Statistics Hacks By Bruce Frey Publisher: O'Reilly Pub Date: May 2006 Print ISBN-10: 0-596-10164-3 Print ISBN-13: 978-0-59-610164-0 Pages: 356 Table of Contents | Index Want to calculate the probability that an event will happen? Be able to spot fake data? Prove beyond doubt whether one thing causes another? Or learn to be a better gambler? You can do that and much more with 75 practical and fun hacks packed into Statistics Hacks These cool tips, tricks, and mind-boggling solutions from the world of statistics, measurement, and research methods will not only amaze and entertain you, but will give you an advantage in several real-world situations-including business This book is ideal for anyone who likes puzzles, brainteasers, games, gambling, magic tricks, and those who want to apply math and science to everyday circumstances Several hacks in the first chapter alone-such as the "central limit theorem,", which allows you to know everything by knowing just a little-serve as sound approaches for marketing and other business objectives Using the tools of inferential statistics, you can understand the way probability works, discover relationships, predict events with uncanny accuracy, and even make a little money with a well-placed wager here and there Statistics Hacks presents useful techniques from statistics, educational and psychological measurement, and experimental research to help you solve a variety of problems in business, games, and life You'll learn how to: Play smart when you play Texas Hold 'Em, blackjack, roulette, dice games, or even the lottery Design your own winnable bar bets to make money and amaze your friends Predict the outcomes of baseball games, know when to "go for two" in football, and anticipate the winners of other sporting events with surprising accuracy Demystify amazing coincidences and distinguish the truly random from the only seemingly random even keep your iPod's "random" shuffle honest Spot fraudulent data, detect plagiarism, and break codes How to isolate the effects of observation on the thing observed Whether you're a statistics enthusiast who does calculations in your sleep or a civilian who is entertained by clever solutions to interesting problems, Statistics Hacks has tools to give you an edge over the world's slim odds Statistics Hacks By Bruce Frey Publisher: O'Reilly Pub Date: May 2006 Print ISBN-10: 0-596-10164-3 Print ISBN-13: 978-0-59-610164-0 Pages: 356 Table of Contents | Index credits Credits Preface Chapter 1 The Basics Hack 1 Know the Big Secret Hack 2 Describe the World Using Just Two Numbers Hack 3 Figure the Odds Hack 4 Reject the Null Hack 5 Go Big to Get Small Hack 6 Measure Precisely Hack 7 Measure Up Hack 8 Power Up Hack 9 Show Cause and Effect Hack 10 Know Big When You See It Chapter 2 Discovering Relationships Hack 11 Discover Relationships Hack 12 Graph Relationships Hack 13 Use One Variable to Predict Another Hack 14 Use More Than One Variable to Predict Another Hack 15 Identify Unexpected Outcomes Hack 16 Identify Unexpected Relationships Hack 17 Compare Two Groups Hack 18 Find Out Just How Wrong You Really Are Hack 19 Sample Fairly Hack 20 Sample with a Touch of Scotch Hack 21 Choose the Honest Average Hack 22 Avoid the Axis of Evil Chapter 3 Measuring the World Hack 23 See the Shape of Everything Hack 24 Produce Percentiles Hack 25 Predict the Future with the Normal Curve Hack 26 Give Raw Scores a Makeover Hack 27 Standardize Scores Hack 28 Ask the Right Questions Hack 29 Test Fairly Hack 30 Improve Your Test Score While Watching Paint Dry Hack 31 Establish Reliability Hack 32 Establish Validity Hack 33 Predict the Length of a Lifetime Hack 34 Make Wise Medical Decisions Chapter 4 Beating the Odds Hack 35 Gamble Smart Hack 36 Know When to Hold 'Em Hack 37 Know When to Fold 'Em Hack 38 Know When to Walk Away Hack 39 Lose Slowly at Roulette Hack 40 Play in the Black in Blackjack Hack 41 Play Smart When You Play the Lottery Hack 42 Play with Cards and Get Lucky Hack 43 Play with Dice and Get Lucky Hack 44 Sharpen Your Card-Sharping Hack 45 Amaze Your 23 Closest Friends Hack 46 Design Your Own Bar Bet Hack 47 Go Crazy with Wild Cards Hack 48 Never Trust an Honest Coin Hack 49 Know Your Limit Chapter 5 Playing Games Hack 50 Avoid the Zonk Hack 51 Pass Go, Collect $200, Win the Game Hack 52 Use Random Selection as Artificial Intelligence Hack 53 Do Card Tricks Through the Mail Hack 54 Check Your iPod's Honesty Hack 55 Predict the Game Winners Hack 56 Predict the Outcome of a Baseball Game Hack 57 Plot Histograms in Excel Hack 58 Go for Two Hack 59 Rank with the Best of Them Hack 60 Estimate Pi by Chance Chapter 6 Thinking Smart Hack 61 Outsmart Superman Hack 62 Demystify Amazing Coincidences Hack 63 Sense the Real Randomness of Life Hack 64 Spot Faked Data Hack 65 Give Credit Where Credit Is Due Hack 66 Play a Tune on Pascal's Triangle Hack 67 Control Random Thoughts Hack 68 Search for ESP Hack 69 Cure Conjunctionitus