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```Table of Contents
Preface		xiii
Acknowledgments		xix
Chapter 1 Graphical Presentation of Data		1
1.1 Introduction		1
1.2 Types of Data		1
1.3 Bar Charts		2
1.4 Histograms		3
1.5 Dotplots		4
1.6 Stem-and-Leaf Plots		4
1.7 Box-and-Whisker Plots		5
1.8 Scatter Plots		6
1.9 Multi-Vari Charts		7
1.10 An Introduction to MINITAB		9
1.10.1 Starting MINITAB		9
1.10.2 MINITAB Windows		9
1.10.3 Using the Command Prompt		11
1.10.4 Customizing MINITAB		11
1.10.5 Entering Data		12
1.10.6 Graphing Data		13
1.10.7 Printing Data and Graphs		13
1.10.8 Saving and Retrieving Information		14
1.10.9 MINITAB Macros		15
1.10.10 Summary of MINITAB Files		17
Chapter 2 Descriptive Statistics		19
2.1 Introduction		19
2.2 Selection of Samples		19
2.3 Measures of Location		20
2.3.1 The Median		20
2.3.2 The Mean		21
2.4 Measures of Variation		21
2.4.1 The Range		21
2.4.2 The Standard Deviation		22
2.4.3 Degrees of Freedom		24
2.4.4 The Calculating Form for the Standard Deviation		25
2.5 The Normal Distribution		26
2.6 Counting		30
2.6.1 Multiplication of Choices		30
2.6.2 Factorials		31
2.6.3 Permutations		31
2.6.4 Combinations		32
2.7 MINITAB Commands to Calculate Descriptive Statistics		34
Chapter 3 Inferential Statistics		37
3.1 Introduction		37
3.2 The Distribution of Sample Means (_ Known)		38
3.3 Confidence Interval for the Population Mean		41
3.4 Hypothesis Test for One Sample Mean (_ Known)		42
3.4.1 Hypothesis Test Rationale		42
3.4.2 Decision Limits Based on Measurement Units		44
3.4.3 Decision Limits Based on Standard (z) Units		45
3.4.4 Decision Limits Based on the p Value		46
3.4.5 Type 1 and Type 2 Errors		49
3.4.6 One-Tailed Hypothesis Tests		51
3.5 The Distribution of Sample Means (_ Unknown)		52
3.5.1 Student's t Distribution		52
3.5.2 A One-Sample Hypothesis Test for the Population Mean (_ Unknown)		54
3.5.3 A Confidence Interval for the Population Mean (_ Unknown) 		55
3.6 Hypothesis Tests for Two Means		56
3.6.1 Two Independent Samples (_21 and _22 Known)		56
3.6.2 Two Independent Samples (_21 and _22 Unknown But Equal)		56
3.6.3 Two Independent Samples (_21 and _22 Unknown and Unequal)		58
3.6.4 Paired Samples		59
3.7 Inferences About One Variance (Optional)		61
3.7.1 The Distribution of Sample Variances		61
3.7.2 Hypothesis Test for One Sample Variance		63
3.7.3 Confidence Interval for the Population Variance		64
3.8 Hypothesis Tests for Two Sample Variances		65
3.9 Quick Tests for the Two-Sample Location Problem		68
3.9.1 Tukey's Quick Test		69
3.9.2 Boxplot Slippage Tests		71
3.10 General Procedure for Hypothesis Testing		73
3.11 Testing for Normality		75
3.11.1 Normal Probability Plots		75
3.11.2 Quantitative Tests for Normality		78
3.12 Hypothesis Tests and Confidence Intervals with MINITAB		79
3.12.1 Confidence Interval for _ When _ is Known		79
3.12.2 Hypothesis Tests for One Sample Mean (_ Known)		80
3.12.3 Normal Probability Plots with MINITAB		82
3.13 Sample-Size Calculations		82
3.13.1 Sample-Size Calculations for Confidence Intervals		83
3.13.2 Sample-Size Calculations for Hypothesis Tests		86
Chapter 4 DOE Language and Concepts		93
4.1 Introduction		93
4.2 Design of Experiments: Definition, Scope, and Motivation		93
4.3 Experiment Defined		94
4.4 Identification of Variables and Responses		94
4.5 Types of Variables		96
4.6 Types of Responses		97
4.7 Interactions		98
4.8 Types of Experiments		99
4.9 Types of Models		100
4.10 Selection of Variable Levels		105
4.10.1 Qualitative Variable Levels		105
4.10.2 Quantitative Variable Levels		105
4.11 Nested Variables		106
4.12 Covariates		107
4.14 Types of Designs		108
4.15 Randomization		109
4.16 Replication and Repetition		113
4.17 Blocking		114
4.18 Confounding		117
4.19 Occam's Razor and Effect Heredity		118
4.20 Data Integrity and Ethics		119
4.21 General Procedure for Experimentation		120
4.21.1 Step 1: Cause-and-Effect Analysis		121
