book

JMP Start Statistics, 6th Edition

by John Sall, Mia L. Stephens, Ann Lehman, Sheila Loring

February 2017

Intermediate to advanced

660 pages

14h 27m

English

SAS Institute

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The SoftwareHow to Get JMPJMP Start Statistics, Sixth EditionSASJMP versus JMP ProThis Book
What You Need to Know…about statisticsLearning about JMP…on your own with JMP Help…hands-on examples…using Tutorials…reading about JMPChapter OrganizationTypographical Conventions
Hello!First SessionTip of the DayThe JMP Starter (Macintosh)The JMP Home Window (Windows)Open a JMP Data TableLaunch an Analysis PlatformInteract with the Report SurfaceSpecial ToolsCustomize JMPModeling TypeAnalyze and GraphNavigating Platforms and Building ContextContexts for a HistogramContexts for the t-TestContexts for a ScatterplotContexts for Nonparametric StatisticsThe Personality of JMP
OverviewThe Ins and Outs of a JMP Data TableSelecting and Deselecting Rows and ColumnsMousing around a Data Table: Cursor FormsCreating a New JMP TableDefine Rows and ColumnsEnter DataThe New Column CommandPlot the DataImporting DataImporting Text FilesImporting Other File TypesCopy, Paste, and Drag DataMoving Data Out of JMPSaving Graphs and ReportsCopy and PasteDrag Report ElementsSave JMP Reports and GraphsCreate Interactive Web ReportsPop-up Menu CommandsJuggling Data TablesData ManagementGive New Shape to a Table: Stack ColumnsCreating Summary StatisticsCreate Summary Statistics with the Summary CommandCreate Summary Statistics with TabulateWorking with ScriptsCreating ScriptsRunning Data Table ScriptsOpening and Running Stand-alone Scripts
OverviewThe Formula Editor WindowThe Formula Editor and the JMP Scripting LanguageA Quick Example: Standardizing DataMaking a New Formula ColumnUsing Popular Formula FunctionsWriting Conditional ExpressionsSummarizing Data with the Formula EditorGenerating Random DataLocal Variables and Table VariablesWorking with DatesTips on Building FormulasExamining Expression ValuesCutting, Dragging, and Pasting FormulasSelecting ExpressionsExercises
OverviewPonderingsThe Business of StatisticsThe Yin and Yang of StatisticsThe Faces of StatisticsDon’t PanicPreparationsThree Levels of UncertaintyProbability and RandomnessAssumptionsData Mining?Statistical Terms
OverviewRolling DiceRolling Several DiceFlipping Coins, Sampling Candy, or Drawing MarblesProbability of Making a TriangleConfidence IntervalsData Table-Based SimulationsOther JMP SimulatorsExercises
OverviewLooking at DistributionsProbability DistributionsTrue Distribution Function or Real-World Sample DistributionThe Normal DistributionDescribing Distributions of ValuesGenerating Random DataHistogramsStem-and-Leaf PlotsDot PlotsOutlier and Quantile Box PlotsMean and Standard DeviationMedian and Other QuantilesMean versus MedianOther Summary Statistics: Skewness and KurtosisExtremes, Tail DetailStatistical Inference on the MeanStandard Error of the MeanConfidence Intervals for the MeanTesting Hypotheses: TerminologyThe Normal z-Test for the MeanCase Study: The Earth’s EclipticStudent’s t-TestComparing the Normal and Student’s t DistributionsTesting the MeanThe p-Value AnimationPower of the t-TestPractical Significance versus Statistical SignificanceExamining for NormalityNormal Quantile PlotsStatistical Tests for NormalitySpecial Topic: Practical DifferenceSpecial Topic: Simulating the Central Limit TheoremSeeing Kernel Density EstimatesExercises
OverviewTwo Independent GroupsWhen the Difference Isn’t SignificantCheck the DataLaunch the Fit Y by X PlatformExamine the PlotDisplay and Compare the MeansInside the Student’s t-TestEqual or Unequal Variances?One-Sided Version of the TestAnalysis of Variance and the All-Purpose F-TestHow Sensitive Is the Test?How Many More Observations Are Needed?When the Difference Is SignificantNormality and Normal Quantile PlotsTesting Means for Matched PairsThermometer TestsLook at the DataLook at the Distribution of the DifferenceStudent’s t-TestThe Matched Pairs Platform for a Paired t-TestOptional Topic:An Equivalent Test for Stacked DataTwo Extremes of Neglecting the Pairing Situation: A DramatizationA Nonparametric ApproachIntroduction to Nonparametric MethodsPaired Means: The Wilcoxon Signed-Rank TestIndependent Means: The Wilcoxon Rank Sum TestExercises
OverviewWhat Is a One-Way Layout?Comparing and Testing MeansMeans Diamonds: A Graphical Description of Group MeansStatistical Tests to Compare MeansMeans Comparisons for Balanced DataMeans Comparisons for Unbalanced DataAdjusting for Multiple ComparisonsAre the Variances Equal across the Groups?Testing Means with Unequal VariancesNonparametric MethodsReview of Rank-Based Nonparametric MethodsThe Three Rank Tests in JMPExercises

