Statistics Success Stories and Cautionary Tales 统计学的成功案例和警示 故事LESSON 1 第一课 1.1 WHAT IS STATISTICS ? 什么是统计学Statistics is a collection of procedures and principle for gathering data and analyzing information in order to help people make decisions when faced with uncertainty. 统计学是一套收集数据和分 析信息的方法和原则，以帮 助人们在面对不确定性时制 定决策。The odds of finding two identical fingerprints were 1 in 64 billion. Francis Galton两个随机个体具有相同DNA 图形的概率为310-11；如 果同时用两种探针进行比较 ，两个个体完全相同的概率 小于510-19。每支枪的枪管都有独一无二 的特征，这种特征影响了它 所发射的每一发子弹。 司法弹道学航空公司通过抽样而省钱最早的英文原版打败庄家1.2 SEVEN STATISTICAL STORIES WITH MORALS 7个包含寓义的统计学故事There are three kinds of lies: lies, damned lies and statistics。Benjamin Disraeli (British Prime Minister, 1804 1881)CASE STUDY 1Who are Those Speedy Drivers? 谁是快车手？“Whats the fastest you have ever driven a car?”-Penn State University, 1994110 109 90 140 105 150 120 110 110 90 115 95 145 140 110 105 85 95100 115 124 95 100 125 140 85 120115105 125 102 85 120 110 120 115 94 125 80 85 140 120 92 130 125 110 90 110 110 95 95 110 105 80 100 110 130 105 105 120 90 100 105 100 120 100 100 80 100 120 105 60 125 120 100 115 95 110 101 80 112 120 110 115 125 55 9087 Males80 75 83 80 100 100 90 75 95 85 90 90 90 120 85 100 120 75 85 80 70 85110 85 75 105 95 75 70 90 70 82 85 100 90 95 90 110 80 80 110 110 95 75 130 95 110 110 80 90 105 90 110 75 100 90 110 85 90 80 80 85 50 80 100 80 80 80 95 100 90 100 95 80 80 50 88 90 90 85 70 90 30 85 85 87 85 90 85 75 90 102 80 100 95 110 80 95 90 80 90 102 FemalesResponses to “Whats the fastest youve ever driven?”DotplotMALESFastest speed (mph)FEMALESFastest speed (mph)Responses to “Whats the fastest youve ever driven?”Five-number summaryMalesMales (87 Students)(87 Students)FemalesFemales (102 Students)(102 Students) MedianMedian1101108989 QuartilesQuartiles959512012080809595 ExtremesExtremes55551501503030130130一条平均水深0.4m河流绝不会比一个平均水深0.6m 的游泳池更安全Responses to “Whats the fastest youve ever driven?”Five-number summaryMalesMales (87 Students)(87 Students)FemalesFemales (102 Students)(102 Students) MedianMedian1101108989 QuartilesQuartiles959512012080809595 ExtremesExtremes55551501503030130130 Definition: The median is the value in the middle when the numbers are put in order. The lower quartile and upper quartile are (roughly) the medians of the lower and upper halves of the data.Moral of the story13013030301501505555ExtremesExtremes959580801201209595QuartilesQuartiles8989110110MedianMedianFemalesFemales (102 Students)(102 Students)MalesMales (87 Students)(87 Students)Simple summaries of data can tell an interesting story and are easier to digest than long lists.CASE STUDY 2Disaster in the Skies? 空中的灾难？“Planes get closer in midair as traffic control errors rise. Errors by air traffic controllers climbed from 746 in fiscal 1997 to 878 in fiscal 1998, an 18% increase”-USA TODAY, Levin, 1999“The errors per million flights handled by controllers climbed from 4.8 to 5.5” 5.54.8=114.6%Definition: The rate is simply the number of times something occurs per number of opportunities for it to occur. Baseline rate is the rate at a beginning time period or under specific conditions.Moral of the story When discussing the change in the rate or risk of occurrence of something, make sure you also include the base rate or baseline risk.CASE STUDY 3Did anyone ask you whom youve been dating?“According to a new USA Today/Gallup Poll of teenagers across the country, 57 percent of teens who go out on dates say theyve been out with someone of another race or ethnic group.”-USA TODAY, Perterson, 1997CASE STUDY 3“In most cases, parents arent a major obstacle. Sixty-four percent of teens says their parents dont mind that they date interracially, or wouldnt mind if they did.”-Sacramento Bee, Hiram , 1997How could the polltakers manage to ask so many teenagers these question?Question 1Could such a small sample possibly tell us anything about the millions of teenagers in the United States ?Question 2Yes -if those teens constituted a random sample from the population of interest.How accurate could this sample possibly be ?Question 3The results of this poll are accurate to within a margin of error of about 4.5% (95% confidence interval).Moral of the storyA representative sample of only a few thousand, or perhaps even a few hundred, can give reasonably accurate information about a population of many millions.CASE STUDY 4Who Are Those Angry Women?“A well-conducted survey can be very informative, but a poorly conducted one can be a complete disaster.”-Statistics: Concepts and Controversives, David S. Moore“The women who responded were fed up with men and eager to fight them. For example, 91% of those who were divorced said they had initiated the divorce. The anger of women toward men became the theme of the book.” -Women and Love, Shere. HiteShere Hite sent questionnaires to 100,000 women asking about love, sex, and relationships.The H