Better Business Decisions from Data: Statistical Analysis for Professional Success PDF
Preview Better Business Decisions from Data: Statistical Analysis for Professional Success
® BOOKS FOR PROFESSIONALS BY PROFESSIONALS Kenny Better Business Decisions RELATED from Data Everyone encounters statistics on a daily basis. They are used in proposals, reports, requests, and advertisements, among others, to support assertions, opinions, and theories. Unless you’re a trained statistician, it can be bewildering. What are the numbers really saying or not saying? Better Business Decisions from Data: Statistical Analysis for Professional Success provides the answers to these questions and more. It will show you how to use statistical data to improve small, every-day management judgments as well as major business decisions with potentially serious consequences. Author Peter Kenny—with deep experience in industry and education—believes that “while the methods of statistics can be complicated, the meaning of statistics is not.” He first outlines the ways in which we are frequently misled by statistical results, either because of our lack of understanding or because we are being misled intentionally. Then he offers sound approaches for understanding and assessing statistical data to make excellent decisions. Kenny assumes no prior knowledge of statistical techniques. He explains simply and with a touch of playfulness how the basic tools of probability, sampling, reliability, regression, distribution and other statistical techniques can be usefully applied to various business situations. This book teaches you, among other things: • How statistics can help you assess the probability of a successful outcome • How data is collected, sampled, and best interpreted • How to make effective forecasts based on the data at hand • How to spot the misuse or abuse of statistical evidence in advertisements, reports, and proposals • How to commission a statistical analysis • How to evaluate the potential of big data to inform your business decisions and reveal opportunities through statistical analysis Arranged in seven parts—Uncertainties, Data, Samples, Comparisons, Relationships, Forecasts, and Big Data—Better Business Decisions from Data is a guide for busy people in general manage- ment, finance, marketing, operations, and other business disciplines who run across statistics on a daily or weekly basis. You’ll return to it again and again as new challenges emerge, making better decisions each time that boost your organization’s fortunes as well as your own. ISBN 978-1-4842-0185-5 US $39.99 53999 Shelve in Business/Management User level: Beginner–Intermediate 9781484201855 www.apress.com For your convenience Apress has placed some of the front matter material after the index. Please use the Bookmarks and Contents at a Glance links to access them. Contents Preface ix about the author xi acknowledgments xiii introduction xv Part i: uncertainties 1 chapter 1: the Scarcity of certainty 3 chapter 2: Sources of uncertainty 7 chapter 3: Probability 13 Part ii: Data 23 chapter 4: Sampling 25 chapter 5: the raw Data 33 Part iii: Samples 45 chapter 6: Descriptive Data 47 chapter 7: numerical Data 55 Part iV: comparisons 87 chapter 8: levels of Significance 89 chapter 9: General Procedure for comparisons 91 chapter 10: comparisons with numerical Data 93 chapter 11: comparisons with Descriptive Data 103 chapter 12: types of error 115 Part V: relationships 119 chapter 13: cause and effect 121 chapter 14: relationships with numerical Data 125 chapter 15: relationships with Descriptive Data 149 chapter 16: Multivariate Data 155 viii Contents Part Vi: forecasts 177 chapter 17: extrapolation 179 chapter 18: forecasting from Known Distributions 183 chapter 19: time Series 197 chapter 20: control charts 205 chapter 21: reliability 211 Part Vii: Big Data 219 chapter 22: Data Mining 221 chapter 23: Predictive analytics 229 chapter 24: Getting involved with Big Data 243 chapter 25: concerns with Big Data 251 appendix: references and further reading 257 index 261 Introduction The man who is denied the opportunities of taking decisions of importance begins to regard as important the decisions he is allowed to take. He becomes fussy about filing, keen on seeing that pencils are sharpened, eager to ensure that the windows are open (or shut) and apt to use two or three different-coloured inks. —c. northcote Parkinson statistics are not popular. one might even say they are disliked. not by statisti- cians, of course, but by the millions who have to cope with the steady flow of statistics supporting all kinds of assertions, opinions, and theories. received wisdom harrumphs, “You can prove anything by statistics”—and then sneers, “Lies, damned lies, and statistics.” my sympathies do not lie with these senti- ments, which, i believe, have their origins in the misuse of statistics. i believe that statisticians are skilled in their work and act professionally, sincerely desiring their results to be interpreted and used correctly. the misuse arises when statements by those who have limited understanding of the subject are claimed to be justified by statistics. the misuse is frequently due to misunderstanding. results of statistical inves- tigations often have to be worded with many qualifications and precise defini- tions, and this does not ease the understanding of the casual reader. misguided attempts to summarize or simplify statistical findings are another cause of distortion. and undoubtedly an element of intentional misrepresentation is sometimes involved. often, the misuse arises from a desperate attempt to justify a viewpoint with what is seen to be a scientific statement. Hence the suggestion that statistics are sometimes used as a drunk uses a lamp post: more for support than illumination. this book is not for practitioners or would-be practitioners of statistics: it is, as the title implies, for those who have to make