book

JMP® Start Statistics: A Guide to Statistics and Data Analysis Using JMP®, 4th Edition

Name: JMP® Start Statistics: A Guide to Statistics and Data Analysis Using JMP®, 4th Edition
ISBN: 9781599945729

by John Sall, Lee Creighton, Ann Lehman

September 2007

Beginner

628 pages

12h 29m

English

SAS Institute

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Copyright
Preface
The SoftwareJMP Start Statistics, Fourth EditionSASThis Book
1. Preliminaries
1.1. What You Need to Know1.1.1. ...about your computer1.1.2. ...about statistics1.2. Learning About JMP1.2.1. ...on your own with JMP Help1.2.2. ...hands-on examples1.2.3. ...using Tutorials1.2.4. ...reading about JMP1.3. Chapter Organization1.4. Typographical Conventions
2. JMP Right In
2.1. Hello!2.2. First Session2.2.1. Open a JMP Data Table2.2.2. Launch an Analysis Platform2.2.3. Interact with the Surface of the Report2.2.3.1. Row Highlighting2.2.3.2. Disclosure Icons2.2.3.3. Contextual Popup Menus2.2.3.4. Resizing Graphs2.2.4. Special Tools2.3. Modeling Type2.3.1. Analyze and Graph2.3.2. The Analyze Menu2.3.2.1. Modeling2.3.2.2. Multivariate Methods2.3.2.3. Survival and Reliability2.3.3. The Graph Menu2.3.4. Navigating Platforms and Building Context2.3.5. Contexts for a Histogram2.3.6. Contexts for the t-Test2.3.7. Contexts for a Scatterplot2.3.8. Contexts for Nonparametric Statistics2.4. The Personality of JMP
3. Data Tables, Reports, and Scripts
3.1. Overview3.2. The Ins and Outs of a JMP Data Table3.2.1. Selecting and Deselecting Rows and Columns3.2.2. Mousing Around a Spreadsheet: Cursor Forms3.2.2.1. Arrow cursor ()3.2.2.2. I-beam cursor ()3.2.2.3. Selection cursor ()3.2.2.4. Double Arrow cursor ()3.2.2.5. List Check and Range Check cursors ()3.2.2.6. Popup Pointer cursor ()3.3. Creating a New JMP Table3.3.1. Define Rows and Columns3.3.1.1. Add Columns3.3.1.2. Set Column Characteristics3.3.1.3. Add Rows3.3.2. Enter Data3.3.3. The New Column Command3.3.4. Plot the Data3.3.5. Importing Data3.3.6. Importing Text Files3.3.7. Importing Microsoft Excel Files3.3.8. Using ODBC3.3.9. Opening Other File Types3.3.10. Copy, Paste, and Drag Data3.3.10.1. Copy3.3.10.2. Paste3.3.10.3. Drag3.4. Moving Data Out of JMP3.4.1. Windows3.4.2. Macintosh3.4.3. Linux3.5. Working with Graphs and Reports3.5.1. Copy and Paste3.5.2. Drag Report Elements3.5.3. Context Menu Commands3.5.3.1. Context Commands for Report Tables3.6. Juggling Data Tables3.6.1. Data Management3.6.2. Give New Shape to a Table: Stack Columns3.7. The Summary Command3.7.1. Create a Table of Summary Statistics3.8. Working with Scripts3.8.1. Opening and Running Scripts on Windows and Linux3.8.2. Opening and Running Scripts on the Macintosh
4. Formula Editor Adventures
4.1. Overview4.2. The Formula Editor Window4.3. A Quick Example4.4. Formula Editor: Pieces and Parts4.4.1. Terminology4.4.2. The Formula Editor Control Panel4.5. The Keypad Functions4.5.1. Section214.5.1.1. Arithmetic keys4.5.1.2. Insert and Delete keys4.5.1.3. Raise to a Power4.5.1.4. Root4.5.1.5. Switch Terms4.5.1.6. Unary Sign Function4.5.1.7. Local Variable Assignment Key4.5.1.8. Peel Expression4.6. The Formula Display Area4.7. Function Browser Definitions4.7.1. Row Function Examples4.7.1.1. Lag(column,n)4.7.1.2. Row()4.7.1.3. Dif(column,n)4.7.1.4. NRow ()4.7.1.5. Subscript4.7.1.6. Using a Subscript4.7.2. Conditional Expressions and Comparison Operators4.7.2.1. Using the If function4.7.2.2. Using the Match Function4.7.3. Summarize Down Columns or Across Rows4.7.3.1. The Quantile Function4.7.3.2. Using the Summation Function4.7.4. Random Number Functions4.7.4.1. The Uniform Distribution4.7.4.2. The Normal Distribution4.7.4.3. The Col Shuffle Command4.7.4.4. Local Variables and Table Variables4.8. Tips on Building Formulas4.8.1. Examining Expression Values4.8.2. Cutting, Dragging, and Pasting Formulas4.8.3. Selecting Expressions4.8.4. Tips on Editing a Formula4.9. Exercises
