book

Statistics Hacks

by Bruce Frey

May 2006

Beginner

356 pages

10h 49m

English

O'Reilly Media, Inc.

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About the AuthorContributorsAcknowledgments
Why Statistics Hacks?How This Book Is OrganizedConventions Used in This BookSafari EnabledHow to Contact UsGot a Hack?
1. Know the Big SecretThe Big SecretA Smaller, Dirtier Secret2. Describe the World Using Just Two NumbersSome Quick Statistics BasicsMeanStandard deviationCentral Limit TheoremSo What?Applying the Central Limit TheoremWhere Else It Works3. Figure the OddsQuestions About the FutureLikelihood of a Specific OutcomeLikelihood of a Group of OutcomesLikelihood of a Series of OutcomesWhat Probability MeansAnalytic viewRelative frequency view4. Reject the NullHypothesis TestingStatistical Hypothesis TestingWhy It Works5. Go Big to Get SmallLaying Down the LawImproving AccuracyWhy It WorksGamblingErrorImplicationsSee Also6. Measure PreciselyClassical Test TheoryStandard Error of MeasurementBuilding Confidence IntervalsWhy It WorksWhat It Means7. Measure UpUsing Numbers as LabelsUsing Numbers to Show SequenceUsing Numbers to Show DistanceUsing Numbers to Count in Concrete WaysChoosing Your Level of MeasurementControversial Tools8. Power UpPowerConducting a Power AnalysisMaking Inferences About Beautiful RelationshipsWhy It WorksWhere It Doesn’t Work9. Show Cause and EffectDesigning Effective ExperimentsDoes Weight Cause Height?Fighting Threats to ValiditySee Also10. Know Big When You See ItSeeing Effect Sizes EverywhereFinding or Computing Effect SizesInterpreting Effect SizesInterpreting Research FindingsWhy It Works
11. Discover RelationshipsTesting Hypotheses About RelationshipsComputing a Correlation CoefficientInterpreting a Correlation CoefficientStatistical Significance and CorrelationsWhere Else It WorksDire Warning About Correlations12. Graph RelationshipsDrawing a Picture of the FutureConnecting the DotsPlaying “What If?”Why It WorksWhere It Doesn’t Work13. Use One Variable to Predict AnotherCooking Up the EquationPredicting ScoresWhy It WorksWhere Else It WorksWhere It Doesn’t Work14. Use More Than One Variable to Predict AnotherChoosing Predictor VariablesBuilding a Multiple Regression EquationMaking Predictions and Understanding RelationshipsWhy It WorksWhere Else It Works15. Identify Unexpected OutcomesDetermining Whether Something Is Going OnCalculating the Chi-SquareDetermining if the Chi-Square Is “Really Big”Why It WorksWhere Else It WorksSee Also16. Identify Unexpected RelationshipsAnswering Relationship QuestionsConduct preliminary analysesCompute the two-way chi-squareDetermine if the chi-square is big enoughWhy It WorksSee Also17. Compare Two GroupsProving Uncle Frank Wrong (or Right)Interpreting the t ValueWhy It WorksWhere Else It Works18. Find Out Just How Wrong You Really AreCalibrating Error and Calculating PrecisionMean EstimatesProportion EstimatesEstimates of Future PerformanceUsing Standard ErrorsUncle Frank’s Campaign for DogcatcherWhy It Works19. Sample FairlyUsing Samples to Make InferencesConstructing the Best Random SampleSampling Strategies for the Real WorldChoosing a Sample SizeSee Also20. Sample with a Touch of ScotchA Sampling ProblemUsing Metaphor to Solve the ProblemWhere Else It Works21. Choose the Honest AverageMeasures of Central TendencyChoosing the Middle GroundWhere It Doesn’t WorkHow to Choose the Honest Average22. Avoid the Axis of EvilChoosing the Honest GraphGraphic ViolenceSee Also
