Example: stock market

INTRODUCTION Uses of Probability and Statistics

8 Resampling: The New StatisticsIntroductionWhat Kinds of Problems Shall We Solve?Probabilities and DecisionsWhether to Buy More TrucksTypes of StatisticsLimitations of Probability and StatisticsIntroductionUses of Probabilityand StatisticsThis chapter introduces you to Probability and Statistics . Firstcome examples of the kinds of practical problems that thisknowledge can solve for us. Next this INTRODUCTION discussesthe relationship of probabilities to decisions. Then comes a dis-cussion of the two general types of Statistics , descriptive andinferential. Following this is a discussion of the limitations ofprobability and Statistics . And last is a brief history of statis-tics. Most important, the chapter describes the types of prob-lems the book will the term statistic often scares and confuses people and indeed, the term has several sorts of meanings the chap-ter includes a short section on Types of Statistics .

IntroductionUses of Probability and Statistics 9 statistics, I suggest that you merely glance over this Introduc-tion and then proceed directly with Chapter 1.

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Transcription of INTRODUCTION Uses of Probability and Statistics

1 8 Resampling: The New StatisticsIntroductionWhat Kinds of Problems Shall We Solve?Probabilities and DecisionsWhether to Buy More TrucksTypes of StatisticsLimitations of Probability and StatisticsIntroductionUses of Probabilityand StatisticsThis chapter introduces you to Probability and Statistics . Firstcome examples of the kinds of practical problems that thisknowledge can solve for us. Next this INTRODUCTION discussesthe relationship of probabilities to decisions. Then comes a dis-cussion of the two general types of Statistics , descriptive andinferential. Following this is a discussion of the limitations ofprobability and Statistics . And last is a brief history of statis-tics. Most important, the chapter describes the types of prob-lems the book will the term statistic often scares and confuses people and indeed, the term has several sorts of meanings the chap-ter includes a short section on Types of Statistics .

2 Descrip-tive Statistics are numbers that summarize the information con-tained in a group of data. Inferential Statistics are proceduresto estimate unknown quantities; that is, these procedures in-fer estimates and conclusions based on whatever descriptivestatistics are the foundation of sound decision-making lies the ability tomake accurate estimates of the probabilities of future problems confront everyone from the businessperson considering plant expansion, to the scientist testing anew wonder drug, to the individual deciding whether to carryan umbrella to those interested only in learning resampling Statistics , orwho have some previous acquaintance with Probability andINTRODUCTION9 INTRODUCTION uses of Probability and Statisticsstatistics, I suggest that you merely glance over this Introduc-tion and then proceed directly with Chapter you want to find out quickly about the resampling method.

3 You might skim the next few chapters and perhaps skip allthe way to Chapter kinds of problems shall we solve?These are some examples of the kinds of problems that we canhandle with the methods described in this book:1. You are a doctor trying to develop a cure for cancer. Currentlyyou are working on a medicine labeled CCC. You have datafrom patients to whom medicine CCC was given. You want tojudge on the basis of those results whether CCC really curescancer or whether it is no better than a sugar You are the campaign manager for the Republicrat candidatefor President of the United States. You have the results from arecent poll taken in New Hampshire. You want to know thechance that your candidate would win in New Hampshire ifthe election were held You are the manager and part owner of a small constructioncompany. You own 20 earthmoving trucks.

4 The chance thatany one truck will break down on any given day is about onein ten. You want to know the chance on a particular day tomorrow that four or more of them will be out of A machine gauged to produce screws inches long pro-duces a batch on Tuesday that averaged inches. Giventhe record of screws produced by this machine over the pastmonth, we want to know whether something about the ma-chine has changed, or whether this unusual batch has occurredjust by core of all these problems, and of the others that we willdeal with in this book, is that you want to know the chance or Probability different words for the same idea thatsome event will or will not happen, or that something is trueor false. To put it another way, we want to answer questionsabout What is the Probability , given the body of in-formation that you have in question What is the Probability is usually notthe ultimate question that interests us at a given : The New StatisticsEventually, a person wants to use the estimated Probability tohelp make a decision concerning some action one might are the kinds of decisions, related to the questions aboutprobability stated above, that ultimately we would like tomake:1.