Hack 70 Break Codes with Etaoin Shrdlu Hack 71 Discover a New Species Hack 72 Feel Connected Hack 73 Learn to Ride a Votercycle Hack 74 Live Life in the Fast Lane (You're Already In) Hack 75 Seek Out New Life and New Civilizations Colophon Index Credits About the Author Bruce Frey, Ph.D., is a comic book collector and film buff In his spare time, he teaches statistics to graduate students and conducts research in his secret identity as an assistant professor in Educational Psychology and Research at the University of Kansas He is an award-winning teacher, and his scholarly research interests are in the areas of teacher-made tests and classroom assessment, the measurement of spirituality, and program evaluation methods Bruce's honors include taking third place in the Kansas Monopoly Championship as a teenager, second place in the Kansas Film Festival as a college student, and a respectable third-place finish in the Lawrence, Kansas, Texas Hold 'Em Poker Tournament as a middle-aged man He is proudest of two accomplishments: his marriage to his sweet wife, and his purchase of a low-grade copy of Showcase #4, a comic book wherein the "Silver Age Flash first appears," whatever that means Contributors The following people contributed their hacks, writing, and inspiration to this book: Joseph Adler is the author of Baseball Hacks (O'Reilly), and a researcher in the Advanced Product Development Group at VeriSign, focusing on problems in user authentication, managed security services, and RFID security Joe has years of experience analyzing data, building statistical models, and formulating business strategies as an employee and consultant for companies including DoubleClick, American Express, and Dun & Bradstreet He is a graduate of the Massachusetts Institute of Technology with an Sc.B and an M.Eng in computer science and computer engineering Joe is an unapologetic Yankees fan, but he appreciates any good baseball game Joe lives in Silicon Valley with his wife, two cats, and a DirecTV satellite dish Ron Hale-Evans is a writer, thinker, and game designer who earns his daily sandwich with frequent gigs as a technical writer He has a Bachelor's degree in Psychology from Yale, with a minor in Philosophy Thinking a lot about thinking led him to create the Mentat Wiki (http://www.ludism.org/mentat), which led to his recent book, Mind Performance Hacks (O'Reilly) You can find his multinefarious [sic] other projects at his home page, http://ron.ludism.org, including his award-winning board games, a list of his Short-Duration Personal Saviors, and his blog Ron's next book will probably be about game systems, especially since his series of articles on that topic for the dearly departed The Games Journal (http://www.thegamesjournal.com) has been relatively popular among both gamers and academics If you want to email Ron the names of some gullible publishers, or if you just want to bug him, you can reach him at rwhe@ludism.org (rhymes with nudism and has nothing to do with Luddism) Brian E Hansen, 27, grew up in the Dallas, Texas area After serving a two-year religious mission in Spain, he attended Texas A&M University and graduated in 2004 with a B.S degree in Petroleum Engineering He currently works as a Reservoir Engineer for a large independent oil and gas exploration and production company headquartered in Irving, Texas Jill H Lohmeier received her Ph.D in Cognitive Psychology from The University of Massachusetts, Amherst She is currently the Evaluation Director for the School Program Evaluation and Research group at the University of Kansas Jill likes outdoor sports, especially running, hiking, and playing soccer with her kids Ernest E Rothman is a Professor and Chair of the Mathematical Sciences Department at Salve Regina University (SRU) in Newport, Rhode Island Ernie holds a Ph.D in Applied Mathematics from Brown University and held positions at the Cornell Theory Center in Ithaca, New York before coming to SRU His interests are primarily in scientific computing, mathematics and statistics education, and the Unix underpinnings of Mac OS X You can keep abreast of his latest activities at http://homepage.mac.com/samchops Neil J Salkind is a sometimes faculty member at the University of Kansas with an office opposite that of Bruce Frey, of Statistics Hacks fame In addition to being the author of Statistics for People Who (Think They) Hate Statistics (SAGE), Neil is a developmental psychologist who collects books, cooks, works on old houses and a p1800 Volvo, and is active in Masters swimming He has also written over 100 trade books and textbooks, and works with StudioB Literary Agency in New York William Skorupski is currently an assistant professor in the School of Education at the University of Kansas, where he teaches courses in psychometrics and statistics He earned his Bachelor's degree in educational research and psychology from Bucknell University in 2000, and his