23. See the Shape of EverythingApplying Areas Under the Normal CurvePredicting test performanceSetting standardsAppreciating the Beauty of the Normal Curve24. Produce PercentilesProducing and Reporting Percentile RanksOrganize your dataCompute frequencies and percentagesDetermine percentile ranksInterpreting the Percentile RankWhere It Doesn’t WorkSee Also25. Predict the Future with the Normal CurveThe Table of Areas Under the Normal CurveDeciphering the TableEstimating the Chance of Scoring Above or Below Any ScoreEstimating the Chance of Scoring Between Any Two ScoresProducing Percentile RanksDetermining Statistical SignificanceWhy It WorksSee Also26. Give Raw Scores a MakeoverCalculating z ScoresUnderstanding PerformanceIdentifying the Rarity of Your PerformanceWhy It Works27. Standardize ScoresProblems with z ScoresCreating and Interpreting T ScoresCreating Customized Standardized ScoresCreate Your Own Standardized ScoreWhy It WorksUnderstanding Norm-Referenced Scoring28. Ask the Right QuestionsConstructing a Good QuestionAsking a Question at the Right LevelChoosing the right cognitive levelDesigning questions at different cognitive levelsWhen to use Bloom’s TaxonomySee Also29. Test FairlyItem AnalysisThree Types of Classroom Assessment ProblemsAre my test questions too hard?Is each test question measuring what it is supposed to?Why did my students miss a question?Conducting Item Analyses and Interpreting ResultsSuggestions for Item Analysis and Test Fairness30. Improve Your Test Score While Watching Paint DryRegressing to the MeanWhy It WorksPredicting the Likelihood of a Higher Score31. Establish ReliabilityWhy Reliability MattersCalculating ReliabilityInternal reliabilityTest-retest reliabilityInter-rater reliabilityParallel forms reliabilityInterpreting Reliability EvidenceImproving Test ReliabilityWhy It Works32. Establish ValidityStrategies for Winning the Validity ArgumentContent-Based ArgumentsCriterion-Based ArgumentsConstruct-Based ArgumentsConsequences-Based ArgumentsChoosing from the Menu of Validity Options33. Predict the Length of a LifetimeIn ActionHow It WorksIn Real LifeEndnotes34. Make Wise Medical DecisionsStatistics and Medical ScreeningUnderstanding Breast Cancer ScreeningWhy It WorksMaking Informed DecisionsSee Also
35. Gamble SmartThe Gambler’s FallacyCasinos and MoneySystems36. Know When to Hold ‘EmHow It WorksExample 1Example 2Why It WorksOther Places It WorksWhere It Doesn’t Work37. Know When to Fold ‘EmPot OddsWhy It WorksWhere Else It WorksWhere It Doesn’t Work38. Know When to Walk AwayRecognizing a Short-Stacked SituationTwelve times the big blind or lessEight times the big blind or lessFour times the big blind or lessStatistical Decision MakingGetting Your Mind Right39. Lose Slowly at RouletteBasic WagersWhy It Works40. Play in the Black in BlackjackBasic StrategyWhy It WorksSimple Card-Counting MethodsCounting AcesCounting Aces and 10sGoing by the point system41. Play Smart When You Play the LotteryPowerball OddsPowerball PayoffEasiest prizePowerball onlyGrand prizeWinning PowerballDon’t Split the Prize42. Play with Cards and Get LuckyGetting a Li’l FlushThe betWhy it worksFinding a Match with Two Decks of CardsThe betWhy it works43. Play with Dice and Get LuckyDistribution of Dice OutcomesBar Bets with DiceWhy It Works44. Sharpen Your Card-SharpingImproving Your HandProbabilitiesImplicationsReading the Community Cards in a Flash45. Amaze Your 23 Closest FriendsGetting StartedApplying the Law of Total ProbabilityCalculating the Probability of Independent EventsSolving the Birthday ProblemSolving for Almost Any Group Size46. Design Your Own Bar BetPrinciple 1Principle 2Rolling Your Own Bar BetLetters of the alphabetPick a number, any numberOn your ownMake Sure the Sucker Isn’t You!47. Go Crazy with Wild CardsThe Problem with Wild CardsWhy It WorksThe Other Problem with Wild Cards48. Never Trust an Honest CoinShiny New PenniesBinomial ExpectationsWhere It Doesn’t WorkSee Also49. Know Your LimitThe Game of St. PetersburgStatistical AnalysisWhy It Doesn’t WorkInfinite is a lotDecreasing marginal utilityRisk versus rewardInfinity doesn’t existSee Also
