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Overview
Product Details
| ISBN-13: | 9780738204956 |
|---|---|
| Publisher: | Basic Books |
| Publication date: | 08/28/2001 |
| Series: | Mathematics Series |
| Edition description: | Revised ed. |
| Pages: | 248 |
| Product dimensions: | 5.50(w) x 8.25(h) x (d) |
About the Author
Read an Excerpt
Statistics and Serendipity in a London Haberdashery
Let nature and let art do what they please, When all is done, life's an incurable disease.-ABRAHAM COWLEY
Introduction
How would you like to have a book that would enable you to predict the winning numbers in a state lottery? How would you like to have a book that would enable you to win to jackpot at a slot machine in a Las Vegas casino whenever you decided you needed some extra cash? How would you like to have a book that would invariably guide you to picking the winning team when making a bet on sports with the neighborhood bookie? Well, we would like to have that very same book, so please send it to us in care of the publisher if you should happen to run across it.Because our readers are much more interested in learning about deep intellectual topics, we have decided not to waste our time passing on foolproof schemes for striking it rich in the nation's casinos. Mind you, we could go for the cheap applause by providing the winning numbers for all of the state lotteries that will be held next year. But passing out these numbers would certainly have no appeal to our readers, who are very intelligent people with much better things to do with their time than stuff their bank accounts with a few million dollars.
This book is about statistics. Now, statistics is not a popular subject for discussion in trade publishing circles because it is viewed with as much enthusiasm as the Ebola virus. This is not to say that statistics books are any more tedious than the textbooks for any other class one might take in college. But statistics books have very few pictures of fuzzy animals or attractive celebrities. Indeed, you would probably have a very difficult time naming a movie actress who could truthfully talk about the positive glow she felt after reading a few pages from her introductory statistics book every morning. Moreover, statistics has never really found its way into the popular culture like certain other branches of modern science. Many would-be pharmacists, for example, have not let their lack of formal education or moral scruples stand in their way of making a living by peddling narcotics on the street. Their desire to provide a quality product to the nation's addicts serves as a sad example for the rest of us of the depths to which money-grubbing individuals can sink.
Similarly, chemistry has become all the rage among disaffected loners and paramilitary groups who have learned of the wondrous variety of explosive devices that can be made with a few simple ingredients found in the kitchen cabinet. No one can doubt the sparkle in a young child's eye when he makes his first pipe bomb or packs his wagon full of explosives and leaves it in front of the neighborhood bulls house. Statistics admittedly suffers somewhat by comparison because you cannot really use statistics to get involved in the drug trade or to build devices of mass destruction. Moreover, it is difficult to highlight the principles of statistics in a television situation comedy because such basic concepts as bell curves and degrees of confidence do not readily lend themselves to knee-slapping jokes.
So statistics has something of an image problem. It is not considered to be a particularly glamorous topic for discussion. Most young boys, for example, would rather lead a football team to a national championship than memorize detailed tables of binomial probabilities. This inexplicable preference has been borne out in survey after survey. Sadly, statistics has no greater appeal among young girls, who would prefer to model designer gowns on a Paris runway or even date deviants instead of calculating the standard deviations of a given population. This reluctance of the nation's youth to embrace statistics is disheartening to the many dozens of individuals who have worked tirelessly to convince the rest of us that statistics is full of fun and excitement. Because most people do not believe that statistics is full of fun and excitement, however, these efforts have been largely ignored.
The real tragedy of this situation is that statistics, like broccoli, is a very good thing even though both may have a slightly malodorous aftertaste. Statistics is even more useful than broccoli in helping companies make decisions about the types of products they should produce, the ways in which they should market those products, and the production processes that are to be used to make those products. Broccoli, by contrast, is of very little use in formulating a marketing plan or operating a factory, even though it is a good source of iron.
Thus, statistics is an orphan in the national consciousness even though we have to deal with it almost every day. Every time we see a poll in which people reveal, for example, that they would rather wear purple lingerie to a wine-tasting party than to a funeral, we are, in a sense, using our knowledge of statistical principles.
One of the most common elements of any such survey is the clarification usually noted during the survey regarding the possible margin of error (e.g., "plus or minus 3%"). This margin of error merely refers to the potential variations that could cloud the results of the survey. Moreover, statistics is used in almost every industry to monitor such things as the rate of defects among various products and, hence, the efficiency of the manufacturing process itself.
Of course such commercial applications would not necessarily impress those individuals who live in caves and eat raw animals because of their disdain for modern technological devices such as matches. But if these very same individuals like to gamble and wager their hardearned piles of rocks and kindling in high-stakes poker games, then they may reconsider their negative attitudes toward statistics. After all, poker is ultimately concerned with probabilities, and statistics is the study of probabilities. Therefore, the habitual gambler and the statistician can find common ground with each other and perhaps bet their car titles together at the poker table. If they know how to calculate the probability that a particular card will be drawn, they can make a somewhat educated guess as to the most likely cards that will be dealt. Of course it is not always so easy to count the cards and thereby determine which cards are more or less likely to turn up.
