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Rational Thinking

Rational Thinking. It’s Easy to Make Mistakes. Logical mistakes Statistical mistakes. Post Hoc Ergo Propter Hoc. As the number of pirates has decreased, global warming has increased. ? Therefore, global warming is caused by a lack of pirates. . Post Hoc Ergo Propter Hoc.

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Rational Thinking

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  1. Rational Thinking

  2. It’s Easy to Make Mistakes • Logical mistakes • Statistical mistakes

  3. Post Hoc Ergo Propter Hoc • As the number of pirates has decreased, global warming has increased. • ? Therefore, global warming is caused by a lack of pirates.

  4. Post Hoc Ergo Propter Hoc • In research hospitals, a higher percentage of patients die than in community hospitals. • ? Therefore, you should avoid going to a research hospital.

  5. Post Hoc Ergo Propter Hoc • Whenever ice cream sales increase, so do drowning deaths. • ? Therefore, ice cream causes drowning.

  6. Post Hoc Ergo Propter Hoc • The more firemen fighting a fire, the more likely there is to be very serious damage. • ? Therefore, extra fireman shouldn’t be called in.

  7. Post Hoc Ergo Propter Hoc • People who slept with their shoes on are very likely to wake up with a headache. • ? Therefore, sleeping with shoes on causes headache.

  8. Post Hoc Ergo Propter Hoc • Women who took hormone replacement therapy (HRT) after menopause have a lower than average incidence of coronary artery disease. • ? Therefore, HRT protects against coronary heart disease.

  9. Post Hoc Ergo Propter Hoc • Overweight septuagenarians live longer. • ? Therefore, older folks should eat more brownies. http://news.yahoo.com/s/afp/20100128/hl_afp/healthagingusaustralia

  10. Post Hoc Ergo Propter Hoc • Young children who sleep with the light on are much more likely to develop myopia in later life. • ? Therefore, sleeping with the light on causes myopia.

  11. Post Hoc Ergo Propter Hoc • Previous studies have linked drinking diet soda with a higher risk of diabetes, among other health problems. • ? Therefore, no more http://healthland.time.com/2011/04/22/study-diet-soda-may-not-raise-risk-of-diabetes-after-all/?artId=31132?contType=article?chn=us

  12. Post Hoc Ergo Propter Hoc • Previous studies have linked drinking diet soda with a higher risk of diabetes, among other health problems. • ? Therefore, no more “Though past studies have suggested that people who regularly drink diet soda may be at higher risk of developing diabetes than non-soda-drinkers, that association may have more to do with the type of person who drinks diet soda to begin with — not the diet soda itself. People who are overweight or already at risk for diabetes may be more likely than others to drink diet soda, the authors of the new study suggest.” http://healthland.time.com/2011/04/22/study-diet-soda-may-not-raise-risk-of-diabetes-after-all/?artId=31132?contType=article?chn=us

  13. Post Hoc Ergo Propter Hoc From Marijuana: Facts Parents Need to Know, 2005 (The National Institute on Drug Abuse): Question: Does using marijuana lead to other drugs? Answer: Long-term studies of high school students and their patterns of drug use show that very few young people use other drugs without first trying marijuana, alcohol, or tobacco. …

  14. Post Hoc Ergo Propter Hoc From A. K. Cline: Statistical Nonsense to Mislead Parents. (Never actually to be published) : Question: Does using water lead to other drugs? Answer: Long-term studies of high school students and their patterns of drug use show that absolutelyno young people use other drugs without first trying water. ……

  15. Post Hoc Ergo Propter Hoc Teen pregnancy boosts girls' risk of getting fat http://www.reuters.com/article/healthNews/idUSTRE5384GQ20090409

  16. Post Hoc Ergo Propter Hoc Working after retirement good for your health. http://news.yahoo.com/s/nm/20091022/hl_nm/us_working_retirement_1

  17. Post Hoc Ergo Propter HocThe PR Problem Some bad things will happen to people who have just gotten swine flu shots. http://www.nytimes.com/2009/09/28/health/policy/28vaccine.html?partner=rss&emc=rss

  18. Correlation vs Causality Elementary school children who wear expensive shoes have larger vocabularies. ? Therefore we should invest in good shoes for all children.

  19. Correlation vs Causality Elementary school children who wear expensive shoes have larger vocabularies. Elementary school children who have fewer cavities have larger vocabularies.

  20. Correlation vs Causality Elementary school children who eat sushi at least twice a month have larger vocabularies. ? Therefore school cafeterias should serve sushi.

  21. Correlation vs Causality Older women toe out when they walk more than younger women do. • ? Toeing out causes you to get older.

  22. Correlation vs Causality Older women toe out when they walk more than younger women do. • ? Toeing out causes you to get older. • ? Getting older causes toeing out.

  23. Correlation vs Causality Older women toe out when they walk more than younger women do. • ? Toeing out causes you to get older. • ? Getting older causes toeing out. • ? Older women learned to walk when toeing out was fashionable. Younger women learned when it was not.