50. Avoid the ZonkThe Monty Hall Problem and Game Show StrategyWhy You Should Always Switch51. Pass Go, Collect $200, Win the GameMonopoly Statistical BasicsKey PropertiesImportance of the Monopoly Prison SystemSee Also52. Use Random Selection as Artificial IntelligenceTrial-and-Error LearningBuilding a Tic-Tac-Toe MachineOperating the ComputerWhy It WorksHacking the Hack53. Do Card Tricks Through the MailHow It WorksProbability of SuccessSee Also54. Check Your iPod’s HonestyAssessing iTunes’s Selection ProceduresCalculating the Statistics of the Selection ProcessExplaining Statistical SurprisesSee Also55. Predict the Game WinnersChoosing Predictor VariablesEntering the Data into a SpreadsheetBuilding a Regression EquationInterpreting and Applying the Regression EquationImproving Your Regression Equation56. Predict the Outcome of a Baseball GameHow It WorksWhy It WorksProving It WorksOther Places It WorksWhere It Doesn’t Work57. Plot Histograms in ExcelThe CodeHacking the Hack58. Go for TwoTraditional Two-Point Conversion ChartsModern Super-Scientific ChartHow It Works59. Rank with the Best of ThemHow to Rank FairlyTotal pointsMean performanceTotal winsComparing the Three MethodsThe End of the Story60. Estimate Pi by ChancePiPi and Falling NeedlesProbability and PiEstimating Pi Using Probability
61. Outsmart SupermanLucky Lois LaneThe GuessesThe CalculationsGuess 1Guess 2Guess 3Guess 4Final Probability62. Demystify Amazing CoincidencesCompare the Number of Possible OutcomesFigure Out the Actual OddsRemove Meaning Assigned to Meaningless Events63. Sense the Real Randomness of LifeWhat Does Random Look Like?How to Spot Random OutcomesHow to Calculate CombinationsWhen to Be Suspicious64. Spot Faked DataHow It WorksLaying Down the LawStreet addressesStock pricesMore General Statements of Benford’s LawWhere Else It WorksScale invarianceBase invarianceWhy It WorksWhere It Doesn’t WorkSee Also65. Give Credit Where Credit Is DueBuilding a ModelFactor AnalysisSee Also66. Play a Tune on Pascal’s TrianglePresenting Pascal’s TriangleCalculating Probability Using the TriangleAssessing the probability of flipped coin outcomesAssessing the probability of a bad car tripWhy It Works67. Control Random ThoughtsMind ControlProbability and Word AssociationBuilding a List of Word AssociationsWhy It WorksWhere Else It WorksWhere It Doesn’t Work68. Search for ESPIdentifying Psychic AbilitiesAnalyzing the ResultsHow Much Is Enough?69. Cure ConjunctionitusThe ProblemConjunction Junction, What’s Your Function?The CureSee Also70. Break Codes with Etaoin ShrdluSingle Substitution CiphersUsing Probability to Decode Substitution CiphersETAOIN SHRDLUStatistical Analysis of Coded TextsOther Common Letter PatternsSee Also71. Discover a New SpeciesIdentifying Species with StatisticsCollect some dataChoose a statistical methodSelect a hypothesis and analyze the dataInterpret resultsTwo Possum SpeciesSee Also72. Feel ConnectedSix Degrees of SeparationDoing a Big StudyChoose a targetRecruit participatesTrain participatesCollect and analyze the resultsDoing a Small StudyMilgram via emailThrow a partyJust Doing the MathSee Also73. Learn to Ride a VotercycleVote CyclingHow It WorksGetting Off the Votercycle74. Live Life in the Fast Lane (You’re Already In)Skips, Slips, and EpochsProbability and Traffic PatternsMaking Wise Lane-Changing DecisionsSee Also75. Seek Out New Life and New CivilizationsEstimating the Number of Smart PlanetsApplying Drake’s EquationFinding our Space ChumsData Analysis