Statistical Analysis and Data Display: An Intermediate Course with Examples in R

1 Audience......Page 8
 3 Structure......Page 9
  4.1 R......Page 10
  4.3 S-Plus, now called S+......Page 11
  5.1 Revised Chapters......Page 12
 Acknowledgments: First Edition......Page 13
 Acknowledgments......Page 14
Contents......Page 16
Author Bios......Page 32
1 Introduction and Motivation......Page 33
 1.1 Statistics in Context......Page 35
  1.2.1 Investigation of Salary Discrimination......Page 36
  1.2.4 Surveys......Page 37
  1.3.1 Fundamentals......Page 38
  1.3.2 Linear Models......Page 39
  1.3.3 Other Techniques......Page 40
  1.3.5 Appendices on Software......Page 41
  1.3.7 Appendices on Statistical Analysis and Writing......Page 42
 2.1 Types of Data......Page 44
 2.2 Data Display and Calculation......Page 45
  2.2.2 Rounding......Page 46
  2.3.1 Datasets for This Book......Page 47
 2.4 Analysis with Missing Values......Page 48
 2.6 Tables and Graphs......Page 49
 2.7 R Code Files for Statistical Analysis and Data Display (HH)......Page 50
 2.A Appendix: Missing Values in R......Page 52
 3.1 A Brief Introduction to Probability......Page 59
 3.2 Random Variables and Probability Distributions......Page 60
  3.2.1 Discrete Versus Continuous Probability Distributions......Page 61
  3.2.2 Displaying Probability Distributions—Discrete Distributions......Page 63
  3.2.3 Displaying Probability Distributions—Continuous Distributions......Page 65
  3.3.1 Expectation and Variance of Random Variables......Page 66
  3.3.2 Median of Random Variables......Page 67
  3.3.3 Symmetric and Skewed Distributions......Page 68
   3.3.4.1 Histogram......Page 69
   3.3.4.2 Stem-and-Leaf Display......Page 71
   3.3.4.3 Boxplots......Page 72
  3.3.5 Multivariate Distributions—Covarianceand Correlation......Page 74
 3.4 Three Probability Distributions......Page 77
  3.4.1 The Binomial Distribution......Page 78
  3.4.2 The Normal Distribution......Page 79
  3.4.3 The (Student's) t Distribution......Page 80
 3.5 Sampling Distributions......Page 84
 3.6 Estimation......Page 85
  3.6.1 Statistical Models......Page 87
  3.6.3 Criteria for Point Estimators......Page 88
  3.6.4 Confidence Interval Estimation......Page 90
  3.6.6 Example—One-Sided Confidence Intervals......Page 91
 3.7 Hypothesis Testing......Page 92
 3.8 Examples of Statistical Tests......Page 98
 3.9 Power and Operating Characteristic (O.C.) (Beta) Curves......Page 99
 3.10 Efficiency......Page 101
 3.11 Sampling......Page 104
  3.11.1 Simple Random Sampling......Page 105
  3.11.2 Stratified Random Sampling......Page 106
  3.11.3 Cluster Random Sampling......Page 107
  3.11.5 Standard Errors of Sample Means......Page 108
  3.11.6 Sources of Bias in Samples......Page 109
 3.12 Exercises......Page 110
4 Graphs......Page 115
 4.1 What Is a Graph?......Page 116
 4.2 Example—Ecological Correlation......Page 117
 4.3 Scatterplots......Page 118
 4.4 Scatterplot Matrix......Page 119
 4.5 Array of Scatterplots......Page 122
  4.6.1 Study Objectives......Page 123
  4.6.3 Initial Graphs......Page 124
 4.7 Scatterplot Matrices—Continued......Page 125
 4.8 Data Transformations......Page 130
 4.9 Life Expectancy Example—Continued......Page 134
 4.10 Color Vision......Page 137
 4.11 Exercises......Page 138
  4.A.1 Cartesian Products......Page 141
  4.A.3 Implementation of Trellis Graphics......Page 142
  4.A.5 Cartesian Product of Model Parameters......Page 143
  4.A.6 Examples of Cartesian Products......Page 144
  4.A.7 latticeExtra—Extra Graphical Utilities Basedon Lattice......Page 145
