Understanding statistics and statistical myths : how to become a profound learner

Content: Myth 1: Two Types of Data-Attribute/Discrete and Measurement/ContinuousBackgroundMeasurement Requires ScaleGauges or Instruments vs. No GaugesDiscrete, Categorical, Attribute versus Continuous, Variable: Degree of InformationCreating Continuous Measures by Changing the "Thing" MeasuredDiscrete versus Continuous: Half TestNominal, Ordinal, Interval, RatioMeasurement to CompareScale Type versus Data TypeScale TaxonomyPurpose of Data ClassificationMyth 2: Proportions and Percentages Are Discrete DataBackgroundDenominator for Proportions and PercentagesProbabilitiesClassification of Proportions, Percentages, and ProbabilitiesMyth 3: s = â [Σ(Xi- x)2/(n- 1)] The Correct Formula for Sample Standard DeviationBackgroundCorrectness of EstimationsEstimators and EstimatesProperties of EstimatorsMyth 4: Sample Standard Deviation â [Σ(Xi-x)2/(n- 1)] Is UnbiasedBackgroundDegrees of Freedomt DistributionDefinition of BiasRemoving Bias and Control ChartsMyth 5: Variances Can Be Added but Not Standard DeviationsBackgroundSums of Squares and Square Roots: Pythagorean TheoremFunctions and OperatorsRandom VariablesIndependence of FactorsOther PropertiesMyth 6: Parts and Operators for an MSA Do Not Have to Be Randomly SelectedBackgroundTypes of Analyses of VarianceMaking Measurement System Look Better than It Is: Selecting Parts to Cover the Range of Process VariationSelecting Both Good and Bad PartsMyth 7: % Study (% Contribution, Number of Distinct Categories) Is the Best Criterion for Evaluating a Measurement System for Process ImprovementBackground% Contribution versus % StudyP/T Ratio versus % StudyDistinguishing between Good and Bad PartsDistinguishing Parts That Are DifferentMyth 8: Only Sigma Can Compare Different Processes and MetricsBackgroundSigma and SpecificationsSigma as a PercentageMyth 9: Capability Is Not Percent/Proportion of Good UnitsBackgroundCapability Indices: Frequency Meeting SpecificationsCapability: Actual versus PotentialCapability IndicesProcess Capability Time-DependentMeaning of Capability: Short-Cut CalculationsMyth 10: p = Probability of Making an ErrorBackgroundOnly Two Types of ErrorsDefinition of an Error about Deciding What Is TrueCalculation of p and Evidence for a HypothesisProbability of Making an Error for a Particular CaseProbability of Data Given Ho versus Probability of Ho Given DataNon-probabilistic DecisionsMyth 11: Need More Data for Discrete Data than Continuous Data AnalysisBackgroundDiscrete Examples When n = 1Factors That Determine Sample SizeRelevancy of DataMyth 12: Nonparametric Tests Are Less Powerful than Parametric TestsBackgroundDistribution Free versus NonparametricComparing Power for the Same ConditionsDifferent Formulas for Testing the Same HypothesesAssumptions of TestsComparing Power for the Same CharacteristicConverting Quantitative Data to Qualitative DataMyth 13: Sample Size of 30 Is Acceptable (for Statistical Significance)BackgroundA Rationale for n = 30Contradictory Rules of ThumbUses of DataSample Size as a Function of Alpha, Beta, Delta, and SigmaSample Size for Practical UseSample Size and Statistical SignificanceMyth 14: Can Only Fail to Reject Ho, Can Never Accept HoBackgroundProving Theories: Sufficient versus NecessaryProve versus Accept versus Fail to Reject: ActionsInnocent versus Guilty: Problems with ExampleTwo-Choice TestingSignificance Testing and Confidence IntervalsHypothesis Testing and PowerNull Hypothesis of â ¥ or â ¤Practical CasesWhich Hypothesis Has the Equal Sign?Bayesian Statistics: Probability of HypothesisMyth 15: Control Limits Are ±3 Standard Deviations from the Center LineBackgroundStandard Error versus Standard DeviationWithin- versus between-Subgroup Variation: How Control Charts WorkI Chart of IndividualsMyth 16: Control Chart Limits Are Empirical LimitsBackgroundDefinition of EmpiricalEmpirical Limits versus Limits Justified EmpiricallyShewhart's Evidence of Limits Being EmpiricalWheeler's Empirical RuleEmpirical Justification for a PurposeMyth 17: Control Chart Limits Are Not Probability LimitsBackgroundAssociation of Probabilities and Control Chart LimitsCan Control Limits Be Probability Limits?False Alarm Rates for All Special Cause PatternsWheeler Uses Probability LimitsOther Uses of Probability LimitsMyth 18: ±3 Sigma Limits Are the Most Economical Control Chart LimitsBackgroundEvidence for 3-Standard Error Limits Being Economically BestEvidence against 3-Standard Error Limits Being the Best EconomicallyCounterexamples: Simple Cost Model Other Out-of-Control