some criticisms that we offered of Gilovich’s approach. The clustering illusion the idea that coin flips should alternate between heads and tails more than they do. Conditionals in Logic Understand the truth table for conditionals. No idea. Modus ponens the rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the antecedent ( p ) holds, then the consequent ( q ) may be inferred Modus tollens the rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the consequent does not hold ( notq ), then the negation of the antecedent ( notp ) can be inferred. Reductio ad absurdum common form of argument which seeks to demonstrate that a statement is true by showing that a false, untenable, or absurd result follows from its denial, or in turn to demonstrate that a statement is false by showing that a false, untenable, or absurd result follows from its acceptance Affirming the consequent a formal fallacy of inferring the converse from the original statement. The corresponding argument has the general form: If P, then Q. Q. Therefore, P. Denying the antecedent s a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form: If P, then Q. Not P. Therefore, not Q. Know which of these argument forms are valid and which are fallacious. **Note, If there’s something wrong on this study sheet and you get it wrong on the test as a result, I am not responsible. I’ve reread all of the documents and tried my best, but there still may be something wrong.** PHI 115 Final Exam Study Sheet Fall 2015 Thomas Gilovich, How We Know What Isn’t So , chs. 2 – 4. Understand some of the factors that cause people to see patterns that may not really be there or may only be there because of chance (and no other reason) There are multiple reasons for this. Looking to the basketball example yields some answers. Hitting a streak of 4, 5, or 6 shots in a row does not violate having a 50 percent chance of hitting each shot. People see 6 in a row and think “That’s not what random looks like.” It is stated in this chapter that people’s ideas of what random is and what it actually is are very different. The clustering illusion plays a role. The clustering illusion is the intuition that random events such as coin flips should alternate between heads and tails more than they actually do. Over application of Representativeness reflective tendency to assess the similarity of outcomes, instances, and categories on relatively salient and even superficial features, and then to use these assessments of similarities as the basis of judgment. Belief that causes resemble their effects. Misconception of random dispersions The excessive impact of confirmatory information o When things agree with each other, such as saying “all Greeks are mortals” vs. “All nonmortals are nonGreeks” humans give it much more evidential weight. The tendency to seek confirmatory information o When people are given a confirming hypothesis they seek to validate it, rather than seeking to disprove it. People look for similarity when asked about a hypothesis of similarity, and look for differences when asked about dissimilarity. Hidden and absent data Understand the respects in which a short run pattern or frequency may or may not reflect the long run pattern or frequency There are always variations with data, a drunkards walk per say. You can get 6 head coin tosses in a row, despite it being 50/50. Due to this, short run patterns rarely reflect the long term pattern. Law of large numbers the larger the number of tests, the closer to the average the outcome will become. Understand the “law” of small numbers, which is not actually a real law. People think that small samples are more accurate than they really are. Understand the lesson behind our discussion of making predictions on the basis of hidden codes in the Bible. Sharpshooter fallacy can be a powerful tool. When you choose what to draw the target around you can create almost any set or string of words. Understand the basic problems with the predictions that appear in horoscopes. They are vague and appeal to a large group of people. They prey on hidden and absent data along with seemingly fulfilled prophecies. Know the following terms: confirmation bias only looking for information that aligns with what you believe Selffulfilling prophecies accepting a change in the world with little consideration of how things might have been if we had acted differently. Usually contain a kernel of truth. o True selffulfilling prophecy a person’s expectation elicits the very behavior that was originally anticipated. o Seemingly fulfilled prophecy expectations that alter another person’s world, or limit another’s responses, in such a way that it is difficult or impossible for the expectations to be disconfirmed. Causes negative first impressions to stick more than positive ones. the Lake Wobegon Effect people think of themselves as more above average than they really are Type I error false positive. Says you have cancer when you actually don’t. Calls wolf but there isn’t a wolf. Type II error False negative. You have cancer, but test negative. hindsight bias Fundamental attribution error When you explain your successes you credit your inner qualities. When things go poorly you blame things other than yourself. Variable window not specifying a window of time with regards to a statement. Not being specific enough. Two sided events events that the outcome doesn’t matter it will still impact the person emotionally. One sided events events when only one outcome makes an emotional impact. o Confirmatory events are much more vivid and easier to remember than events that do not confirm events in the present. Hedonic Asymmetries events that go well are rarely noticed, events that go poorly are always noticed Pattern asymmetries we notice things when they are uncommon vs. things that are common. Base rate departures moving away from the norm causes concern Goffmans negatively eventful action we only notice things when someone doesn’t honor the normal act. Understand how the example of the London bombing illustrates issues concerning the clustering illusion and the sharpshooter fallacy. Despite the fact that the bombs were truly random, people saw that they were clustered in different areas. This led them to believe that they were aimed. Later, a newspaper drew areas that helped him prove that they were clustered in different