5. What Are Statistics?
5.1. Overview5.2. Ponderings5.2.1. The Business of Statistics5.2.2. The Yin and Yang of Statistics5.2.3. The Faces of Statistics5.2.4. Don't Panic5.2.4.1. Abstract Mathematics5.2.4.2. Lingo5.2.4.3. Awkward Phrasing5.2.4.4. A Bad Reputation5.2.4.5. Uncertainty5.3. Preparations5.3.1. Three Levels of Uncertainty5.3.1.1. Random Events5.3.1.2. Unknown Parameters5.3.1.3. Unknown Models5.3.2. Probability and Randomness5.3.3. Assumptions5.3.3.1. Ceteris Paribus5.3.3.2. Is the Model Correct?5.3.3.3. Is the Sample Valid?5.3.4. Data Mining?5.4. Statistical Terms5.4.1. Model5.4.2. Parameters5.4.3. Hypotheses5.4.4. Two-Sided versus One-Sided, Two-Tailed versus One-Tailed5.4.5. Statistical Significance5.4.6. Significance Level, p-value, α-level5.4.7. Power, ß-level5.4.8. Confidence Intervals5.4.9. Biased, Unbiased5.4.10. Sample Mean versus True Mean5.4.11. Variance and Standard Deviation, Standard Error5.4.12. Degrees of Freedom
6. Simulations
6.1. Overview6.2. Rolling Dice6.2.1. Rolling Several Dice6.2.2. Flipping Coins, Sampling Candy, or Drawing Marbles6.3. Probability of Making a Triangle6.4. Confidence Intervals
7. Univariate Distributions: One Variable, One Sample
7.1. Overview7.2. Looking at Distributions7.2.1. Probability Distributions7.2.2. True Distribution Function or Real-World Sample Distribution7.2.3. The Normal Distribution7.3. Describing Distributions of Values7.3.1. Generating Random Data7.3.2. Histograms7.3.3. Stem-and-Leaf Plots7.3.4. Outlier and Quantile Box Plots7.3.5. Mean and Standard Deviation7.3.6. Median and Other Quantiles7.3.7. Mean versus Median7.3.8. Higher Moments: Skewness and Kurtosis7.3.9. Extremes, Tail Detail7.4. Statistical Inference on the Mean7.4.1. Standard Error of the Mean7.4.2. Confidence Intervals for the Mean7.4.3. Testing Hypotheses: Terminology7.4.4. The Normal z- Test for the Mean7.4.5. Case Study: The Earth's Ecliptic7.4.6. Student's t-Test7.4.7. Comparing the Normal and Student's t Distributions7.4.8. Testing the Mean7.4.9. The p-Value Animation7.4.10. Power of the t-Test7.5. Practical Significance vs. Statistical Significance7.6. Examining for Normality7.6.1. Normal Quantile Plots7.6.2. Statistical Tests for Normality7.7. Special Topic: Practical Difference7.8. Special Topic: Simulating the Central Limit Theorem7.9. Seeing Kernel Density Estimates7.10. Exercises
8. The Difference between Two Means
8.1. Overview8.2. Two Independent Groups8.2.1. When the Difference Isn't Significant8.2.2. Check the Data8.2.3. Launch the Fit Y by X Platform8.2.4. Examine the Plot8.2.5. Display and Compare the Means8.2.6. Inside the Student's t-Test8.2.7. Equal or Unequal Variances?8.2.8. One-Sided Version of the Test8.2.9. Analysis of Variance and the All-Purpose F-Test8.2.10. How Sensitive Is the Test?8.2.11. How Many More Observations Are Needed?8.2.12. When the Difference Is Significant8.3. Normality and Normal Quantile Plots8.4. Testing Means for Matched Pairs8.4.1. Thermometer Tests8.4.2. Look at the Data8.4.3. Look at the Distribution of the Difference8.4.4. Student's t-Test8.4.5. The Matched Pairs Platform for a Paired t-Test8.4.6. Optional Topic: An Equivalent Test for Stacked Data8.5. The Normality Assumption8.6. Two Extremes of Neglecting the Pairing Situation: A Dramatization8.7. A Nonparametric Approach8.7.1. Introduction to Nonparametric Methods8.7.2. Paired Means: The Wilcoxon Signed-Rank Test8.7.3. Independent Means: The Wilcoxon Rank Sum Test8.8. Exercises

