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Unformatted text preview: Probability II Probability How many deaths in the US from each of these causes? causes?
Cause of death
Botulism Flood Heart disease Homicide Motor vehicle accidents Pregnancy Stomach cancer tornado Estimated deaths Estimated per year per 40,000 After the VA tech shooting, many recommended a number of safety measures on campus, such as heavy doors, a campus wide alert system, etc. Would this be better spent on public health measures? measures? One element of this is evaluating the future One probability of this event as well as the probability of other events (e.g. drunk driving deaths) of Last time Last Interpretation of probability Rules for calculating probabilities Expected Values more on calculating probabilities and some more common problems in interpreting probabilities common This time Availability heuristic: when people mistakenly Availability when assess the probability of an event by the ease with which occurrences can be brought to mind with
Media attention Memorable examples E.g. homicides are judged as frequent as strokes, but E.g. the latter claim about 11 times as many lives the - 9/11 9/11 Conjunction fallacy: two events occurring Conjunction two together cannot be higher than the probability of either event occurring alone either One example is the representativeness heuristic, iin n One representativeness which we assign higher probabilities to events based on how we would imagine them happening on For example, we draw a person at random from the For population. Which is more likely: this person is a) a Republican or b) a Republican earning more than $70,000 a year? $70,000 Overconfidence: people place to much confidence in their ability to Overconfidence people rate the odds that they are correct rate Fischoff, Slovic and Lichtensten (1977) 100s of q’s on general Fischoff, knowledge (does Time or Playboy have a greater circulation) knowledge the q’s on which people were more confident were more likely to deviate the from the truth from E.g. on q’s with 100% confidence, only 80% of responses were correct E.g. while those on which 50% confidence, 53% of answers correct while Conservatism: people are reluctant to change their own initial beliefs Optimism bias in own abilities in Better than average driver? On questionnaire, I asked if people thought On they had a better sense of humor than most in the class; 2/3 thought that they were either a) Funnier than almost everyone or b) Funnier than most people in the class than Another type of bias… Another Consider a population with 30 engineers and Consider 70 lawyers 70 Dick is a 30 year old man. He is married with Dick no children. A man of high abilities and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues. Ignoring base rates: the strongest piece of Ignoring the information in the example are the base rates of the population rates Yet another common mistake… Yet Which is more probable: HTHTTH HHHTTT (The order matters in this example) Gambler’s fallacy: the mistaken belief that Gambler’s the random events should be self correcting random For example, a string of bad luck should For be followed by a string of good luck be Whenever possible, look at long-run Whenever frequencies frequencies Make sure to use proper baseline How to improve our assessments of risks and probabilities? probabilities? How many deaths by stroke per 100,000 How versus deaths by homicide per 100,000 versus Don’t be fooled by detailed scenarios Don’t Don’t be fooled by more prominent Don’t examples examples 9/11, homicides, etc. When possible, break relevant probabilities into pieces to more rigorously evaluate the probability of an event occurring occurring For example, HIV example Calculate expected values of different actions when possible actions Should you buy a lottery ticket? Be willing to update beliefs with new information information Be aware of optimism; avoid thinking that Be bad things only happen to other people bad These are series of coin flips produced by an eighth grade class; one is real, one is fake-that is, the real one is produced by someone actually flipping a coin, the fake one is someone just writing down 1’s and 0’s in a way to appear random (1=H, 0=T) random 001110001100100001000010001000100 000000100110010101100001111110011 000101011001001000100000001111100 1 010001010011000101001110100110001 111010001110100011000110111100010 010110110111000110010001001000010 0 The bottom one is fake The How many deaths in the US from each of these causes? causes? Cause of death Estimated deaths
Cause of death
Botulism Flood Heart disease Homicide Motor vehicle accidents Pregnancy Stomach cancer tornado 2 200 800,000 11,000 40,000 450 90,000 90 Estimated deaths per year per These past 2 lectures should be helpful in giving a sense of the interpretation of probability and how to use it in decisionprobability making The next few lectures will discuss using The probability to test hypotheses in research probability Questions? Questions? ...
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- Fall '09