  4.B.2 Combining Panels......Page 146
  4.B.4 Graphs Requiring Multiple Calls to xyplot......Page 147
  4.B.6 Rotated Plots......Page 149
  4.B.10 Alternate Presentations......Page 150
 5.1 Normal (z) Intervals and Tests......Page 152
  5.1.1 Test of a Hypothesis Concerning the Mean of a Population Having Known Standard Deviation......Page 153
  5.1.2 Confidence Intervals for Unknown Population Proportion p......Page 155
  5.1.4 Example—One-Sided Hypothesis Test Concerning a Population Proportion......Page 156
 5.2 t-Intervals and Tests for the Mean of a Population Having Unknown Standard Deviation......Page 158
  5.2.1 Example—Inference on a Population Mean μ......Page 159
 5.3 Confidence Interval on the Variance or Standard Deviation of a Normal Population......Page 160
  5.4.1 Confidence Intervals on the Difference Between Two Population Proportions......Page 162
  5.4.2 Confidence Interval on the Difference Between Two Means......Page 163
  5.4.3 Tests Comparing Two Population Means When the Samples Are Independent......Page 164
  5.4.4 Comparing the Variances of Two Normal Populations......Page 167
 5.5 Paired Data......Page 168
  5.5.1 Example—t-test on Matched Pairs of Means......Page 169
 5.6 Sample Size Determination......Page 171
  5.6.1 Sample Size for Estimation......Page 172
  5.6.2 Sample Size for Hypothesis Testing......Page 173
 5.7 Goodness of Fit......Page 177
  5.7.1 Chi-Square Goodness-of-Fit Test......Page 178
  5.7.2 Example—Test of Goodness-of-Fit to a Discrete Uniform Distribution......Page 179
  5.7.3 Example—Test of Goodness-of-Fit to a Binomial Distribution......Page 180
 5.8 Normal Probability Plots and Quantile Plots......Page 181
  5.8.1 Normal Probability Plots......Page 184
  5.8.2 Example—Comparing t-Distributions......Page 185
  5.9.1 Example—Kolmogorov–Smirnov Goodness-of-Fit Test......Page 187
  5.10.1 Maximum Likelihood Estimation......Page 190
  5.10.2 Likelihood Ratio Tests......Page 191
 5.11 Exercises......Page 192
 6.1 Example—Catalyst Data......Page 195
 6.2 Fixed Effects......Page 197
 6.3 Multiple Comparisons—Tukey Procedure for Comparing All Pairs of Means......Page 200
 6.4 Random Effects......Page 201
 6.5 Expected Mean Squares (EMS)......Page 203
 6.6 Example—Catalyst Data—Continued......Page 204
 6.7 Example—Batch Data......Page 205
  6.8.1 Study Objectives......Page 206
  6.8.2 Data Description......Page 207
  6.8.4 Interpretation......Page 209
  6.8.5 Specification of Analysis......Page 211
 6.9 Contrasts......Page 212
  6.9.1 Mathematics of Contrasts......Page 213
   6.9.2.2 Normalized Scaling......Page 215
 6.10 Tests of Homogeneity of Variance......Page 216
 6.11 Exercises......Page 217
 6.A Appendix: Computation for the Analysis of Variance......Page 221
 6.B Object Oriented Programming......Page 224
7 Multiple Comparisons......Page 226
  7.1.1 Bonferroni Method......Page 227
  7.1.3 The Dunnett Procedure for Comparing One Mean with All Others......Page 228
   7.1.3.1 Computing Note—Specifying the Alternative Hypothesis......Page 230
   7.1.4.1 The Scheffé Procedure......Page 233
   7.1.4.2 Scheffé Intervals with the Turkey Data......Page 234
   7.1.4.3 The Extended Tukey Procedure......Page 238
  7.2.1 Difficulties with Standard Displays......Page 239
   7.2.2.1 Construction of the Mean–Mean Scatterplot......Page 244
   7.2.2.2 Interpretation of the Mean–Mean Scatterplot......Page 247
   7.2.3.1 Scaling......Page 249
   7.2.3.3 Labeling......Page 250
  7.2.4 Display of an Orthogonal Basis Set of Contrasts......Page 251
