Design and Analysis of Experiments (Paperback)

Preface v 1 Introduction to Designed Experiments 1 1.1 Strategy of Experimentation 1 1.2 Some Typical Applications of Experimental Design 8 1.3 Basic Principles 11 1.4 Guidelines for Designing Experiments 14 1.5 A Brief History of Statistical Design 21 1.6 Summary: Using Statistical Techniques in Experimentation 22 1.7 Problems 23 2 Basic Statistical Methods 25 2.1 Introduction 25 2.2 Basic Statistical Concepts 27 2.3 Sampling and Sampling Distributions 30 2.4 Inferences About the Differences in Means, Randomized Designs 36 2.4.1 Hypothesis Testing 36 2.4.2 Confidence Intervals 43 2.4.3 Choice of Sample Size 44 2.4.4 The Case Where 48 2.4.5 The Case Where and Are Known 50 2.4.6 Comparing a Single Mean to a Specified Value 50 2.4.7 Summary 51 2.5 Inferences About the Differences in Means, Paired Comparison Designs 53 2.5.1 The Paired Comparison Problem 53 2.5.2 Advantages of the Paired Comparison Design 56 2.6 Inferences About the Variances of Normal Distributions 57 2.7 Problems 59 3 Analysis of Variance 65 3.1 An Example 66 3.2 The Analysis of Variance 68 3.3 Analysis of the Fixed Effects Model 70 3.3.1 Decomposition of the Total Sum of Squares 71 3.3.2 Statistical Analysis 73 3.3.3 Estimation of the Model Parameters 78 3.3.4 Unbalanced Data 79 3.4 Model Adequacy Checking 80 3.4.1 The Normality Assumption 80 3.4.2 Plot of Residuals in Time Sequence 82 3.4.3 Plot of Residuals Versus Fitted Values 83 3.4.4 Plots of Residuals Versus Other Variables 88 3.5 Practical Interpretation of Results 89 3.5.1 A Regression Model 89 3.5.2 Comparisons Among Treatment Means 90 3.5.3 Graphical Comparisons of Means 91 3.5.4 Contrasts 92 3.5.5 Orthogonal Contrasts 94 3.5.6 Scheffe's Method for Comparing All Contrasts 96 3.5.7 Comparing Pairs of Treatment Means 97 3.5.8 Comparing Treatment Means with a Control 101 3.6 Sample Computer Output 102 3.7 Determining Sample Size 105 3.7.1 Operating Characteristic Curves 105 3.7.2 Specifying a Standard Deviation Increase 108 3.7.3 Confidence Interval Estimation Method 109 3.8 Other Examples of Single-Factor Experiments 110 3.8.1 Chocolate and Cardiovascular Health 110 3.8.2 A Real Economy Application of a Designed Experiment 110 3.8.3 Discovering Dispersion Effects 114 3.9 The Random Effects Model 116 3.9.1 A Single Random Factor 116 3.9.2 Analysis of Variance for the Random Model 117 3.9.3 Estimating the Model Parameters 118 3.10 The Regression Approach to the Analysis of Variance 125 3.10.1 Least Squares Estimation of the Model Parameters 125 3.10.2 The General Regression Significance Test 126 3.11 Nonparametric Methods in the Analysis of Variance 128 3.11.1 The Kruskal-Wallis Test 128 3.11.2 General Comments on the Rank Transformation 130 3.12 Problems 130 4 Experiments with Blocking Factors 139 4.1 The Randomized Complete Block Design 139 4.1.1 Statistical Analysis of the RCBD 141 4.1.2 Model Adequacy Checking 149 4.1.3 Some Other Aspects of the Randomized Complete Block Design 150 4.1.4 Estimating Model Parameters and the General Regression Significance Test 155 4.2 The Latin Square Design 158 4.3 The Graeco-Latin Square Design 165 4.4 Balanced Incomplete Block Designs 168 4.4.1 Statistical Analysis of the BIBD 168 4.4.2 Least Squares Estimation of the Parameters 172 4.4.3 Recovery of Interblock Information in the BIBD 174 4.5 Problems 177 5 Factorial Experiments 183 5.1 Basic Definitions and Principles 183 5.2 The Advantage of Factorials 186 5.3 The Two-Factor Factorial Design 187 5.3.1 An Example 187 5.3.2 Statistical Analysis of the Fixed Effects Model 189 5.3.3 Model Adequacy Checking 198 5.3.4 Estimating the Model Parameters 198 5.3.5 Choice of Sample Size 201 5.3.6 The Assumption of No Interaction in a Two-Factor Model 202 5