areas. This is the sharpshooter fallacy. Understand the factors that cause us to see patterns that may not really be there. Confirmation bias, clustering illusion. Wobegon effect, fallacies. Understand various ways in which our expectations and desires can affect what we see. Ambiguous information can be tailored in such a way that it suits us Know steps we can take to avoid seeing what we expect to see. We can think rationally. Understand the issues involved in evaluating the probability of some specific event occurring vs. the probability of some more general event occurring. Understand the difference between expecting the next student or baseball player to have a certain characteristic vs. expecting some student or baseball player to have that characteristic at some point. Understand how this distinction is similar to the distinction between the probability of a sequence of events vs. the probability of a set of events. General events are always far more probably. This specific person breaking a record is rare, but some person in all of baseball breaking a record is almost a certainty. Sequences using “or” are much more likely than sequences using “and.” Understand the complex relationship between probability and randomness. ? Know the answer to the following question: If an arrangement of data points displays more randomness than another arrangement, is the first arrangement more improbable than the second? No. Often times people will think that, but on the short term, it’s not true. Know what Kolmogorov complexity is. How easy it is to break it down in code. The more complex it is, the more random it is. Understand the ways in which the mean values of small samples can diverge from the population mean. The law of large numbers requires there to be many tests in order for it to be close to the mean. Thinking that a small sample will be accurate falls prey to the law of small numbers. In a random sequence there can be massive variations from the average. Understand some common ways that people misinterpret incomplete data They jump to conclusions, they cluster, they fill in the gaps, and they tailor the information to their needs. Understand the importance of knowing “as compared to what” when thinking about the significant of various claims. Know how different kinds of graphs can distort the “as compared to” part. CNN graphs where they modify the Y axis. It can make it look like a massive difference when in reality it’s quite small. Understand the difference between fiveyear survival rates and mortality rates and how people have confused or abused the distinction between them. When testing early you gain knowledge that you have the disease sooner. That starts the clock. 5 years from now if you are still alive, the 5 year survival is good. The problem is when diseases take longer than 5 years to kill. This happened with prostate cancer in Britain v US. They tested later, around 70. We tested earlier. Both people were killed at the same time, but our 5 year survival was much better. Morality rates is a question of if the disease you had killed you. Understand the difference between an absolute risk increase (how many more out of 1000) and a relative risk increase (e.g., a 100% increase) and some common mistakes people make in thinking about these. Britans birth control issue. The chance of getting something bad went from 1 in 14000 to one in 7000. This is a 100 percent increase, but relatively only an actual increase of 1 person. Leonard Mlodinow, The Drunkard’s Walk , chs. 2, 3, 5, 9, 10 Understand what a sample space is and how the sizes of subsets of sample spaces can be used to calculate probabilities. The possible outcomes of a random sequence can be thought of as the points in a space. In simple sequences the space might just be a few points, but in more complex situations it can be a continuum, just like the space we live in. Know what the Monty Hall problem and the twodaughter problem are and what the correct answers to them are. Monty hall it is always better to switch. You start out with a one in 3 chance of choosing the right door. After the host opens one it goes to 1 in 2. Switching then increases your odds from 33 percent to 50. Two daughter problem o Sample space boy boy, girl boy, girl girl, girl boy. o Chance that one of them will be a girl 75 percent. (25 percent of both being girls + 50 percent of one being a girl = 75.) o If one is already a girl, the possibility of the same space boy boy is eliminated. o This leaves 3 outcomes. Girl boy, boy girl, girl gril. o In the situation of not knowing which is a girl the chance of both being a girl is 33 percent. o If the girl is first, the odds go up to 50 percent, since boy boy and boy girl are eliminated. Be able to explain the twodaughter problem, i.e., why the following questions have different answers: A couple has two children. What’s the probability they have 2 girls? What’s the probability they have 2 girls if 1st first child is girl? What’s the probability they have 2 girls if 1 child is girl? (ch. 3) See above. Be able to explain what the Gambler’s Fallacy is, how it is a mistake, and how there is something almost halfright about it. (ch. 5) Previous rolls of a dice effect the next rolls of a dice. Mistake because the rolls before do not communicate with the next rolls. It doesn’t work that way. Half right due to regression of the mean. Be able to discuss the following questions: If an arrangement of data points displays more randomness than another arrangement, is the first arrangement more improbable than the second? No. Randomness is random. One could look structured while another could look random. Be able to explain the practical benefits that creatures like us might enjoy from our tendency to see (or at least think we see) patterns everywhere (e.g., hot hands, the face of Jesus, etc.), even if they’re not always there, or even if they are not always meaningful. Evolutionarily it has helped. Seeing prey, seeing food, etc. Know the following terms: Type I error false positive. Type II error false negative. False positive you don’t have the disease but the test says you do. False negative you have the disease but the test says you don’t. Benfords law Numbers arising in a cumulative fashion are not random but rather biased in favor of lower digits. Frequency interpretation of randomness