Preface xiii 1 Introduction 1 Statistics, 1 Application of Statistics, 1 Scientific Method, 2 Statistical Null Hypothesis, 4 Type I Error (α), 5 Type II Error (β), 5 Power of the Test, 6 P-Value Misuse, 8 Effect Size, 9 Diagnostic Tests, 10 Bias, 12 Summary, 13 SAS Code, 14 R Code, 19 JMP Method, 21 References, 25 Additional Reading, 25 2 Data Management 27 Data Management Plan, 27 Organize Files, 28 Data Workbooks, 29 Backup, 33 Securing Data, 33 Data Analysis, 33 Data Preservation, 34 Data Sharing, 35 Summary, 35 Additional Reading, 35 3 Distributions 37 Measures of Central Tendency, 37 Dispersion, 38 Accuracy and Precision, 41 Normal Distribution, 42 Normal Probability Plot, 43 Measures of Departures from Normality, 44 Tests of Normality, 45 Comparing Distributions, 48 Comparing Two Mean Estimates, 50 Student''s t-Test, 50 Wald Z-Test, 54 Bootstrap, 54 Summary, 57 SAS Code, 58 R Code, 63 JMP Method, 68 References, 80 Additional Reading, 81 4 Goodness-of-fit 83 χ 2 Distribution, 83 Enumeration Data, 83 Two Cell Tests, 85 Sample Size to Differentiate Alternative Ratios, 87 Contingency Tests, Goodness-of-Fit, 88 Contingency Tests, No Expected Distribution, 89 Meta-Analysis, 92 Summary, 94 SAS Code, 95 R Code, 100 JMP Method, 106 References, 121 Additional Reading, 121 5 Variance Analyses--gaussian 123 Factors, 123 Experimental Unit, 124 Effect Types, 124 One-Factor Analysis, 125 Experimental Error, 126 F-Distribution, 127 Replication, 128 Randomized Complete Block, 129 Arrangement, 130 Variance Analysis, 132 Block: Fixed or Random Effect?, 133 Mixed Model Analysis, 134 REML Estimation, 135 Significance of Effects, 136 Generalized Linear Mixed Model, 137 Conditional and Marginal Models, 138 Covariance Structure, 139 Negative Variance Estimates, 140 Means Comparisons, 142 Contrasts, 143 Estimate of a Difference, 144 BLUE and BLUP Estimates, 145 Multiplicity Adjustment, 146 Letter Codes, 147 Test CV, 148 Power Analyses, 148 Summary, 149 SAS Code, 149 R Code, 164 JMP Method, 173 References, 187 Additional Reading, 187 6 Correlation and Regression 189 Rank Correlations, 191 Linear Regression, 192 Model I, 194 Model II, 194 Prediction of Y from X, 196 Broad and Narrow Inference, 197 Regression Through the Origin, 198 Inverse Prediction, 198 Transformations for Linear Regression, 199 Nonlinear Regression, 203 Dosage Response, 206 Segmented or Spline Regression, 208 Logistic Regression, 209 Creating Plots for Publication, 213 Summary, 214 SAS Code, 214 R Code, 226 JMP Method, 236 References, 277 Additional Reading, 277 7 Regression in Anova 279 Unequally Spaced or Unequally Balanced Treatments, 281 Dummy Variables, 284 Optimum Treatment Level, 286 Comparison of Regression Response, 287 Comparison of Responses, 289 Non-Gaussian Data, 290 Summary, 291 SAS Code, 292 R Code, 300 JMP Method, 307 References, 324 Additional Reading, 324 8 Checking Model Fit 325 Violation of Assumptions, 326 Fit the Model to the Data, 326 Checking Assumptions, 326 Residual Types, 327 Residual Adjustment, 327 Plots of Residuals, 328 Model Modifications, 335 Fit Statistics, 337 Chi-Square/DF, 339 Link Function, 340 Outliers and Influential Observations, 340 Influence Statistics for Generalized Models, 342 Pea Study, Epilogue, 344 Summary, 345 SAS Code, 346 R Code, 355 JMP Method, 359 References, 374 Additional Reading, 375 9 Non-gaussian Data 377 Denominator df, 378 Quantitative Data, 378 Count Data, 379 Zero-Inflated Models, 382 Proportion Data, Continuous, 383 Values of 0 and 1, 383 Proportion Data, Discrete, 384 Multinomial Data, 