Design and Analysis of Experiments 10th
Edition – Test Bank
by Douglas C. Montgomery (Author)
,TABLE OF CONTENTS
1 Introduction 1
1.1 Strategy of Experimentation 1
1.2 Some Typical Applications of Experimental Design 7
1.3 Basic Principles 11
1.4 Guidelines for Designing Experiments 13
1.5 A Brief History of Statistical Design 19
1.6 Summary: Using Statistical Techniques in Experimentation 20
2 Simple Comparative Experiments 22
2.1 Introduction 22
2.2 Basic Statistical Concepts 23
2.3 Sampling and Sampling Distributions 27
2.4 Inferences About the Differences in Means, Randomized Designs 32
2.4.1 Hypothesis Testing 32
2.4.2 Confidence Intervals 38
2.4.3 Choice of Sample Size 39
2.4.4 The Case Where 𝜎21 ≠ 𝜎22 43
2.4.5 The Case Where 𝜎21 and 𝜎22 Are Known 45
2.4.6 Comparing a Single Mean to a Specified Value 46
2.4.7 Summary 47
2.5 Inferences About the Differences in Means, Paired Comparison Designs 47
2.5.1 The Paired Comparison Problem 47
,2.5.2 Advantages of the Paired Comparison Design 50
2.6 Inferences About the Variances of Normal Distributions 52
3 Experiments with a Single Factor: The Analysis of Variance 55
3.1 An Example 55
3.2 The Analysis of Variance 58
3.3 Analysis of the Fixed Effects Model 59
3.3.1 Decomposition of the Total Sum of Squares 60
3.3.2 Statistical Analysis 62
3.3.3 Estimation of the Model Parameters 66
3.3.4 Unbalanced Data 68
3.4 Model Adequacy Checking 68
3.4.1 The Normality Assumption 69
3.4.2 Plot of Residuals in Time Sequence 71
3.4.3 Plot of Residuals Versus Fitted Values 71
3.4.4 Plots of Residuals Versus Other Variables 76
3.5 Practical Interpretation of Results 76
3.5.1 A Regression Model 77
3.5.2 Comparisons Among Treatment Means 78
3.5.3 Graphical Comparisons of Means 78
3.5.4 Contrasts 79
3.5.5 Orthogonal Contrasts 82
3.5.6 Scheffé’s Method for Comparing All Contrasts 83
3.5.7 Comparing Pairs of Treatment Means 85
, 3.5.8 Comparing Treatment Means with a Control 88
3.6 Sample Computer Output 89
3.7 Determining Sample Size 93
3.7.1 Operating Characteristic and Power Curves 93
3.7.2 Confidence Interval Estimation Method 94
3.8 Other Examples of Single-Factor Experiments 95
3.8.1 Chocolate and Cardiovascular Health 95
3.8.2 A Real Economy Application of a Designed Experiment 97
3.8.3 Discovering Dispersion Effects 99
3.9 The Random Effects Model 101
3.9.1 A Single Random Factor 101
3.9.2 Analysis of Variance for the Random Model 102
3.9.3 Estimating the Model Parameters 103
3.10 The Regression Approach to the Analysis of Variance 109
3.10.1 Least Squares Estimation of the Model Parameters 110
3.10.2 The General Regression Significance Test 111
3.11 Nonparametric Methods in the Analysis of Variance 113
3.11.1 The Kruskal–Wallis Test 113
3.11.2 General Comments on the Rank Transformation 114
4 Randomized Blocks, Latin Squares, and Related Designs 115
4.1 The Randomized Complete Block Design 115
4.1.1 Statistical Analysis of the RCBD 117
4.1.2 Model Adequacy Checking 125
Edition – Test Bank
by Douglas C. Montgomery (Author)
,TABLE OF CONTENTS
1 Introduction 1
1.1 Strategy of Experimentation 1
1.2 Some Typical Applications of Experimental Design 7
1.3 Basic Principles 11
1.4 Guidelines for Designing Experiments 13
1.5 A Brief History of Statistical Design 19
1.6 Summary: Using Statistical Techniques in Experimentation 20
2 Simple Comparative Experiments 22
2.1 Introduction 22
2.2 Basic Statistical Concepts 23
2.3 Sampling and Sampling Distributions 27
2.4 Inferences About the Differences in Means, Randomized Designs 32
2.4.1 Hypothesis Testing 32
2.4.2 Confidence Intervals 38
2.4.3 Choice of Sample Size 39
2.4.4 The Case Where 𝜎21 ≠ 𝜎22 43
2.4.5 The Case Where 𝜎21 and 𝜎22 Are Known 45
2.4.6 Comparing a Single Mean to a Specified Value 46
2.4.7 Summary 47
2.5 Inferences About the Differences in Means, Paired Comparison Designs 47
2.5.1 The Paired Comparison Problem 47
,2.5.2 Advantages of the Paired Comparison Design 50
2.6 Inferences About the Variances of Normal Distributions 52
3 Experiments with a Single Factor: The Analysis of Variance 55
3.1 An Example 55
3.2 The Analysis of Variance 58
3.3 Analysis of the Fixed Effects Model 59
3.3.1 Decomposition of the Total Sum of Squares 60
3.3.2 Statistical Analysis 62
3.3.3 Estimation of the Model Parameters 66
3.3.4 Unbalanced Data 68
3.4 Model Adequacy Checking 68
3.4.1 The Normality Assumption 69
3.4.2 Plot of Residuals in Time Sequence 71
3.4.3 Plot of Residuals Versus Fitted Values 71
3.4.4 Plots of Residuals Versus Other Variables 76
3.5 Practical Interpretation of Results 76
3.5.1 A Regression Model 77
3.5.2 Comparisons Among Treatment Means 78
3.5.3 Graphical Comparisons of Means 78
3.5.4 Contrasts 79
3.5.5 Orthogonal Contrasts 82
3.5.6 Scheffé’s Method for Comparing All Contrasts 83
3.5.7 Comparing Pairs of Treatment Means 85
, 3.5.8 Comparing Treatment Means with a Control 88
3.6 Sample Computer Output 89
3.7 Determining Sample Size 93
3.7.1 Operating Characteristic and Power Curves 93
3.7.2 Confidence Interval Estimation Method 94
3.8 Other Examples of Single-Factor Experiments 95
3.8.1 Chocolate and Cardiovascular Health 95
3.8.2 A Real Economy Application of a Designed Experiment 97
3.8.3 Discovering Dispersion Effects 99
3.9 The Random Effects Model 101
3.9.1 A Single Random Factor 101
3.9.2 Analysis of Variance for the Random Model 102
3.9.3 Estimating the Model Parameters 103
3.10 The Regression Approach to the Analysis of Variance 109
3.10.1 Least Squares Estimation of the Model Parameters 110
3.10.2 The General Regression Significance Test 111
3.11 Nonparametric Methods in the Analysis of Variance 113
3.11.1 The Kruskal–Wallis Test 113
3.11.2 General Comments on the Rank Transformation 114
4 Randomized Blocks, Latin Squares, and Related Designs 115
4.1 The Randomized Complete Block Design 115
4.1.1 Statistical Analysis of the RCBD 117
4.1.2 Model Adequacy Checking 125