9. Comparing Many Means: One-Way Analysis of Variance
9.1. overview9.2. What Is a One-Way Layout?9.3. Comparing and Testing Means9.4. Means Diamonds: A Graphical Description of Group Means9.5. Statistical Tests to Compare Means9.6. Means Comparisons for Balanced Data9.7. Means Comparisons for Unbalanced Data9.8. Adjusting for Multiple Comparisons9.9. Are the Variances Equal Across the Groups?9.9.1. Testing Means with Unequal Variances9.10. Nonparametric Methods9.10.1. Review of Rank-Based Nonparametric Methods9.10.2. The Three Rank Tests in JMP9.11. Exercises
10. Fitting Curves through Points: Regression
10.1. Overview10.2. Regression10.2.1. Least Squares10.2.2. Seeing Least Squares10.2.3. Fitting a Line and Testing the Slope10.2.4. Testing the Slope by Comparing Models10.2.4.1. C Total10.2.4.2. Error10.2.4.3. Model10.2.4.4. Mean Square10.2.4.5. Root Mean Square Error10.2.5. The Distribution of the Parameter Estimates10.2.5.1. Std Error10.2.5.2. t-Ratio10.2.5.3. Prob>|t|10.2.6. Confidence Intervals on the Estimates10.2.7. Examine Residuals10.2.8. Exclusion of Rows10.2.9. Time to Clean Up10.3. Polynomial Models10.3.1. Look at the Residuals10.3.2. Higher-Order Polynomials10.3.3. Distribution of Residuals10.4. Transformed Fits10.4.1. Spline Fit10.5. Are Graphics Important?10.6. Why It's Called Regression10.7. What Happens When X and Y Are Switched?10.8. Curiosities10.8.1. Sometimes It's the Picture That Fools You10.8.2. High-Order Polynomial Pitfall10.8.3. The Pappus Mystery on the Obliquity of the Ecliptic10.9. Exercises
11. Categorical Distributions
11.1. Overview11.2. Categorical Situations11.3. Categorical Responses and Count Data: Two Outlooks11.4. A Simulated Categorical Response11.4.1. Simulating Some Categorical Response Data11.4.2. Variability in the Estimates11.4.3. Larger Sample Sizes11.4.4. Monte Carlo Simulations for the Estimators11.4.5. Distribution of the Estimates11.5. The X2 Pearson Chi-Square Test Statistic11.6. The G2 Likelihood-Ratio Chi-Square Test Statistic11.6.1. Likelihood Ratio Tests11.6.2. The G2 Likelihood Ratio Chi-Square Test11.7. Univariate Categorical Chi-Square Tests11.7.1. Comparing Univariate Distributions11.7.2. Charting to Compare Results11.8. Exercises
12. Categorical Models
12.1. Overview12.2. Fitting Categorical Responses to Categorical Factors: Contingency Tables12.2.1. Testing with G2 and X212.2.2. Looking at Survey Data12.2.2.1. Contingency Table: Country by Sex12.2.2.2. Mosaic Plot12.2.2.3. Testing Marginal Homogeneity12.2.3. Car Brand by Marital Status12.2.4. Car Brand by Size of Vehicle12.3. Two-Way Tables: Entering Count Data12.3.1. Expected Values Under Independence12.3.2. Entering Two-Way Data into JMP12.3.3. Testing for Independence12.4. If You Have a Perfect Fit12.5. Special Topic: Correspondence Analysis— Looking at Data with Many Levels12.6. Continuous Factors with Categorical Responses: Logistic Regression12.6.1. Fitting a Logistic Model12.6.2. Degrees of Fit12.6.3. A Discriminant Alternative12.6.4. Inverse Prediction12.6.5. Polytomous Responses: More Than Two Levels12.6.6. Ordinal Responses: Cumulative Ordinal Logistic Regression12.7. Surprise: Simpson's Paradox: Aggregate Data versus Grouped Data12.8. Generalized Linear Models12.9. Exercises
13. Multiple Regression
13.1. Overview13.2. Parts of a Regression Model13.2.1. response, Y13.2.2. regressors, X's13.2.3. coefficients, parameters13.2.4. intercept term13.2.5. error, residual13.3. A Multiple Regression Example13.3.1. Residuals and Predicted Values13.3.2. The Analysis of Variance Table13.3.3. The Whole Model F-Test13.3.4. Whole-Model Leverage Plot13.3.5. Details on Effect Tests13.3.6. Effect Leverage Plots13.4. Collinearity13.4.1. Exact Collinearity, Singularity, Linear Dependency13.5. The Longley Data: An Example of Collinearity13.6. The Case of the Hidden Leverage Point13.7. Mining Data with Stepwise Regression13.8. Exercises