4.21.2 Step 2: Document the Process		123
4.21.3 Step 3: Write a Detailed Problem Statement		124
4.21.4 Step 4: Preliminary Experimentation		125
4.21.5 Step 5: Design the Experiment		126
4.21.6 Step 6: Sample Size, Randomization, and Blocking		127
4.21.7 Step 7: Run the Experiment		128
4.21.8 Step 8: Analyze the Data		129
4.21.9 Step 9: Interpret the Results		130
4.21.10 Step 10: Run a Confirmation Experiment		130
4.21.11 Step 11: Report the Experiment		131
4.22 Experiment Documentation		136
4.23 Why Experiments Go Bad		139
Chapter 5 Experiments for One-Way Classifications		143
5.1 Introduction		143
5.2 Analysis by Comparison of All Possible Pairs Means		144
5.3 The Graphical Approach to ANOVA		145
5.4 Introduction to ANOVA		147
5.4.1 The ANOVA Rationale		147
5.4.2 ANOVA Assumptions and Validation		150
5.4.3 The ANOVA Table		154
5.5 The Sum of Squares Approach to ANOVA Calculations		155
5.6 The Calculating Forms for the Sums of Squares		159
5.7 ANOVA for Unbalanced Experiments		160
5.8 After ANOVA: Comparing the Treatment Means		161
5.8.1 Introduction		161
5.8.2 Bonferroni's Method		161
5.8.3 Sidak's Method		163
5.8.4 Duncan's Multiple Range Test		164
5.8.5 Tukey's Multiple Comparisons Test		166
5.8.6 Dunnett's Test		167
5.9 ANOVA with MINITAB		167
5.10 The Completely Randomized Design		172
5.11 Analysis of Means		176
5.12 Response Transformations		177
5.12.1 Introduction		177
5.12.2 The Logarithmic Transform		179
5.12.3 Transforming Count Data		182
5.12.4 Transforming Fraction Data		183
5.12.5 The Rank Transform		184
5.13 Sample Size for ANOVA		185
5.14 Design Considerations for One-Way Classification Experiments		188
Chapter 6 Experiments for Multi-Way Classifications		191
6.1 Introduction		191
6.2 Rationale for the Two-Way ANOVA 		192
6.2.1 No-Way Classification		192
6.2.2 One-Way Classification		193
6.2.3 Two-Way Classification		196
6.3 The Sums of Squares Approach for Two-Way ANOVA (One Replicate)		202
6.4 Interactions		203
6.5 Interpretation of Two-Way Experiments		210
6.5.1 Introduction		210
6.5.2 The Randomized Complete Block Design		211
6.5.3 a ¥ b Factorial Experiments		212
6.6 Factorial Designs		213
6.7 Multi-Way Classification ANOVA with MINITAB		215
6.7.1 Two-Way ANOVA with MINITAB		215
6.7.2 Creating and Analyzing Factorial Designs in MINITAB		221
6.8 Design Considerations for Multi-Way Classification Designs		227
Chapter 7 Advanced ANOVA Topics		231
7.1 Incomplete Factorial Designs		231
7.2 Latin Squares and Other Squares		232
7.3 Fixed and Random Variables		235
7.3.1 One-Way Classification (Fixed Variable)		235
7.3.2 Two-Way Classification (Both Variables Fixed)		237
7.3.3 One-Way Classification (Random Variable)		238
7.3.4 Two-Way Classification (One Fixed and One Random Variable)		241
7.3.5 Two-Way Classification (Both Variables Random)		242
7.4 Nested Designs		248
7.4.1 Nested Variables		248
7.4.2 Two-Stage Nested Design: B (A)		248
7.4.3 Analysis of Nested Designs in MINITAB		249
7.5 Power Calculations		250
7.5.2 General Introduction to Power Calculations		252
7.5.3 Factorial Designs with All Variables Fixed		254
7.5.4 Factorial Designs with Random Variables		256
7.5.5 Nested Designs		261
7.5.6 General Method to Determine the Power for a Fixed Variable		263
7.5.7 General Method to Determine the Power for a Random Variable		266
Chapter 8 Linear Regression		273
8.1 Introduction		273
8.2 Linear Regression Rationale		273
8.3 Regression Coefficients		277
8.4 Linear Regression Assumptions		282
8.5 Hypothesis Tests for Regression Coefficients		285
8.6 Confidence Limits for the Regression Line		289
8.7 Prediction Limits for the Observed Values		290
8.8 Correlation		293
8.8.1 The Coefficient of Determination		293
8.8.2 The Correlation Coefficient		294
8.8.3 Confidence Interval for the Correlation Coefficient		295
8.8.4 The Adjusted Correlation Coefficient		298
8.9 Linear Regression with MINITAB		299
8.10 Transformations to Linear Form		301
8.11 Polynomial Models		306