  7.2.5 Hsu and Peruggia's Pulmonary Example......Page 255
 7.3 Exercises......Page 259
 8.1 Introduction......Page 261
  8.2.2 Data Description......Page 262
  8.2.3 Data Input......Page 263
  8.3.1 Algebra......Page 264
  8.3.3 Calculations......Page 266
  8.3.5 New Observations......Page 273
 8.4 Diagnostics......Page 280
 8.5 ECDF of Centered Fitted Values and Residuals......Page 282
 8.6 Graphics......Page 285
 8.7 Exercises......Page 286
 9.1 Regression with Two Predictors—Least-Squares Geometry......Page 289
 9.2 Multiple Regression—Two-X Analysis......Page 290
 9.3 Multiple Regression—Algebra......Page 292
  9.3.1 The Hat Matrix and Leverage......Page 295
  9.3.2 Geometry of Multiple Regression......Page 296
  9.4.1 Model Specification......Page 297
  9.5.1 Study Objectives......Page 298
  9.5.3 Data Input......Page 299
 9.6 Partial F-Tests......Page 300
 9.7 Polynomial Models......Page 303
 9.8 Models Without a Constant Term......Page 307
 9.9 Prediction......Page 311
  9.10.2 Data Description......Page 313
  9.10.3 Discussion......Page 314
 9.11 Collinearity......Page 316
 9.12 Variable Selection......Page 318
  9.12.1 Manual Use of the Stepwise Philosophy......Page 319
  9.12.2 Automated Stepwise Regression......Page 323
  9.12.3 Automated Stepwise Modeling of the Longley Data......Page 325
  9.13.1 Partial Residuals......Page 327
  9.13.3 Partial Correlation......Page 329
   9.13.5.2 Residuals Against Each of the Predictors......Page 330
   9.13.5.4 Partial Residual Plots......Page 331
 9.14 Example—U.S. Air Pollution Data......Page 332
 9.15 Exercises......Page 336
 9.A Appendix: Computation for Regression Analysis......Page 340
 10.1 Dummy (Indicator) Variables......Page 341
  10.2.1 Study Objectives......Page 342
  10.2.3 Data Problems......Page 343
  10.2.4 Three Variants on the Analysis......Page 346
 10.3 Equivalence of Linear Independent X-Variables (such as Contrasts) for Regression......Page 348
 10.4 Polynomial Contrasts and Orthogonal Polynomials......Page 351
 10.5 Analysis Using a Concomitant Variable (Analysis of Covariance—ANCOVA)......Page 356
  10.6.3 One-Way ANOVA......Page 358
  10.6.4 Concomitant Explanatory Variable—ANCOVA......Page 359
  10.6.5 Tests of Equality of Regression Lines......Page 366
 10.7 ancovaplot Function......Page 367
 10.8 Exercises......Page 368
  11.1.2 Data Description......Page 371
  11.1.3 Rent Levels......Page 372
  11.1.4 Alfalfa Rent Relative to Other Rent......Page 376
  11.2.2 Residual Plots......Page 382
 11.3 Case Statistics......Page 388
  11.3.1 Leverage......Page 389
  11.3.2 Deleted Standard Deviation......Page 390
  11.3.3 Standardized and Studentized Deleted Residuals......Page 391
  11.3.4 Cook's Distance......Page 392
  11.3.5 DFFITS......Page 393
  11.3.6 DFBETAS......Page 395
  11.3.7 Residuals vs Leverage......Page 397
  11.3.8 Calculation of Regression Diagnostics......Page 398
 11.4 Exercises......Page 399
  12.1.1 Study Objectives......Page 402
  12.1.3 Analysis Goals......Page 403
 12.2 Statistical Model......Page 407
 12.3 Main Effects and Interactions......Page 408
 12.4 Two-Way Interaction Plot......Page 410
 12.5 Sums of Squares in the Two-Way ANOVA Table......Page 411
 12.6 Treatment and Blocking Factors......Page 412
 12.8 Randomized Complete Block Designs......Page 413
  12.9.1 Study Objectives......Page 414
  12.9.3 Analysis......Page 415
 12.10 Random Effects Models and Mixed Models......Page 418
 12.11 Example—Display Panel Data—Continued......Page 419