Doctorate in psychometric methods from the University of Massachusetts, Amherst in 2004 His primary research interest is in the application of mathematical models to psychometric data, including the use of Bayesian statistics for solving practical measurement problems He also enjoys applying his knowledge of statistics and probability to everyday situations, such as playing poker against the author of this book! Acknowledgments I'd like to thank all the contributors to this book, both those who are listed in the "Contributors" section and those who helped with ideas, reviewed the manuscript, and provided suggestions of sources and resources Thanks in this capacity especially go to Tim Langdon, neon bender, whose gift of Harry Blackstone, Jr.'s paperback book There's One Born Every Minute (Jove Publications) provided great inspiration for many of the hacks herein I'd like to thank my editor, Brian Sawyer, who shepherded this project with a strong hand and a strong vision of what is and is not a hack He was right most of the time (Though not all the time, Brian That hack about using a monkey to pick the winner of the Kentucky Derby should have made it in Maybe next time ) Brian was instrumental in bringing this project to completion, especially during a string of unlucky rolls where the odds of success looked slim I'd like to thank Neil Salkind, statistics writer supreme, for his help with many facets of my professional life and this book Most importantly, thanks to Bonnie Johnson, my sweet wife, whom I vaguely recall, but who I think will be waiting for me at home when I finally turn in the last revision of this book Preface Chance plays a huge part in your life, whether you know it or not Your particular genetic makeup mutated slightly when you were created, and it did so based on specific laws of probability Performance in school involves human errors, yours and others', which tends to keep your actual ability level from being reflected precisely in your report card or on those high-stakes tests Research on careers even suggests that what you do for a living was probably not a result of careful planning and preparation, but more likely due to happenstance And, of course, chance determines your fate in games of chance and plays a large role in the outcome of sporting events Fortunately, an entire set of scientific tools, the various applications of statistics, can be used to solve the problems caused by our fate-influenced system Inferential statistics, a field of science based entirely on the nature of probability, allows us to understand the way things work, discover relationships among variables, describe a huge population by seeing just a small bit of it, make uncannily accurate predictions, and, yes, even make a little money with a wellplaced wager here and there This book is a collection of statistical tricks and tools Statistics Hacks presents useful tools from statistics, of course, but also from the realms of educational and psychological measurement and experimental research design It provides solutions to a variety of problems in the world of social science, but also in the worlds of business, games, and gambling If you are already a top scientist and do statistical calculations in your sleep, you'll enjoy this book and the creative applications it finds for those rusty old tools you know so well If you just like the scientific approach to life and are entertained by cool ideas and clever solutions to interesting problems, don't research designs categories of 2nd threats to validity research hypothesis 2nd 3rd 4th response rate Rhine, J B riffle shuffles 2nd 3rd rising sequences river Rodriguez, M.C Rothman, Ernest E roulette fair payouts gambler's fallacy about overview ROUND function 2nd ROUNDDOWN function 2nd ROUNDUP function 2nd rule of four rule of two rule of two plus two Index [SYMBOL] [A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [V] [W] [X] [Y] [Z] Sackrowitz, Harold 2nd safe cracking Sagan, Carl 2nd Salkind, Neil 2nd sample size coin toss and effect size and 2nd sampling error and statistical significance and 2nd samples t tests and cluster defined 2nd discrete/continuous objects in efficient extraterrestrial life inferential statistics and predicting baseball games statistical significance of sampling errors 2nd sampling frame 2nd sampling unit 2nd SAS software SAT 2nd Saxbe, Darby scale invariance scores [See also scores: (see also test scores\\] [See also scores: (see also test scores\\] central tendency of consistency in correlation coefficient defined error high level of measurement likelihood of higher observed 2nd 3rd ordinal level of measurement percentage of predicting 2nd reliability of 2nd 3rd standardized 2nd T scores 2nd true 2nd 3rd validity of Search for Extraterrestrial Intelligence (SETI) sensitivity serendipity, interpreting SETI (Search for Extraterrestrial Intelligence) Shadish, W.R shared variance 2nd short-stacked shuffling