  24. Correlation vs Causality What makes us happy? According to Daniel Gilbert, Professor Happiness: “Churchgoers are happier than nonchurch goers” http://www.rd.com/living-healthy/joy-the-readers-digest-version/article173696-4.html#slide

  25. Correlation vs Causality Living Together First Doesn’t Make Marriage Last Couples who live together before they get married are less likely to stay married, a new study has found. But their chances improve if they were already engaged when they began living together. The likelihood that a marriage would last for a decade or more decreased by six percentage points if the couple had cohabited first, the study found. “From the perspective of many young adults, marrying without living together first seems quite foolish,” said Prof. Pamela J. Smock, a research professor at the Population Studies Center at the University of Michigan, Ann Arbor. “Just because some academic studies have shown that living together may increase the chance of divorce somewhat, young adults themselves don’t believe that.” http://www.nytimes.com/2010/03/03/us/03marry.html?partner=rss&emc=rss

  26. Correlation vs Causality http://www.boingboing.net/2011/03/08/passport-ownership-p.html

  27. Correlation vs Causality http://www.cs.utexas.edu/~ear/nsc110/ScienceAndSociety/Lectures/FastFoodStrokes.doc

  28. Correlation vs Causality “Young men who ate fish more than once a week scored nearly 11 percent higher on IQ tests than males who rarely ate seafood.” “A 2007 study of nearly 12,000 pregnant women found that children born to mothers who ate more than 12 ounces of seafood per week during pregnancy scored six points higher on tests of verbal IQ than kids born to mothers who had other foods on the menu.” http://www.rd.com/living-healthy/fish-made-easy-seafood-healthy-eating-and-food-safety-/article158044.html

  29. Correlation vs Causality http://www.webmd.com/cancer/news/20091105/obesity-linked-to-many-cancer-cases-in-us

  30. Correlation vs Causality http://www.npr.org/blogs/health/2012/04/09/150250294/study-warns-of-autism-risk-for-children-of-obese-mothers

  31. Correlation vs Causality Claim: Women who have more sexual partners are more likely to develop cervical cancer.

  32. Correlation vs Causality Artificial light and rates of breast and prostate cancer http://www.rd.com/living-healthy/artificial-light-a-hidden-cancer-risk/article128447.html

  33. Science Reporting Often Gets It Wrong Children who are exposed to second hand smoke at home get lower scores on tests of reading, math, and reasoning. http://www.cincinnatichildrens.org/research/project/enviro/hazard/tobacco.htm

  34. But Sometimes They Get it Right Study: Spacing babies close may raise autism risk http://news.yahoo.com/s/ap/20110110/ap_on_he_me/med_autism_birth_spacing

  35. Sets and Probabilities These are hard ideas. Many people have trouble getting them right.

  36. Comparable Samples http://news.yahoo.com/s/ap/20110419/ap_on_re_us/us_ap_poll_grading_the_schools

  37. "To what extent do you believe the following represents the word of God?“ Those Who Say "All" or "Most" is Word of God (Harris Poll, Nov., 2007)

  38. In the 2004, presidential election, of those Texans who voted for either Kerry or Bush, 62% voted for Bush and 38% for Kerry. Of the Massachusetts residents who voted for either Kerry or Bush, 37% voted for Bush and 63% for Kerry. Bill was a Kerry voter. He comes from either Texas or Massachusetts but I know nothing more about him. Is it more likely that Bill comes from Texas or from Massachusetts?

  39. More Facts • In Texas there were 7.4 million voters for either Kerry or Bush. • In Massachusetts there were only 2.9 million such voters.

  40. More Facts • In Texas there were 7.4 million voters for either Kerry or Bush. • In Massachusetts there were only 2.9 million such voters. • Thus, of the Kerry voters from the two states, 61% came from Texas and only 39% came from Massachusetts.

  41. Conditional Probability P(measles | spots) = P(measles  spots) definition P(spots)

  42. Conditional Probability P(measles | spots) = P(measles  spots) definition P(spots) P(measles  spots) = P(measles | spots) P(spots) P(measles  spots) = P(spots | measles) P(measles) P(measles | spots) = P(spots | measles)  P(measles) Bayes Rule P(spots)

  43. Bayes Rule P(A | B) = P(B | A)  P(A) P(B)

  44. Using Bayes Rule P(Texas | Kerry-voter) = P(Kerry-voter | Texas)  = .38  P(Mass | Kerry-voter) = P(Kerry-voter | Mass)  = .63

  45. Bayes Rule P(Texas | Kerry-voter) = P(Kerry-voter | Texas)  P(Texas) P(Kerry-voter) = .38  .72 .45 = .27 / .45 = .61 P(Mass | Kerry-voter) = P(Kerry-voter | Mass)  P(Mass) P(Kerry-voter) = .63  .28 .45 = .18 / .45 = .39

  46. Bayes Rule P(Texas | Kerry-voter) = P(Kerry-voter | Texas)  P(Texas) P(Kerry-voter) = .38  .72 .45 = .27 / .45 = .61 P(Mass | Kerry-voter) = P(Kerry-voter | Mass)  P(Mass) P(Kerry-voter) = .63  .28 .45 = .18 / .45 = .39 Our goal: Choose an oval

  47. Argmax To choose the most likely value x from a set of possibilities, given some evidence, choose: Bayes Rule Constant denominator

  48. Bayes Rule P(Texas | Kerry-voter) = P(Kerry-voter | Texas)  P(Texas) = .38  .72 = .27 P(Mass | Kerry-voter) = P(Kerry-voter | Mass)  P(Mass) = .63  .28 = .18 Our goal: Choose an oval

  49. Choosing Actions Under Uncertainty decision 1 2 3 n payoff1 payoff2 payoff3 payoffn $50 $100 $200 - $500

  50. Choosing Actions Under Uncertainty decision .01 .01 .01 .97 1 2 3 n payoff1 payoff2 payoff3 payoffn $50 $100 $200 - $500

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