OverviewRegressionLeast SquaresSeeing Least SquaresFitting a Line and Testing the SlopeTesting the Slope By Comparing ModelsThe Distribution of the Parameter EstimatesConfidence Intervals on the EstimatesExamine ResidualsExclusion of RowsTime to Clean UpPolynomial ModelsLook at the ResidualsHigher-Order PolynomialsDistribution of ResidualsTransformed FitsSpline FitAre Graphics Important?Why It’s Called RegressionWhat Happens When X and Y Are Switched?CuriositiesSometimes It’s the Picture That Fools YouHigh-Order Polynomial PitfallThe Pappus Mystery on the Obliquity of the EclipticExercises
OverviewCategorical SituationsCategorical Responses and Count Data: Two OutlooksA Simulated Categorical ResponseSimulating Some Categorical Response DataVariability in the EstimatesLarger Sample SizesMonte Carlo Simulations for the EstimatorsDistribution of the EstimatesThe X2 Pearson Chi-Square Test StatisticThe G2 Likelihood-Ratio Chi-Square Test StatisticLikelihood Ratio TestsThe G2 Likelihood Ratio Chi-Square TestUnivariate Categorical Chi-Square TestsComparing Univariate DistributionsCharting to Compare ResultsExercises
OverviewFitting Categorical Responses to Categorical Factors: Contingency TablesTesting with G2 and X2 StatisticLooking at Survey DataCar Brand by Marital StatusCar Brand by Size of VehicleTwo-Way Tables: Entering Count DataExpected Values under IndependenceEntering Two-Way Data into JMPTesting for IndependenceIf You Have a Perfect FitSpecial Topic: Correspondence Analysis— Looking at Data with Many LevelsContinuous Factors with Categorical Responses: Logistic RegressionFitting a Logistic ModelDegrees of FitA Discriminant AlternativeInverse PredictionPolytomous (Multinomial) Responses: More Than Two LevelsOrdinal Responses: Cumulative Ordinal Logistic RegressionSurprise: Simpson’s Paradox: Aggregate Data versus Grouped DataGeneralized Linear ModelsExercises
OverviewParts of a Regression ModelRegression DefinitionsA Multiple Regression ExampleResiduals and Predicted ValuesThe Analysis of Variance TableThe Whole Model F-TestWhole-Model Leverage PlotDetails on Effect TestsEffect Leverage PlotsCollinearityExact Collinearity, Singularity, and Linear DependencyThe Longley Data: An Example of CollinearityThe Case of the Hidden Leverage PointMining Data with Stepwise RegressionExercises
OverviewThe General Linear ModelTypes of Effects in Linear ModelsCoding Scheme to Fit a One-Way ANOVA as a Linear ModelRegressor ConstructionInterpretation of ParametersPredictions Are the MeansParameters and MeansAnalysis of Covariance: Continuous and Categorical Terms in the Same ModelThe Prediction EquationThe Whole-Model Test and Leverage PlotEffect Tests and Leverage PlotsLeast Squares MeansLack of FitSeparate Slopes: When the Covariate Interacts with a Categorical EffectTwo-Way Analysis of Variance and InteractionsOptional Topic: Random Effects and Nested EffectsNestingRepeated MeasuresMethod 1: Random Effects-Mixed ModelMethod 2: Reduction to the Experimental UnitMethod 3: Correlated Measurements-Multivariate ModelVarieties of AnalysisClosing ThoughtsExercises
OverviewIntroductionKey ConceptsJMP DOEA Simple DesignThe ExperimentEnter the Response and FactorsDefine the ModelIs the Design Balanced?Perform Experiment and Enter DataAnalyze the ModelFlour Paste ConclusionsDetails of the Design: Confounding StructureUsing the Custom DesignerHow the Custom Designer WorksChoices in the Custom DesignerAn Interaction Model: The Reactor DataAnalyzing the Reactor DataWhere Do We Go from Here?Some Routine Screening ExamplesMain Effects Only (a Review)All Two-Factor Interactions Involving a Single FactorAlias Optimal DesignsResponse Surface DesignsThe Odor ExperimentResponse Surface Designs in JMPAnalyzing the Odor Response Surface DesignPlotting Surface EffectsSpecifying Response Surface Effects ManuallyThe Custom Designer versus the Response Surface Design PlatformSplit-Plot DesignsThe Box Corrosion Split-Plot ExperimentDesigning the ExperimentAnalysis of Split-Plot DesignsDesign StrategiesDOE Glossary of Key TermsExercises