decisions on the basis of statistics. most of us, at one time or another, make use of statistics. the use may be to make a trivial decision, such as buying a tube of toothpaste in the face of claims that nine out of ten dentists recommend it; or it may be to com- mit a large sum of money to a building project on the basis of an anticipated increase in sales. We are decision makers in our work and in our domestic affairs, and our decisions are frequently based on or influenced by statistical considerations. xvi Introduction my aim in writing this book is to help decision makers to appreciate what the statistics are saying and what they are not saying. in order to have this appre- ciation, it is not necessary to understand in detail how the statistics have been processed. the key is to understand the underlying perspective that is the foundation of the various procedures used and thereby understand the char- acteristic features of results from statistical investigations. this is the under- standing that this book is intended to provide, by means of easy-to-follow explanations of basic methods and overviews of more complicated methods. the decision makers i have primarily in mind are managers in business and industry. Business decisions are frequently taken on the basis of statistics. Whether to expand, whether to move into new areas, or whether to cut back on investment can make a big difference to the fortunes of a company. the building of houses, new roads, and new facilities of various kinds affects large numbers of people, and getting it wrong can be economically and socially disastrous for years ahead. those who have to make such decisions are rarely statisticians, but the evidence on which they have to operate, whether in-house or from consultants, is frequently based on statistics. these people—the executives, planners, and project managers in all kinds of business—i aim to address, in the belief that, while the methods of statistics can be complicated, the meaning of statistics is not. a better appreciation of statistics not only helps the decision makers in assessing what the statisticians have concluded, but also allows a more reliable judgment at the outset of what they should be asked to provide—recognizing what is possible, what the limitations are, and with what levels of uncertainty the answers are likely to be qualified. this is particularly important when con- sultants are to be involved, their fees being not insignificant. i also have in mind students—the managers of the future—but not students who are studying statistics, as there are many excellent text books that they will know of and will be using (though some beginners might welcome a friendly introduction to the subject). the students who, i believe, will find this book useful are those who need to have an understanding of statistics without being involved directly in applying statistical methods. many students of medicine, engineering, social sciences, and business studies, for example, fall into this category. as i mentioned previously, we are all subjected to a regular deluge of sta- tistics in our domestic affairs, and i therefore believe that interested non- professionals would find the book useful in helping them to adopt a more informed and critical view. readers of newspapers and viewers of television, and that includes most of us, have a daily dose of statistics. We are told that sixty percent of the population think the government is doing a poor job, that there is more chance of being murdered than of winning a million dollars in the lottery, that there are more chickens in the country than people, and so on. shoppers are faced with claims regarding price differentials and value Introduction xvii for money. advertisements constantly make claims for products based on statistical evidence: “ninety percent of women looked younger after using formula 39,” and so on. if this book encourages just a few people to under- stand statistics a little better and thereby question statistics sensibly, rather than simply dismissing all statistics as rubbish, it will have been worthwhile. in its most restricted meaning, statistics (plural) are systematically collected related facts expressed numerically or descriptively, such as lists of prices, weights, birthdays or whatever. statistics (singular) is a science involving the processing of the facts—the raw data—to produce useful conclusions. in total, we have a procedure that starts with facts and moves by mathematical pro- cessing through to final statements, which, although factual, involve probability and uncertainty. We will encounter areas where it is easy to be misled. We will see that we are sometimes misled because the conclusions we are faced with are not giving the whole story. But we shall also see that we can be misled by our own mis- understanding of what we are being told. We are, after all, not statisticians, but we need to understand what the statisticians are saying. our task is to reach that necessary level of understanding without having to become proficient in the mathematical procedures involved. the chapters of the book progress in a logical sequence, though it is not the sequence usually adopted in books aimed at the teaching of statistics. it is a sequence which allows the reader readily to find the section appropriate for his or her immediate needs. most of the chapters are well subdivided, which assists further in this respect. Part i shows why statistics involves uncertainties. this leads to explanations of the basics of probability. of particular interest are examples of how mis- use of probability leads to numerous errors in the media and even in legal proceedings. Part ii concerns raw data—how data can be obtained and the various meth- ods for sampling it. Data may be descriptive, such as geographical location or eye color, or numerical. the various ways that data can be presented and how different impressions of the