14. Fitting Linear Models
14.1. Overview14.2. The General Linear Model14.2.1. Kinds of Effects in Linear Models14.2.1.1. Intercept term14.2.1.2. Continuous effects14.2.1.3. Categorical effects14.2.1.4. Interactions14.2.1.5. Nested effects14.2.2. Coding Scheme to Fit a One-Way anova as a Linear Model14.2.3. Regressor Construction14.2.4. Interpretation of Parameters14.2.5. Predictions Are the Means14.2.6. Parameters and Means14.2.7. Analysis of Covariance: Putting Continuous and Classification Terms into the Same Model14.2.8. The Prediction Equation14.2.9. The Whole-Model Test and Leverage Plot14.2.10. Effect Tests and Leverage Plots14.2.11. Least Squares Means14.2.12. Lack of Fit14.2.13. Separate Slopes: When the Covariate Interacts with the Classification Effect14.3. Two-Way Analysis of Variance and Interactions14.4. Optional Topic: Random Effects and Nested Effects14.4.1. Nesting14.4.2. Repeated Measures14.4.3. Method 1: Random Effects-Mixed Model14.4.4. Method 2: Reduction to the Experimental Unit14.4.5. Method 3: Correlated Measurements-Multivariate Model14.4.6. Varieties of Analysis14.4.7. Summary14.5. Exercises
15. Bivariate and Multivariate Relationships
15.1. Overview15.2. Bivariate Distributions15.3. Density Estimation15.3.1. Bivariate Density Estimation15.3.2. Mixtures, Modes, and Clusters15.3.3. The Elliptical Contours of the Normal Distribution15.4. Correlations and the Bivariate Normal15.4.1. Simulation Exercise15.4.2. Correlations Across Many Variables15.4.3. Bivariate Outliers15.5. Three and More Dimensions15.5.1. Principal Components15.5.2. Principal Components for Six Variables15.5.3. Correlation Patterns in Biplots15.5.4. Outliers in Six Dimensions15.6. Summary15.7. Exercises
16. Design of Experiments
16.1. Overview16.2. Introduction16.2.1. Experimentation Is Learning16.2.2. Controlling Experimental Conditions Is Essential16.2.3. Experiments Manage Random Variation within A Statistical Framework16.3. JMP DOE16.4. A Simple Design16.4.1. The Experiment16.4.2. The Response16.4.3. The Factors16.4.4. The Budget16.4.5. Enter and Name the Factors16.4.6. Define the Model16.4.7. Is the Design Balanced?16.4.8. Perform Experiment and Enter Data16.4.8.1. Examine the Response Data16.4.9. Analyze the Model16.4.10. Details of the Design16.4.10.1. Confounding Structure16.4.11. Using the Custom Designer16.4.11.1. Modify a Design Interactively16.4.11.2. How the Custom Designer Works16.4.12. Using the Screening Platform16.4.12.1. Contrasts and p-values16.4.12.2. Half-Normal Plot16.5. Screening for Interactions: The Reactor Data16.6. Response Surface Designs16.6.1. The Experiment16.6.2. Response Surface Designs in JMP16.6.3. Plotting Surface Effects16.6.4. Designating RSM Designs Manually16.6.5. The Prediction Variance Profiler16.6.5.1. A Quadratic Model16.6.5.2. A Cubic Model16.7. Design Issues16.8. Routine Screening Examples16.8.1. Main Effects Only16.8.1.1. All Two-Factor Interactions Involving Only One Factor16.8.1.2. All Two-Factor Interactions16.9. Design Strategies Glossary
17. Exploratory Modeling
17.1. Overview17.2. The Partition Platform17.2.1. Modeling with Recursive Trees17.2.2. Viewing Large Trees17.2.3. Saving Results17.3. Neural Networks17.3.1. Modeling with Neural Networks17.3.2. Profiles in Neural Nets17.3.3. Using Cross-Validation17.3.4. Saving Columns17.4. Exercises
18. Discriminant and Cluster Analysis
18.1. Overview18.2. Discriminant Analysis18.2.1. Canonical Plot18.2.2. Discriminant Scores18.3. Cluster Analysis18.3.1. A Real-World Example18.4. Exercises
19. Statistical Quality Control