The thought of such shared devotion to the pursuit of knowledge for the sake of knowledge is refreshing in an age as materialistic as the one we live in. But it also illustrates in a limited way the wide sweep of statistics and the many ways in which it can be used during both work and play. Many of the examples used in this book will further drive this point home because we will see a wide variety of situations and circumstances in which statistics can be brought to bear to solve a nagging problem. Who Is Mr. Statistics? The birth of statistics occurred in a tiny haberdashery along one of London's cobblestoned streets in the mid17th century. Its discoverer, John Graunt, was a native of London who boasted no extraordinary intellectual talents but could claim an appreciation for numbers and sound record-keeping. Unlike most of his colleagues, however, Graunt also developed interests outside of the shop, particularly in the areas of mathematics and politics, that would later serve him in his investigations of the births and deaths of his fellow citizens.
The eldest of Henry and Mary Graunt's seven children, John, was born in 1620 in Birchin Lane, London, "at the Sign of the Seven Stars," where his father ran a draper shop. The family also lived at the same address, and Mary Graunt raised a noisy but happy brood of youngsters. John may have learned the tenacity that would later serve him so well in the Hobbesian state of nature that must have existed at the family table when all of the family members sat down for a meal. John rarely ventured beyond his London neighborhood. He received little formal education and was apprenticed to a merchant of small wares at a young age. While working in his master's store, Graunt learned how to manage a shop and, more importantly, how to succeed in the volatile London retailing business. In 1641, he married the former Mary Scott, with whom he had one daughter and three sons.
Graunt was soon the proprietor of his own store and worked hard to attract a loyal clientele. Despite the demands of his daily schedule, he usually spent several hours before sunrise reading and recording his thoughts on subjects dear to his heart. He also became a close friend of Sir William Petty, the author of a widely circulated book on "political arithmetic." Graunt's conversations and correspondences with Petty caused him to wonder about the dynamics of human society as a whole and, more specifically, about the mortality patterns of the human race. Graunt's curiosity somehow prompted him to begin reviewing a weekly church publication issued by the local parish clerks that listed the numbers of births, christenings, and deaths in each parish. These so-called Bills o f Mortality also listed the causes of death, thus providing Graunt with a massive but unorganized mass of information about the ongoing drama of birth and death occurring all around him.
Graunt's investigations of the births and deaths of London parishioners did not arouse great enthusiasm among his friends or family. Indeed, his daily habit of plowing through the Bills was viewed by most of his friends as nothing more than an eccentric quirk or, at the very least, a morbid curiosity. Graunt himself recog- nized that nearly all of the persons who took copies of the Bills of Mortality made little use of them other than to "look at the foot, how the burials increased or decreased; and, among the casualties, what had hap- pened rare, and extraordinary in the week current: so that they might take the same as a text to talk upon, in the next company; and withall, in the plague-time, how the sickness increased, or decreased, so that the rich might judge of the necessity of their removal, and tradesmen might conjecture what doings they were like to have in their respective dealings."1 In other words, the Bills o f Mortality were something akin to tabloid fare; they provided those hardy souls who managed to sur- vive all of the scourges and diseases of 17th-century London with a grim satisfaction that they had managed to avoid the icy reach of death-at least temporarily. Of course the comparatively short average life spans en- joyed by the persons of that era guaranteed that any such feelings of relief would be short lived.
But Graunt was motivated by a nagging feeling that there was something of value to be gained from perusing dozens, and later, hundreds of these publications even though he did not have a clear idea at the outset of what he was attempting to find. From the beginning, however, Graunt took care to organize his data in a way that was probably inspired by his techniques for tracking his shop inventory: He devised tables that were not only easy to read but could also be easily updated. He was not concerned with developing any grand theories of the kind that Isaac Newton would later use to explain the motions of the planets and stars; Graunt merely wanted to find any underlying principles or themes amidst the thousands of yellowed pages of the Bills. Graunt recognized his work would be far more accessible and useful if he and any other future investigators could avoid having to review the dusty piles of documents cluttering his study. So he took great pains to "[reduce] several great confused Volumes into a few perspicuous Tables, and [abridge] such Observations as naturally flowed from them, into a few succinct Paragraphs, without any long Series of multiloquious Deductions ..." 2
Graunt soon discovered that the process by which the Bills o f Mortality were compiled was not a clerking procedure that would normally be found in a shop or school. This procedure began when someone happened to find a corpse in a house or out on the street. A bell would be tolled and a person known as a searcher would go to the corpse and perform both a visual inspection and, in some cases, a primitive autopsy. Through these investigations, the searcher would determine-based upon his or her own extensive medical training or best hunch-the disease or casualty that had caused the death. Armed with this informa- tion, the searcher would file the report with the parish clerk. Once a week, the parish clerk would carry a list of all the burials and christenings that had occurred that week to the clerk of the hall. Acting as a master...
Table of Contents
- 1: Statistics and Serendipity in a London
Haberdashery ..... 1
- 2: Of Populations and Samples ..... 13
- 3: Obvious and Subtle Statistics ..... 39
- 4: Lotteries and Other Improbable Probabilities ..... 67
- 5: From Laboratory Experiments to Casino Glory ..... 91
- 6: Standard Normal Distributions ..... 109
- 7: Sampling the Samples ..... 127
- 8: Test It Yourself ..... 153
- 9: From Test Groups Test Significance ..... 175
- 10: Correlation and Regression ..... 195
- Epilogue: Conquering Statistics? ..... 219
- Endnotes ..... 227
- Bibliography ..... 229
- \Index ..... 231
- 2: Of Populations and Samples ..... 13