Deals with if the number produced is random. Subjective interpretation Poses the question of how did the number come to be. It deals with the process of getting the random number. Zenos paradox Traveling one half of the distance in each step will make it so you never travel anywhere. Bernoulli Trials 1 or 0 problem. Yes or no. Golden theorem law of large numbers. Law of small numbers o Misguided attempt to apply the law of large numbers when the numbers are small. Isomorphism Situation in which one problem is another in disguise. Significance testing formal procedure for calculating the probability of having observed what we ibserved if the hypothesis we are testing is true. If the probability is low, we reject the hypothesis. If it is high, we accept it. Determinism The state of the world at the present determines precicely the manner in which the future will unfold. Butterfly effect small changes can have huge impacts. Normal accident theory We should expect that minor factors we usuall ignore will by chance sometimes cause major accidents. David J. Hand, The Improbability Principle , ch. 5 Understand the importance of having lots of chances to get things right to assessing the probability of events. The law of truly large numbers comes into play. When you have millions of coin flips every day, millions of spins on a roulette wheel, and so on, things that seem unlikely are bound to happen. The more something happens, the more likely unlikely things will happen. Know what The Improbability Principle and The Law of Truly Large Numbers are. Law of truly large numbers the more something happens, the higher the chance something unlikely will happen. Law of combinations A strand of improbability principal which can lead to such a hidden explosion of opportunities. The number of combinations of interacting elemnts increases exponentially with the number of elements. Possion Distribution Math formula to determine how random something is Look elsewhere effect Detection of clusters which have been generated purely bt chance as a consequence of the large number of candidates examined. Self locating string Strings of digits that are to be found at their own position in the decimal expansion of pi. Law of probability lever Minute differences can cause massive change. Reid Hastie & Robyn M. Dawes, Rational Choice in an Uncertain World , ch. 4 Understand how the anchoring and adjustment process works and what its weaknesses are. Understand the different kinds of information people tend to anchor on. People have an anchor their first bit of information. From there they adjust from that anchor. If the anchor comes from their own idea they adjust less than if the anchor came from someone else. It’s weak for a variety of ways. We often get the wrong answer, we misjudge, we think people are like us, and it can lead to misunderstanding situations. Know the following terms: primacy effect o Information considered early in the judgment process tends to be outweighed in the final judgment. This is the adjusting. false consensus effect o We think people are more like us than there really are. Recall the sandwich board people. When they agreed, they thought 70 percent of people would also agree. When someone did not agree, they thought that 75 percent of people would disagree as well. Conservatism new information outweighs old information Most common anchor is the status quo. Projection Making judgments about someone we do not know. Correlation vs. Causation Understand what correlations are, including what positive, negative, strong, and weak correlations are. Correlations are when things are related. Positive the variable goes up. Negative it goes down. Strong 1.0. Weak .13. Understand some of the challenges involved in inferring causation from correlation. Ian Hacking, An Introduction to Probability and Inductive Logic , chs. 4 – 6 Understand the basics of probability and how probabilities can be modeled as ratios of areas in a sample space. Know what conditional probability is, what symbols are used to represent it, and how it can be modeled using ratios of areas in a sample space. Know what it means for P(A) to equal 0, .1, .5, .9, or 1. This shows how strong the probability is. 1 is the strongest, .1 or 0 is the weakest. 1 is definitely going to happen, 0 wont happen. Know which kinds of conditional and unconditional probabilities do or do not sum to 1. Understand and be able to use the rules for calculating the probabilities of conjunctions and disjunctions. Know what mutually exclusive means in the context of probability. Both cant be true Understand what probabilistic independence is. Two events are independent when the occurrence of one does not influence the probability of the occurrence of the other. Understand how the conditional nature of conditional probability enables it to function hypothetically sometimes. Understand how conditional probability can be used to precisely describe probabilistic independence. Know what the conjunction fallacy is and why it is a fallacy. occurs when it is assumed that specific conditions are more probable than a single general one. The more specific something is the less likely it is to happen. Understand the rules for calculating the probabilities of conjunctions and disjunctions. Understand how different conditional probabilities correspond to sensitivity rates, false positive rates, specificity rates, and false negative rates. Understand how pairs of these rates are related. Understand whether raising the sensitivity rate of a test generally raises or lowers its false positive rate. lowers Understand how misunderstanding or confusing these different rates can lead to misunderstandings about the outcomes of medical tests. **Note, If there’s something wrong on this study sheet and you get it wrong on the test as a result, I am not responsible. I’ve reread all of the documents and tried my best, but there still may be something wrong.** “What I’ve learned, above all, is to keep marching forward because the best news is that since chance does play a role, one important factor in success is under our control: the number of at bats, the number of chances taken, the number of opportunities seized. For even a coin weighted toward failure will sometimes land on success.” Leonard Mlodinow
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