19.1. Overview19.2. Control Charts and Shewhart Charts19.2.1. Variables Charts19.2.2. Attributes Charts19.3. The Control Chart Launch Dialog19.3.1. Process Information19.3.1.1. Process19.3.1.2. Sample Label19.3.2. Chart Type Information19.3.3. Limits Specification Panel19.3.3.1. K Sigma19.3.3.2. Alpha19.3.4. Using Known Statistics19.3.5. Types of Control Charts for Variables19.3.5.1. Mean, R, and S Charts19.3.5.2. Individual Measurement and Moving Range Charts19.3.6. Types of Control Charts for Attributes19.3.6.1. p- and np-Charts19.3.6.2. u-Charts19.3.7. Moving Average Charts19.3.7.1. Uniformly Weighted Moving Average (UWMA) Charts19.3.7.2. Exponentially Weighted Moving Average (EWMA) Chart19.3.8. Levey-Jennings Plots19.3.9. Tailoring the Horizontal Axis19.3.10. Tests for Special Causes19.3.11. Westgard Rules19.4. Multivariate Control Charts
20. Time Series
20.1. Overview20.2. Introduction20.3. Lagged Values20.3.1. Testing for Autocorrelation20.4. White Noise20.5. Autoregressive Processes20.5.1. Correlation Plots of AR Series20.6. Estimating the Parameters of an Autoregressive Process20.7. Moving Average Processes20.7.1. Correlation Plots of MA Series20.8. Example of Diagnosing a Time Series20.9. ARMA Models and the Model Comparison Table20.10. Stationarity and Differencing20.11. Seasonal Models20.12. Spectral Density20.13. Forecasting20.14. Exercises
21. Machines of Fit
21.1. Overview21.2. Springs for Continuous Responses21.2.1. Fitting a Mean21.2.2. Testing a Hypothesis21.2.3. One-Way Layout21.2.4. Effect of Sample Size Significance21.2.5. Effect of Error Variance on Significance21.2.6. Experimental Design's Effect on Significance21.2.7. Simple Regression21.2.8. Leverage21.2.9. Multiple Regression21.2.10. Summary: Significance and Power21.3. Machine of Fit for Categorical Responses21.3.1. How Do Pressure Cylinders Behave?21.3.2. Estimating Probabilities21.3.3. One-Way Layout for Categorical Data21.3.4. Logistic Regression
References and Data Sources
Answers to Selected Exercises
21.4. Chapter 4, "Formula Editor Adventures"21.5. Chapter 7, "Univariate Distributions: One Variable, One Sample"21.6. Chapter 8, "The Difference between Two Means"21.7. Chapter 9, "Comparing Many Means: One-Way Analysis of Variance"21.8. Chapter 10, "Fitting Curves through Points: Regression"21.9. Chapter 11, "Categorical Distributions"21.10. Chapter 12, "Categorical Models"21.11. Chapter 13, "Multiple Regression"21.12. Chapter 14, "Fitting Linear Models"21.13. Chapter 15, "Bivariate and Multivariate Relationships"21.14. Chapter 17, "Exploratory Modeling"21.15. Chapter 18, "Discriminant and Cluster Analysis"21.16. Chapter 20, "Time Series"
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Content preview from JMP® Start Statistics: A Guide to Statistics and Data Analysis Using JMP®, 4th Edition

Chapter 14. Fitting Linear Models

Overview

Several techniques, of increasing complexity, have been covered in this book. From fitting single means, to fitting multiple means, to fitting situations where the regressor is a continuous function, specific techniques have been demonstrated to address a wide variety of statistical situations. This chapter introduces a new approach involving general linear models, which will encompass all the models covered so far and extend to many more situations. They are all unified under the technique of least squares, fitting parameters to minimize the sum of squared residuals.

The techniques can be generalized even further to cover categorical response models, and other more specialized applications.

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Statistics: An Introduction Using R, 2nd Edition

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