5 Should you (the researcher) advise doctors to prescribe medicineCCC for patients, or, should you (the researcher) continue tostudy CCC before releasing it for use? A related matter: shouldyou and other research workers feel sufficiently encouragedby the results of medicine CCC so that you should continueresearch in this general direction rather than turning to someother promising line of research? These are just two of the pos-sible decisions that might be influenced by the answer to thequestion about the Probability that medicine CCC cures Should you advise the Republicrat presidential candidate to go toNew Hampshire to campaign? If the poll tells you conclusivelythat he or she will not win in New Hampshire, you might de-cide that it is not worthwhile investing effort to campaign , if the poll tells you conclusively that he or she surelywill win in New Hampshire, you probably would not want tocampaign further there.

6 But if the poll is not conclusive in onedirection or the other, you might choose to invest the effort tocampaign in New Hampshire. Analysis of the chances of win-ning in New Hampshire based on the poll data can help youmake this decision Should your firm buy more trucks? Clearly the answer to thisquestion is affected by the Probability that a given number ofyour trucks will be out of action on a given day. But of coursethis estimated Probability will be only one part of the Should we adjust the screw-making machine after it producesthe batch of screws averaging inches? If its performancehas not changed, and the unusual batch we observed was justthe result of random variability, adjusting the machine couldrender it more likely to produce off-target screws in the kinds of questions to which we wish to find probabilisticand statistical answers may be found throughout the social,biological and physical sciences; in business; in politics; in en-gineering (concerning such spectacular projects as the flightto the moon); and in most other forms of human uses of Probability and StatisticsProbabilities and decisionsThere are two differences between questions about probabili-ties and the ultimate decision problems:1.

7 Decision problems always involve evaluation of the conse-quences that is, taking into account the benefits and the costsof the consequences whereas pure questions about probabili-ties are estimated without evaluations of the Decision problems often involve a complex combination ofsets of probabilities and consequences, together with their evalua-tions. For example: In the case of the contractor s trucks, it isclear that there will be a monetary loss to the contractor if shemakes a commitment to have 16 trucks on a job tomorrow andthen cannot produce that many trucks. Furthermore, the con-tractor must take into account the further consequence thatthere may be a loss of goodwill for the future if she fails tomeet her obligations tomorrow and then again there may notbe any such loss; and if there is such loss of goodwill it mightbe a loss worth $10,000 or $20,000 or $30,000.

8 Here the deci-sion problem involves not only the Probability that there willbe fewer than 16 trucks tomorrow but also the immediatemonetary loss and the subsequent possible losses of goodwill,and the valuation of all these consequences. The complexityof the contractor s decision problem may be seen in the sche-matic diagram called a decision tree shown in Figure to buy more trucksContinuing with the decision concerning whether to do moreresearch on medicine CCC: If you do decide to continue re-search on CCC, (a) you may, or (b) you may not, come up withan important general cure within, say, the next 3 years. If youdo come up with such a general cure, of course it will havevery great social benefits. Furthermore, (c) if you decide notto do further research on CCC now, you can direct your timeand that of other people to research in other directions, withsome chance that the other research will produce a less-generalbut nevertheless useful cure for some relatively infrequentforms of cancer.

9 Those three possibilities have different socialbenefits. The Probability that medicine CCC really has somecurative effect on cancer, as judged by your prior research,obviously will influence your decision on whether or not to12 Resampling: The New StatisticsFigure i-1: Decision Treedo more research on medicine CCC. But that judgment aboutthe Probability is only one part of the overall web of conse-quences and evaluations that must be taken into account whenmaking your decision whether or not to do further researchon medicine CCC. Again, the web of consequences and evalu-ations for the contractor deciding whether to buy more trucksis sketched in the decision tree in Figure does this book limit itself to the specific Probability ques-tions when ultimately we are interested in decisions? A firstreason is division of labor. The more general aspects of thedecision-making process in the face of uncertainty are treatedwell in other books.

10 This book s special contribution is its newapproach to the crucial process of estimating the chances thatan event will , the specific elements of the overall decision-makingprocess taught in this book belong to the interrelated subjectsof Probability theory and inferential Statistics . Though probabi-listic and inferential-statistical theory ultimately is intendedto be part of the general decision-making process, often onlythe estimation of probabilities is done systematically, and therest of the decision-making process for example, the decisionNo immediate lossNo immediate lossBuy one more truckBuy two more trucksBuy two more trucksBuy two more trucksBuy one more truckBuy two more trucksBuy onemore truckBuy one more truckBuy onemore truckBuy onemore truckBuy onemore truckBuy no more trucksBuy no more trucksBuy no more trucksBuy no more trucksBuy no more trucksBuy no more trucksBuy no more trucksProbabilityL=.


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