Practical Data Analysis for Designed Experiments

Preface Part A: Placing Data in Context Practical Data Analysis Effect of Factors Nature of Data Summary Tables Plots for Statistics Computing Interpretation Problems Collaboration in Science Asking Questions Learning from Plots Mechanics of a Consulting Session Philosophy and Ethics Intelligence, Culture and Learning Writing Problems Experimental Design Types of Studies Designed Experiments Design Structure Treatment Structure Designs in This Book Problems Part B: Working with Groups of Data Group Summaries Graphical Summaries Estimates of Means and Variance Assumptions and Pivot Statistics Interval Estimates of Means Testing Hypotheses about Means Formal Inference on the Variance Problems Comparing Several Means Linear Contrasts of Means Overall Test of Difference Partitioning Sums of Squares Expected Mean Squares Power and Sample Size Problems Multiple Comparisons of Means Experiment- and Comparison-Wise Error Rates Comparisons Based on F-Tests Comparisons Based on Range of Means Comparisons of Comparisons Problems Part C: Sorting Out Effects with Data Factorial Designs Cell Means Models Effects Models Estimable Functions Linear Constraints General Form of Estimable Functions Problems Balanced Experiments Additive Models Full Models with Two Factors Interaction Plots Higher Orders Models Problems Model Selection Pooling Interactions Selected the Best Model Model Selection Criteria One Observation per Cell Tukey's Test for Interaction Problems Part D: Dealing with Imbalance Unbalanced Experiments Unequal Samples Additive Model Types I, II, III and IV Problems Missing Cells What Are Missing Cells? Connected Cells and Incomplete Designs Type IV Comparisons Latin Square Designs Fractional Factorial Designs Problems Linear Models Inference Matrix Preliminaries Ordinary Least Squares Weighted Least Squares Maximum Likelihood Restricted Maximum Likelihood Inference for Fixed Effect Models Anova and Regression Models Problems Part E: Questioning Assumptions Residual Plots Departures from Assumptions Incorrect Model Correlated Responses Unequal Variance Non-Normal Data Problems Comparisons with Unequal Variance Comparing Means When Variances Are Unequal Weighted Analysis of Variances Satterthwaite Approximation Generalized Inference Testing for Unequal Variances Problems Getting Free from Assumptions Transforming Data Comparisons Using Ranks Randomization Monte Carlo Methods Problems Part F: Regressing with Factors Ordered Groups Groups in a Line Testing for Linearity Path Analysis Diagrams Regression Calibration Classical Error in Variables Problems Parallel Lines Parallel Lines Model Adjusted Estimates Plots with Symbols Sequential Tests with Multiple Responses Sequential Tests with Driving Covariate Adjusted (Type III) Tests of Hypotheses Different Slopes for Different Groups Problems Multiple Responses Overall Tests for Group Differences Matrix Analog to F Test How Do Groups Differ? Causal Models Part G: Deciding on Fixed or Random Effects Models with Random Effects Single Factor Random Model Test for Class Variation Distribution of Sums of Squares Variance Components Grand Menu Problems General Random Models Two Factor Random Models Unbalanced Two-Factor Random Model General Random Model Quadratic Forms in Random Effects Application to Two Factor Random Model Problems Mixed Effect Models Two Factor Mixed Models General Mixed Models Problems Part H: Nesting Experimental Units Nested Designs Sub-Sampling Blocking Nested and Crossed Factors Nesting of Fixed Effects Nesting of Random Effects Problems Split Plot Design Several Views of Split Plot Split Plot Model Contrasts in a Split Plot Problems General Nested Designs Extensions of Split Plot Split Plot Imbalance in Nested Designs Covariates in Nested Designs Explained Variation in Nested Designs Problems Part I: Repeating Measures on Subjects Repeated Measures as Split Plot Repeated Measures Designs Repeated Measures Model Split Plot More or Less Expected Mean Squares under Sphericity Contrasts under Sphericity Problems Adjustments for Correlation Adjustments to Split Plot Contrasts over Time Multivariate Repeated Measures Problems Cross-Over Design Cross-Over Model Confounding in Cross-Over Designs Partition of Sum of Squares Replicated Latin Square Design General Cross-Over Designs Problems References Index