 12.12 Studentized Range Distribution......Page 421
  12.13.2 Data Description......Page 422
  12.13.3 Analysis Goals......Page 423
  12.14.2 Data Description......Page 425
  12.14.5 Initial Plots......Page 426
  12.14.6 Alfalfa Analysis......Page 428
  12.14.7 Clover Analysis......Page 431
 12.15 Models Without Interaction......Page 442
  12.16.2 Analysis......Page 443
 12.17 Exercises......Page 446
 12.A Appendix: Computation for the Analysis of Variance......Page 450
 13.1 A Three-Way ANOVA—Muscle Data......Page 452
 13.2 Latin Square Designs......Page 460
  13.2.1 Example—Latin Square......Page 462
 13.3 Simple Effects for Interaction Analyses......Page 466
  13.3.3 Data Description......Page 467
  13.3.4 Data Analysis......Page 468
  13.4.1 Example—Gunload Data......Page 473
  13.4.2 Example—Turkey Data (Continued)......Page 476
 13.5 Specification of Model Formulas......Page 481
  13.5.1 Crossing of Two Factors......Page 487
 13.6 Sequential and Conditional Tests......Page 489
  13.6.1 SAS Terminology for Conditional Sums of Squares......Page 491
  13.6.2 Example—Application to Clover Data......Page 493
  13.6.3 Example—Application to Body Fat Data......Page 495
 13.7 Exercises......Page 497
 13.A Appendix: Orientation for Boxplots......Page 503
 14.1 Confounding......Page 504
 14.2 Split Plot Designs......Page 506
 14.3 Example—Yates Oat Data......Page 507
  14.3.1 Alternate Specification......Page 512
  14.3.2 Polynomial Effects for Nitrogen......Page 514
 14.4 Introduction to Fractional Factorial Designs......Page 517
  14.4.1 Example—28-2 Design......Page 518
  14.4.2 Example—25-1 Design......Page 520
 14.5 Introduction to Crossover Designs......Page 522
  14.5.1 Example—Two Latin Squares......Page 523
 14.6 ANCOVA with Blocks: Example—Apple Tree Data......Page 526
  14.6.3 Data Analysis......Page 527
  14.6.4 Model 1:  yield '176 block + pre * treat......Page 529
  14.6.5 Model 2:  yield.block '176 pre.block * treat......Page 531
  14.6.6 Model 3:  yield.block '176 pre.block......Page 533
  14.6.8 Model 5:  yield.block '176 pre.block + treat......Page 534
  14.6.9 Model 6:  yield.block.pre '176 treat......Page 536
  14.6.10 Multiple Comparisons......Page 538
  14.7.2 Data Description......Page 541
  14.7.4 Analysis—ANOVA......Page 542
  14.7.5 Summary of ANOVA......Page 545
  14.8.1 Example—Crash Data—Study Objectives......Page 549
  14.8.3 Data Analysis......Page 550
  14.8.4 Theory......Page 559
 14.9 Exercises......Page 560
  15.1.1 Example—Drunkenness Data......Page 564
  15.1.2 Chi-Square Analysis......Page 567
  15.2.1 Example—Do Juvenile Delinquents Eschew Wearing Eyeglasses?......Page 570
 15.3 Simpson's Paradox......Page 573
  15.4.1 Glasses (Again)......Page 577
   15.4.2.1 Odds Ratio......Page 578
   15.4.2.2 Relative Risk......Page 579
  15.4.3 Example—Treating Cardiac Arrest with Therapeutic Hypothermia......Page 580
 15.5 Retrospective and Prospective Studies......Page 583
 15.6 Mantel–Haenszel Test......Page 584
 15.7 Example—Salk Polio Vaccine......Page 588
 15.8 Example—Adverse Experiences......Page 590
 15.9 Ordered Categorical Scales, Including Rating Scales......Page 592
  15.9.1 Display of Professional Challenges Dataset......Page 593
  15.9.2 Single-Panel Displays......Page 595
   15.9.3.1 One Question with Multiple Subsets of the Sample......Page 597
 15.10 Exercises......Page 598
 16.1 Introduction......Page 602
 16.2 Sign Test for the Location of a Single Population......Page 603
  16.3.1 Sign Test......Page 606
  16.3.2 Wilcoxon Signed-Ranks Test......Page 607
