Israeli Air ForceCoaching / ParentingOur Statistical World OUTLINEExamples1. Sports - Pet Belief: The world of sports is a world of streaks.Expected Value vs Expected Utility OUTLINESome “Real Life” Expected Utility ExamplesPHI2100 EXAM #2 IN-CLASS/ONLINE LECTURE OUTLINE/SUMMARIESHow We Protect Our Pet Beliefs – Part I OUTLINE* PET BELIEFS: Beliefs we have (that we may still hold even when we know evidence suggests AGAINST the Pet Belief). Often has emotional attachments in belief.* We often protect our pet beliefs by “finessing”/choosing/focusing on certain data.(1) Representativeness Heuristic:We tend to make judgments by using stereotypes. * “Stereotypes” – Usually havenegative connotation. But can be useful in making quick decisions.Ex: If you see an Angry bear. Don’t wait to meet bear, RUN!Ex: Person wears a suit & carries a briefcase: Major? Probably Businessa. RH  Clustering Illusion = Our “stereotype” of random sequences = Not many streaks.* ACTUALLY random sequences = Random(anything is possible!) b. RH  Base Rate Paradox = All of Population/factors must be taken into account to make accurate judgement.c. RH  Conjuction Fallacy = Linda is 31 years old, & participated in antinuclear demonstrations in college.Please rank the following statements by their probability, using 1 for the most probable and 3 for the least probable.A. Linda is active in the feminist movement. B. Linda is a bank teller. C. Linda is a bank teller and is activein the feminist movement.ANSWER: Linda does not sound like a stereotypical bank teller; BUT there are more Bank Tellers than feminists SO Answer is : B.* Conjunction fallacy: A more specific / demanding description that fits our stereotype will be seen as more probable than a less specific / demanding description that does not fit our stereotype.* Lesson: We are very good at giving convincing but unsupported explanations for things after they occur.Mary has hot hands. She makes her next two shots.Success breeds confidence which breeds success, which breeds confidence…Mary has hot hands. She misses her next two shots.She got overconfident. She’s cooling off.These “easy” explanations often give you a FALSE sense of understanding. You should always ask yourself:1. Consider the opposite: If something else had occurred, could I have explained that too?2. Prediction: Could I have predicted this BEFORE it happened? If NO: Probably an “easy” explanation that offers a false sense of understanding.(3) Regression Fallacy : We often explain regression effects with unnecessary causal factors.a. Regression to the mean: Whenever occurrences of X vary around a mean, if X1 is extreme, X2 is likely to be closer to mean.- Quack cures- Punishment & Rewardo Israeli Air Force o Coaching / Parenting(4) Convenient Memory (Availability Heuristic): We tend to think events are more probable to the extent they are more available to memory. Our memory is selective. We remember things that are VIVID or DRAMATIC or ANNOYING or FITW/ OUR THEORIES.(5) Biased Interpretation: We often interpret data that contradicts our pet beliefs as BAD LUCK or as ALMOST CONFIRMING our views.How We Protect Our Pet Beliefs II OUTLINE(6) Fortune Cookie Problem: No specific predictionNO experience would disconfirm your pet belief. (Hot hands; children resemble their parents)No time frame. (Bad things happen in threes.)Vague. (Bad things happen in 3’s. Fortune teller, pp. 60-1)(7) Social factors  Biased information (unrepresentative sample)(a) Politeness. People seldom tell you how your interpersonal strategies are failing.(b) Birds of a feather. We tend to associate with people who agree w/ us. * Second hand testimony: Essential to our knowledge of the worldTestimony is sharpened: main point is over emphasized.Testimony is levelled: context, details, qualifications are de-emphasized or ignored.* Consequence of sharpening & levelling: Second hand info produces more extreme views than first hand experience.(8) Optional Stopping: Take an issue that is important to you: politics, abortion, religion, affirmative action, etc. Are you equally critical of reasons that tend to support your view as you are of reasons that tend to undermine your view? PROBABLY NOTNOTE: You’re not IGNORING negative evidence. RATHER: You are treating negative & positive evidence DIFFERENTLY. Our mistake is much more subtle than just ignoring evidence. We “finesse” the evidence so as to protect our pet beliefs.(9) Sample size paradox (or Why Amazing Coincidences Aren’t Really So Amazing): In a large enough sample, extremely low probability events will happen A LOT.1. Mutations are very rare. Some creationists say : Therefore, evolution cannot have come about by mutations.- It’s true: About 1/100,000 genes are mutants.- But: Each of us has about one billion genes. So each of us has about 10,000 mutant genes. (10) Understanding Chance1. Law of Large Numbers : Larger (well chosen) samples are more representative of a population than smaller samples.2. Frequency vs. Absolute spreadSuppose we flip a coin 1, 2, 3, 4, 5…. times.Over time: The frequency of heads / tails will tend toward 50%. But the absolute spread (the difference between the # of H’s & the # of T’s) will not necessarily be exactly 50%.* Just because 10 heads come out, doesn’t mean the next toss will have a greater/lesser chance of being heads/tails.* If something has a certain statistical propensity, that will be reflected in its long run frequency.A fair coin has a tendency to come up Heads (Tails) 50% of the time, in the long run.Our Statistical World OUTLINEIn our everyday lives, most of the world that we’re interested in is RANDOM & STATISTICAL.Fundamentally random: Event E’s occurrence is indeterminate. [This might be true, but isn’t the main point]Epistemically random: Event E’s occurrence can’t be predicted beforehand.Examples1. Sports - Pet Belief: The world of sports is a world of streaks. Hot hands & cold hands in basketballResult: Statistical analyses show that recent history is irrelevant to predicting shots in basketball, hits in baseball.H  51%HH  50%HHH  47%MMM  56%(2) Clusters: Do hits & misses cluster more than would be expected statistically? NO. For a team that hits (about) 50% of its shots, the clusters are just what you’d expect if you were flipping a coin.2. Human performance (music, sports, cooking, teaching, test taking, interviewing, etc.)* People