meaning of the data can arise are discussed. Part iii examines how data samples are summarized and characterized. a sample can give us information relating to the much larger pool of data from which the sample was obtained. By calculating confidence intervals, we see how the concept of reliability of our conclusions arises. Part iV investigates comparisons that can be made using the characteristics of our samples. We need to search for similarities and differences, and to recog- nize whether they are real or imaginary. Part V moves to the question of whether there are relationships between two or more different features. as the number of features represented in the data xviii Introduction increases, the examination of relationships becomes more involved and is usu- ally undertaken with the help of computer packages. for such methods, i have given an overview of what is being done and what can be achieved. Part Vi deals with forecasting. Practical examples are worked through to illustrate the appropriate methods and the variety of situations that can be dealt with. the final part, Part Vii, is devoted to big data. this is the most important development in the application of statistics that has arisen in recent times. Big, in this context, means enormous—so much so that it has affected our basic concepts in statistical thinking. Where examples of data and collections of data are given, they are realistic insofar as they illustrate what needs to be explained. But there the realism ends. i have used simple numbers—often small discrete numbers—for the sake of clarity. the samples that i have shown are small—too small to be considered adequate. in real investigations, samples need to be as large as can be reasonably obtained, but my use of small samples makes the explanation of the processing easier to follow. the examples i have included have been kept to a minimum for the sake of brevity. i have taken the view that one example explained clearly, and perhaps at length, is better than half a dozen all of which might confuse in the same way. to clarify the calculations, i have retained them within the main text rather than relegating them to appendices with formal mathematical presentation. this allows me to add explanatory comments as the calculations proceed and allows the reader to skip the arithmetic while following the procedure. in describing procedures and calculations, i have adopted the stance that we—that is to say you, the reader, and i—are doing the calculations. it would have been messy to repeatedly refer to some third person, even though i realize that you may be predominantly concerned with having to examine and assess procedures and calculations carried out by someone else. i have given references by quoting author and year in the main text, the details being listed at the end of the book. if you have read this far, i hope i have encouraged you to overcome any preju- dices you might entertain against the elegant pastime of statistics and read on. Believe it or not, statistics is a fascinating subject. once you get into the appro- priate way of thinking, it can be as addictive as crossword puzzles or sudoku. as a branch of mathematics, it is unique in requiring only simple arithmetic: the clever bit is getting your head around what is really required. if you have read this far and happen to be a statistician, it must be because you are curious to see if i have got everything right. Being a statistician, you will appreciate that certainty is difficult if not impossible to achieve, so please let me know of any mistakes you find. P A R T I Uncertainties In this world nothing can be said to be certain, except death and taxes. —Benjamin Franklin We need to understand the reasons why statistics embodies uncertainties. This will give us a feel for what statistics can do and what it cannot do, what we can expect from it and what we should not expect. This will prepare us for critically viewing the statistics and the conclusions from them that we are presented with. Some understanding of basic probability, which is required to appreciate uncertainty, is presented without assuming any previous knowledge on the part of the reader. C H A P T E R 1 The Scarcity of Certainty What Time Will the Next Earthquake Be? On the twenty-second of October, 2012, in Italy, six geophysicists and a government civil protection officer were sentenced to six years in prison on charges of manslaughter for underestimating the risk of a serious earthquake in the vicinity of the city of L’Aquila. Following several seismic shocks, the seven had met in committee on March 31, 2009, to consider the risk of a major earthquake. They recorded three main conclusions: that earthquakes are not predictable, that the L’Aquila region has the highest seismic risk in Italy, and that a large earthquake in the short term was unlikely. On April 6, a major earthquake struck with the loss of more than 300 lives. The court’s treatment of the seismologists created concern not only among seismologists working in other countries, but also among experts in other fields who are concerned with risk assessment. All seven filed appeals in March 2013, but it seemed unlikely that there would be a ruling on the case for some years. Whatever that may be, the case highlights the difficulties and the dangers in making decisions that have to be based on data that are statisti- cal. If it is decided that an event is unlikely, but it then occurs, was the decision wrong? The correct answer is no, because unlikely events do happen—but there is a common misperception that the answer is yes. An unfortunate consequence of this perception is either that it becomes more and more difficult to find anyone who is prepared to make a decision where risk is involved, or else that decisions become based on worst-case scenarios and thereby frequently create unwarranted disruption and expense.
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