 16.4 Mann–Whitney Test for Two Independent Samples......Page 611
 16.5 Kruskal–Wallis Test for Comparing the Locations of at Least Three Populations......Page 615
 16.6 Exercises......Page 616
17 Logistic Regression......Page 618
  17.1.2 Data Description......Page 620
  17.1.3 Graphical Display......Page 621
  17.1.4 Numerical Display......Page 624
 17.2 Estimation......Page 628
 17.3 Example—Budworm Data......Page 630
 17.4 Example—Lymph Nodes......Page 634
  17.4.2 Data Analysis......Page 635
  17.4.3 Additional Techniques......Page 637
 17.5 Numerical Printout......Page 644
  17.6.1 Conditioned Scatterplots......Page 645
  17.6.2 Common Scaling in Comparable Plots......Page 646
  17.7.1 Fitting Models When the Response Is Dichotomous......Page 647
  17.7.2 Fitting Models When the Response Is a SampleProportion......Page 648
 17.8 LogXact......Page 649
 17.9 Exercises......Page 650
 18.1 Introduction......Page 655
 18.2 The ARIMA Approach to Time Series Modeling......Page 656
  18.2.1 AutoRegression (AR)......Page 657
  18.2.2 Moving Average (MA)......Page 658
  18.2.4 Autoregressive Integrated Moving Average (ARIMA)......Page 659
  18.3.1 Autocorrelation Function (ACF)......Page 660
 18.4 Analysis Steps......Page 661
  18.5.1 The General ARIMA Model......Page 664
  18.5.2 Special Case—The AR(1) Model......Page 665
 18.6 Graphical Displays for Time Series Analysis......Page 666
  18.7.1 Multiplicative Seasonal ARIMA Models......Page 672
  18.7.3 Determining the Seasonal AR and MA Parameters......Page 673
  18.8.1 Identification of the Model......Page 674
  18.8.2 Parameter Estimation and Diagnostic Checking......Page 676
 18.9 Exercises......Page 685
 18.A Appendix: Construction of Time Series Graphs......Page 716
  18.A.1 Characteristics of This Presentationof the Time Series Plot......Page 718
  18.A.3 Construction of Graphical Displays......Page 719
  18.A.4 Functions in the HH package for R......Page 720
 A.1 Installing R—Initial Installation......Page 722
   A.1.2.1 RExcel......Page 723
   A.1.2.3 Packages Needed for This Book—Windows......Page 724
   A.1.2.5 Windows Potential Complications: Internet, Firewall, and Proxy......Page 725
  A.1.4 `_12`1̃2`$12=-1 XLConnect: All Operating Systems......Page 726
  A.3.1 Starting the R Console......Page 727
  A.3.4 Learning the R Language......Page 728
  A.3.6 Learning the Functions in R......Page 729
  A.3.8 Graphs in an Interactive Session......Page 730
 A.4 S/R Language Style......Page 731
 A.5 Getting Help While Learning and Using R......Page 734
 A.6 R Inexplicable Error Messages—Some Debugging Hints......Page 735
 B.1 Contents of the HH Package......Page 737
  B.2.2 Linux......Page 738
 B.4 HH and S+......Page 739
C Rcmdr: R Commander......Page 740
D RExcel: Embedding R inside Excel on Windows......Page 753
  D.1.2 Install Two R Packages Needed by RExcel......Page 754
  D.1.5 Additional Information on Installing RExcel......Page 755
  D.2.1 Automatic Recalculation of an R Function......Page 756
  D.2.2 Transferring Data To/From R and Excel......Page 757
  D.2.3 Control of a lattice Plot from an Excel/Rcmdr Menu......Page 760
E Shiny: Web-Based Access to R Functions......Page 763
 E.1 NTplot......Page 764
 E.2 bivariateNormal......Page 765
 E.3 bivariateNormalScatterplot......Page 766
 E.4 PopulationPyramid......Page 767
 F.2 Installing and Loading R Packages......Page 768
 F.3 Where Are the Packages on Your Computer?......Page 769
 F.5 Writing and Building Your Own Package......Page 770