386 Ordinal Multinomial Analysis, 387 Nominal Multinomial Analysis, 390 Compositional Data, 392 Summary, 393 SAS Code, 394 R Code, 404 JMP Method, 410 References, 424 Additional Reading, 425 10 Error Control 427 Experimental Error, 428 Variation Within Experimental Units, 428 Heterogeneity Among Experimental Units, 431 Analysis of Covariance, 431 Heterogeneity Within a Study, 436 Minimizing Heterogeneity, 437 Post-hoc Detection of Heterogeneity, 438 Spatial Error-Covariance Adjustment, 442 Beyond the RCBD, 451 Latin Square, 451 Lattice Designs, 452 Balanced Lattice, 452 Partially Balanced Lattice, 453 Simple Lattice Repeated, 454 Rectangular Lattice, 454 α-Designs, 455 Augmented Designs, 456 Partially Replicated Designs, 456 Experimental Design Software, 459 Summary, 459 SAS Code, 460 R Code, 474 JMP Method, 482 References, 503 Additional Reading, 504 11 Factorial Experiments 507 Expected Mean Squares, 509 Estimation of Variance Components, 512 Subsampling, 513 Two-Factor Factorials, 515 Three-Factor Factorials, 515 Split-Plot, 516 Do Not Under- or Over-Specify, 518 Model Specification, 518 Bias Correction, 521 Split-Block, 523 Repeated Measures, 524 Correlated Errors Are Not Restricted to Time, 527 Selection of Covariance Structure, 527 Repeated Measures, Non-Gaussian, 529 No Convergence, 532 Adjusting for Baseline, 533 Combined Experiments, 535 Coefficients for Contrasts and Estimates, 539 Investigating Interactions, 542 Fixed, Random, or a Bit of Both?, 544 Summary, 545 SAS Code, 545 R Code, 571 JMP Method, 579 References, 609 Additional Reading, 610 12 Response Surface 613 First-Order Designs, 614 Second-Order Designs, 615 Central Composite Design, 615 Central Rotatable Composite Design, 616 Mixture and Double Mixture Designs, 618 Plotting Response Surfaces, 623 Hoerl and Spline Models, 624 Avoid Extrapolation, 624 Summary, 627 SAS Code, 627 R Code, 643 JMP Method, 649 References, 661 Additional Reading, 661 13 Multiple Regression 663 Linear Model, 663 Assumptions, 664 Variable Selection--Fixed Effect Models, 664 Variable Selection--Mixed Models, 666 Multimodel Inference, 668 Collinear Variables, 670 Variance Inflation Factor, 670 Collinearity Diagnostics, 671 Adjusting Collinear Variables, 672 Polynomial Models, 672 Prediction Models Involving Collinear Variables, 673 Cross-Validation, 673 Model Validation, 674 Latent Factor Regression, 675 Summary, 680 SAS Code, 681 R Code, 692 JMP Method, 697 References, 714 Additional Reading, 714 14 Multivariate Analyses 717 Analyses of Dependence, 717 Genotypic Correlations, 719 Path Analysis, 720 Analyses of Interdependence, 722 Assumptions, 723 Example Multivariate Dataset (Grin), 723 Dimension Reduction, 726 Value of Variables, 728 Number of Components/Factors, 729 Clustering, 733 Distance Measures, 735 Cluster Methods, 737 Number of Clusters, 739 Groupings Unknown, 740 Partialling Out, 741 Cluster Validation, 743 Groupings Known, 745 Canonical Correlation Analysis, 746 Canonical Discriminant Analysis, 746 Comparing Distance Matrices, 750 Summary, 752 SAS Code, 753 R Code, 768 JMP Method, 774 References, 798 Additional Reading, 799 15 G×e Analysis 801 Fixed or Random Environments?, 802 I. Univariate Models, 803 Mean-CV, 803 Regression Coefficient, 805 Regression Deviation, 806 Random Environment Effect, 807 Yield Stability Index, 810 Superiority Measure, 811 II. Multivariate Models, 812 Biplots, 816 Confidence Intervals, 820 AMMI or GGE?, 821 G×E Analyses-Summary, 822 SAS Code, 822 R Code, 837 JMP Method, 847 References, 863 Additional Reading, 864.