cards significance [See statistical significance] simple linear regression [See linear regression] single substitution format six degrees of separation six-sided dice 2nd skips Skorupski, William 2nd slips SLOPE function slot machines small-world problem 2nd 3rd Smart Shuffle (iTunes) Smith, Will Soter, Steven 2nd Spears, Britney 2nd species, discovering specificity splitting hands 2nd 3rd SPSS software 2nd St Petersburg Paradox standard deviation ACT Central Limit Theorem cut score and defined 2nd of distributions 2nd 3rd effect size and formula linear regression and 2nd normal curve and 2nd 3rd 4th regression formulas and standard error of measurement standard error of the estimate standard error of the mean standardized weights and T scores z score standard error calibrating precision 2nd defined determining Law of Large Numbers overview standard error of measurement defined 2nd formula for 2nd 3rd scores and standard deviation and standard error of the estimate applying defined 2nd determining regression analysis and standard error of the mean applying defined 2nd 3rd 4th standard error of the proportion applying defined sample sizes and standardized scores 2nd standardized weights Stanford-Binet Intelligence Test Stanley, J.C statistical hypothesis statistical significance Central Limit Theorem and chi-square values correlation and 2nd heads or tails increasing power judging importance table of areas under the normal curve stem 2nd 3rd stock market 2nd Stockburger, David stratified sampling street addresses stylometrics substitution ciphers sucker bets Superman surrogate variables synchronicity synthesis level (learning) 2nd systematic sampling Index [SYMBOL] [A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [V] [W] [X] [Y] [Z] T scores 2nd table of areas under the normal curve table of specifications tax returns, fraudulent test scores establishing reliability establishing validity improving norm-referenced scoring precision for predicting performance regression toward the mean standard error of measurement statistical significance test-retest reliability 2nd 3rd testing fairly improving scores validity in tests of significance Texas Hold 'Em improving skills odds for royal flush pot odds ranking players rule of four short-stacked thoughts, random Tibshirani, Robert 2nd 3rd Tic-Tac-Toe traffic patterns trial-and-error learning true score 2nd 3rd true zero turn TV game shows 2nd Tversky, Amos 2nd 3rd two-point conversion (football) two-tailed test two-way chi-square test Type 1 error 2nd Type I error Type II error 2nd Index [SYMBOL] [A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [V] [W] [X] [Y] [Z] validity establishing scores and threats to variables categorical cause-and-effect relationships correlation and 2nd 3rd criterion 2nd 3rd dependent 2nd 3rd 4th dichotomous discovering relationships effect sizes factor analysis and 2nd groupings in independent 2nd 3rd 4th linear regression and measuring correlation predicting outcomes of events predictor 2nd 3rd proxy surrogate variance correlation and defined 2nd shared 2nd Vermeil, Dick Vos Savant, Marilyn voting cycle paradox Index [SYMBOL] [A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [V] [W] [X] [Y] [Z] wagers betting systems based on coin toss outcomes dice and increasing roulette and St Petersburg Paradox Watts, D J Wechsler Intelligence Scales well-defined distribution Wheel of Fortune wild cards (card games) Williams, C.O winning events likelihood of group of outcomes likelihood of series of outcomes likelihood of specific event wired pair word association working universe Index [SYMBOL] [A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [V] [W] [X] [Y] [Z] X-axis, graphs and Index [SYMBOL] [A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [V] [W] [X] [Y] [Z] Y-axis, graphs and Index [SYMBOL] [A] [B] [C] [D] [E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [Q] [R] [S] [T] [V] [W] [X] [Y] [Z] z score coin toss and converting raw scores defined mean and 2nd 3rd normal curve and 2nd 3rd 4th 5th problems with standardized score distribution standardized weights and z score) Z-test Zener cards zero, true zonks ... the invisible visible with these hacks Chapter 3, Measuring the World A variety of tips and tricks for measuring the world around you are presented here You'll learn to ask the right questions, assess accurately, and even increase your own... questions, assess accurately, and even increase your own performance on high-stakes tests Chapter 4, Beating the Odds This chapter is for the gambler Use the odds to your advantage, and make the right decisions in Texas Hold 'Em poker and just about every other game in which probability... variables? Conveniently, past researchers and mathematicians have developed or discovered formulas and theorems and rules of thumb and philosophies and assumptions that provide us with the knowledge of the distributions of these complex values