 F.6 Building Your Own Package with Windows......Page 771
 G.1 Examples......Page 772
 G.2 Floating Point Numbers in the IEEE 754 Floating-PointStandard......Page 774
 G.3 Multiple Precision Floating Point......Page 775
 G.4 Binary Format......Page 776
 G.6 Base-10, 2-Digit Arithmetic......Page 777
 G.9 zapsmall to Round Small Values to Zero for Display......Page 779
 G.10 Apparent Violation of Elementary Factoring......Page 781
 G.12 Variance Calculations at the Precision Boundary......Page 782
 G.13 Can the Answer to the Calculation be Represented?......Page 788
 G.14 Explicit Loops......Page 789
H Other Statistical Software......Page 791
 I.1 Algebra Review......Page 793
  I.1.2 Parabola......Page 794
  I.1.4 Simultaneous Equations......Page 795
  I.1.5 Exponential and Logarithm Functions......Page 796
  I.1.6 Asymptote......Page 797
 I.2 Elementary Differential Calculus......Page 798
 I.3 An Application of Differential Calculus......Page 799
 I.4 Topics in Matrix Algebra......Page 800
  I.4.1 Elementary Operations......Page 802
  I.4.2 Linear Independence......Page 804
  I.4.4 Quadratic Forms......Page 805
  I.4.6 Orthogonal Basis......Page 806
  I.4.8 Modified Gram–Schmidt (MGS) Algorithm......Page 807
  I.4.10 Orthogonal Polynomials......Page 811
  I.4.11 Projection Matrices......Page 812
  I.4.12 Geometry of Matrices......Page 813
  I.4.13 Eigenvalues and Eigenvectors......Page 814
  I.4.14 Singular Value Decomposition......Page 815
  I.4.15 Generalized Inverse......Page 819
   I.4.16.2 n > m = rank(X)......Page 821
  I.5.2 Permutations......Page 822
 I.6 Exercises......Page 823
J Probability Distributions......Page 824
  J.1.1 Beta......Page 825
  J.1.3 Chi-Square......Page 826
  J.1.4 Exponential......Page 827
  J.1.6 Gamma......Page 828
  J.1.7 Log Normal......Page 829
  J.1.8 Logistic......Page 830
  J.1.9 Normal......Page 831
  J.1.10 Studentized Range Distribution......Page 832
  J.1.12 Uniform......Page 833
 J.2 Noncentral Continuous Probability Distributions......Page 834
  J.2.2 T: Noncentral......Page 836
 J.3 Discrete Distributions......Page 837
  J.3.2 Binomial......Page 839
  J.3.3 Geometric......Page 840
  J.3.4 Hypergeometric......Page 841
  J.3.6 Poisson......Page 842
  J.3.7 Signed Rank......Page 843
  J.3.8 Wilcoxon......Page 844
  J.4.1 Multinomial......Page 845
  J.4.2 Multivariate Normal......Page 846
 K.1 Text Editor......Page 847
  K.1.1 Requirements for an Editor......Page 848
 K.2 Types of interaction with R......Page 849
 K.4 Directory Structure......Page 850
  K.4.2 Directory Structure for Users of This Book......Page 851
  K.4.3 Other User Directories......Page 852
 L.1 Typographic Style......Page 853
  L.2.2 Aspect Ratio......Page 857
  L.2.3 Other Features......Page 859
 L.3 English Writing Style......Page 860
 L.4 Programming Style and Common Errors......Page 861
 L.5 Presentation of Results......Page 863
M Accessing R Through a Powerful Editor—With Emacs and ESS as the Example......Page 866
  M.1.2 File Comparison......Page 867
  M.1.3 Buffers......Page 868
 M.2 ESS......Page 869
  M.2.2 Partial Code Evaluation......Page 871
  M.2.4 Process Interaction......Page 872
 M.3 Learning Emacs......Page 873
  M.3.2 Keyboard Interface......Page 874
 M.5 Requirements......Page 875
 N.1 Organization Using LaTeX......Page 877
 N.4 Global Changes: Specification of Fonts......Page 878
 O.1 Microsoft Word......Page 880
  O.1.2 SWord......Page 881
  O.2.3 Excel as a Statistical Calculator......Page 882
References......Page 885
Index of Datasets......Page 898
Index......Page 900