OverviewBivariate DistributionsDensity EstimationBivariate Density EstimationMixtures, Modes, and ClustersThe Elliptical Contours of the Normal DistributionCorrelations and the Bivariate NormalSimulating Bivariate CorrelationsCorrelations across Many VariablesBivariate OutliersOutliers in Three and More DimensionsIdentify Variation with Principal Components AnalysisPrincipal Components for Six VariablesHow Many Principal Components?Discriminant AnalysisCanonical PlotDiscriminant ScoresStepwise Discriminant Variable SelectionCluster AnalysisHierarchical Clustering: How Does It Work?A Real-World ExampleSome Final ThoughtsExercises
OverviewRecursive Partitioning (Decision Trees)Growing TreesExploratory Modeling with PartitionSaving Columns and FormulasNeural NetsA Simple ExampleModeling with Neural NetworksSaving ColumnsProfiles in NeuralExercises
OverviewWhat Does a Control Chart Look LikeTypes of Control ChartsVariables ChartsAttributes ChartsSpecialty ChartsControl Chart BasicsControl Charts for Variables DataVariables Charts Using Control Chart BuilderThe Control Chart Builder Work SpaceControl Chart Builder ExamplesControl Charts for Attributes DataSpecialty ChartsPresummarize ChartsLevey-Jennings ChartsUniformly Weighted Moving Average (UWMA) ChartsExponentially Weighted Moving Average (EWMA) ChartCapability AnalysisWhat Is Process Capability?Capability for One Process MeasurementCapability for Many Process MeasurementsCapability for Time-Ordered DataA Few Words about Measurement SystemsExercises
OverviewSprings for Continuous ResponsesFitting a MeanTesting a HypothesisOne-Way LayoutEffect of Sample Size SignificanceEffect of Error Variance on SignificanceExperimental Design’s Effect on SignificanceSimple RegressionLeverageMultiple RegressionSummary: Significance and PowerMechanics of Fit for Categorical ResponsesHow Do Pressure Cylinders Behave?Estimating ProbabilitiesOne-Way Layout for Categorical DataLogistic Regression
Chapter 4, “Formula Editor”Chapter 7, “Univariate Distributions: One Variable, One Sample”Chapter 8, “The Difference Between Two Means”Chapter 9, “Comparing Many Means: One-Way Analysis of Variance”Chapter 10, “Fitting Curves through Points: Regression”Chapter 11, “Categorical Distributions”Chapter 12, “Categorical Models”Chapter 13, “Multiple Regression”Chapter 14, “Fitting Linear Models”Chapter 15, “Design of Experiments”Chapter 16, “Bivariate and Multivariate Relationships”Chapter 17, “Exploratory Modeling”Chapter 18, “Control Charts and Capability”

Content preview from JMP Start Statistics, 6th Edition

8 The Difference Between Two Means

Overview

Are the mean responses from two groups different? What evidence would it take to convince you? This question opens the door to many of the issues that pervade statistical inference, and this chapter explores these issues. Comparing group means also introduces an important statistical distinction regarding how the measurement or sampling process affects the way the resulting data are analyzed. This chapter also talks about validating statistical assumptions.

When two groups are considered, there are two distinct situations that lead to two different analyses:

Independent Groups—the responses from the two groups are unrelated and statistically independent. For example, the two groups might be two classrooms ...