Rules-Assignable Causes Shewhart Didn't Find but ExistSmall Changes Are Not Critical to Detect versus Taguchi's Loss FunctionImportance of Subgroup Size and Frequency on Economic Value of Control Chart LimitsPurpose to Detect Lack of Control-3-Standard Error Limits MisplacedMyth 19: Statistical Inferences Are Inductive InferencesBackgroundReasoning: Validity and SoundnessInduction versus DeductionFour Cases of Inductive InferencesStatistical Inferences: Probability DistributionsInferences about Population ParametersDeductive Statistical Inferences: Hypothesis TestingDeductive Statistical Inferences: EstimationReal-World Cases of Statistical InferencesMyth 20: There Is One Universe or Population If Data Are HomogeneousBackgroundDefinition of HomogeneousIs Displaying Stability Required for Universes to Exist?Are There Always Multiple Universes If Data Display Instability?Is There Only One Universe If Data Appropriately Plotted Display Stability?Control Chart Framework: Valid and Invalid ConclusionsMyth 21: Control Charts Are Analytic StudiesBackgroundEnumerative versus Analytic Distinguishing CharacteristicsEnumerative Problem, Study, and SolutionAnalytic Problem, Study, and SolutionProcedures for Enumerative and Analytic StudiesAre Control Charts Enumerative or Analytic Studies?Cause-Effect RelationshipAn Analytic Study Answers "When?"Myth 22: Control Charts Are Not Tests of HypothesesBackgroundDefinition and Structure of Hypothesis TestControl Chart as a General Hypothesis TestStatistical Hypothesis Testing: Alpha and pAnalysis of MeansShewhart's View on Control Charts as Tests of HypothesesDeming's Argument: No Definable, Finite, Static PopulationWoodall's Two Phases of Control Chart UseFinite, Static UniverseControl Charts as Nonparametric Tests of HypothesesUtility of Viewing Control Charts as Statistical Hypothesis TestsIs the Process in Control? versus What Is the Probability the Process Changed?Myth 23: Process Needs to Be Stable to Calculate Process CapabilityBackgroundStability and Capability: Dependent or Independent?Actual Performance and Potential Capability versus StabilityProcess Capability: Reliability of EstimatesControl Charts Are FallibleCapable: 100% or Less than 100% Meeting SpecificationsProcess Capability: "Best" Performance versus SustainabilityCp versus P/TRandom SamplingResponse Surface StudiesMyth 24: Specifications Don't Belong on Control ChartsBackgroundRun ChartsCharts of Individual ValuesConfusion Having Both Control and Specification Limits on ChartsStability, Performance, and CapabilitySpecifications on Averages and VariationMyth 25: Identify and Eliminate Assignable Causes of VariationBackgroundAssignable Causes versus Process ChangeIs Increase in Process Variation Always Bad?Good Assignable CausesMyth 26: Process Needs to Be Stable before You Can Improve ItBackgroundHistory of Improvement before the 1920sControl Chart FallibilityStabilizing a Process and Improving ItStability Required versus Four States of a ProcessShewhart's CounterexampleMyth 27: Stability (Homogeneity) Is Required to Establish a BaselineBackgroundPurpose of BaselineJust-Do-It ProjectsNatural ProcessesProcesses Whose Output We Want to Be "Out of Control"Meaning of "Meaningless"Daily Comparisons"True" Process Average: Process, Outputs, Characteristics, and MeasuresWays to CompareUniverse or Population and Descriptive StatisticsRandom SamplingWhen Is Homogeneity/Stability Not Required or Unimportant? Myth 28: A Process Must Be Stable to Be PredictableBackgroundTypes of Predictions: Interpolation and ExtrapolationInterpolation: Stability versus InstabilityConditional PredictionsExtrapolation: Stability versus InstabilityFallibility of Control Chart StabilityControl Charts in Daily LifeStatistical versus Causal ControlMyth 29: Adjusting a Process Based on a Single Defect Is Tampering, Causing Increased Process VariationBackgroundDefinition of Tampering Zero versus One versus Multiple Defects to Define TamperingRole of Theory and Understanding When AdjustingDefects Arise from Special Causes: AnomaliesControl Limits versus Specification LimitsActions for Common Cause Signals versus Special Cause SignalsIs Reducing Common Cause Variation Always Good?Fundamental Change versus TamperingFunnel Exercise: CounterexampleMyth 30: No Assumptions Required When the Data Speak for ThemselvesBackgroundSimpson's ParadoxMath and Descriptive Statistics: Adding versus AggregatingInferences versus Facts: Conditions for ParadoxesAssumptions for ModelingAssumptions for Causal InferencesAssumptions for Inferences from ReasonsEpilogueReferencesIndex