8.12 Goodness of Fit Tests		309
8.12.1 The Quadratic Model as a Test of Linear Goodness of Fit		309
8.12.2 The Linear Lack of Fit Test		312
8.13 Errors in Variables		316
8.14 Weighted Regression		317
8.15 Coded Variables		318
8.16 Multiple Regression		320
8.17 General Linear Models		327
8.18 Sample Size Calculations for Linear Regression		337
8.18.1 Sample Size to Determine the Slope with Specified Confidence		337
8.18.2 Sample Size to Determine the Regression Constant with Specified Confidence		341
8.18.3 Sample Size to Determine the Predicted Value of the Response with Specified Confidence		342
8.18.4 Sample Size to Detect a Slope Different From Zero		343
8.19 Design Considerations for Linear Regression		345
Chapter 9 Two-Level Factorial Experiments		347
9.1 Introduction		347
9.2 The 21 Factorial Experiment		347
9.3 The 22 Factorial Experiment		351
9.4 The 23 Factorial Design		362
9.5 The Addition of Center Cells to 2k Designs		367
9.6 General Procedure for Analysis of 2k Designs		370
9.7 2k Factorial Designs in MINITAB		372
9.7.1 Creating the 2k Designs in MINITAB		372
9.7.2 Analyzing the 2k Factorial Designs with MINITAB		375
9.8 Extra and Missing Values		389
9.9 Propagation of Error		390
9.10 Sample Size and Power		392
9.10.1 Sample Size and Power to Detect Significant Effects		392
9.10.2 Sample Size to Quantify Effects		396
9.11 Design Considerations for 2k Experiments		397
Chapter 10 Fractional Factorial Experiments		399
10.1 Introduction		399
10.2 The 25-1 Half-Fractional Factorial Design		400
10.3 Other Fractional Factorial Designs		406
10.4 Design Resolution		407
10.5 The Consequences of Confounding		411
10.6 Fractional Factorial Designs in MINITAB		415
10.6.1 Creating Fractional Factorial Designs in MINITAB		415
10.6.2 Analysis of Fractional Factorial Designs with MINITAB		417
10.7 Interpretation of Fractional Factorial Designs		421
10.7.1 Resolution V Designs		421
10.7.2 Resolution IV Designs		422
10.7.3 Resolution III Designs		429
10.7.4 Designs of Resolution VI and Higher		430
10.8 Plackett-Burman Designs		432
10.9 Sample-Size Calculations		432
10.10 Design Considerations for Fractional Factorial Experiments		434
Chapter 11 Response-Surface Experiments		437
11.1 Introduction		437
11.2 Terms in Quadratic Models		438
11.3 The 2k Design with Centers		441
11.4 The 3k Factorial Designs		443
11.5 The Box-Behnken Design		444
11.6 Central Composite Designs		448
11.7 Comparison of the Response-Surface Designs		453
11.7.1 Number of Observations and Error Degrees of Freedom		454
11.7.2 Number of Levels of Each Variable		455
11.7.3 Uncertainty About the Safety of Variable Levels		456
11.8 Response Surface Designs in MINITAB		458
11.8.1 Creating Response-Surface Designs in MINITAB		458
11.8.2 Analysis of Response-Surface Designs in MINITAB		458
11.9 Sample-Size Calculations		466
11.9.1 Sample Size for 2k and 2k-p Plus Centers Designs		467
11.9.2 Sample Size for 3k Designs		470
11.9.3 Sample Size for Box-Behnken Designs		471
11.9.4 Sample Size for Central Composite Designs		473
11.10 Design Considerations for Response-Surface Experiments		474
Appendix A Statistical Tables		477
A.1 Greek Characters		477
A.2 Normal Distribution: Values of p = F(-ì < z < zp)		478
A.3 Student's t Distribution: Values of tp where P (tp < t < ì) = p		480
A.4 c2 Distribution: Values of c2p where P (0 < c2 < c2p) = p		481
A.5 F Distribution: Values of Fp where P (Fp < F < ì) = p		482
A.6 Critical Values for Duncan's Multiple Range Test (r0.05,p,dfe)		484
A.7 Critical Values of the Studentized Range Distribution (Q0.05(k))		485
A.8 Critical Values for the One-Way Analysis of Means (h0.05,k,dfe)		486
A.9 Fisher's Z Transformation: Values of 		487
Bibliography		489
Index		491
```

Library of Congress Subject Headings for this publication:

Statistical hypothesis testing.
Experimental design.
Minitab.
Science -- Statistical methods.
Engineering -- Statistical methods.