Statistical Methods for Engineers and Scientists, Third Edition,

This Work Details The Fundamentals Of Applied Statistics And Experimental Design, Presenting A Unified Approach To Data Handling That Emphasizes The Analysis Of Variance, Regression Analysis And The Use Of Statistical Analysis System Computer Programs. This Edition: Discusses Modern Nonparametric Methods; Contains Information On Statistical Process Control And Reliability; Supplies Fault And Event Trees; Furnishes Numerous Additional End-of-chapter Problems And Worked Examples; And More.--provided By Publisher. Cover 1 Half Title 2 Title Page 8 Copyright Page 9 Preface 10 Contents 14 List of Worked Examples 20 List of Tables 26 1. lntroduction 30 2.2 Definition of Probability 36 2.3 Possible Ways for Events to Occur 37 2.3.1 Permutations 38 2.3.2 Combinations 39 2.4 Probability Computation Rules 40 2.4.1 Applications 46 2.5 A Posteriori Probability 52 Problems 54 References 58 3. Distributions 60 3.1 Introduction 60 3.2 Definitions 60 3.3 Theoretical Distributions 61 3.4 Discrete Distributions 64 3.4.1 Binomial Distribution 66 3.4.2 Poisson Distribution 70 3.4.3 Negative Binomial Distribution 74 3.4.4 Hypergeometric Distribution 76 3.5 Continuous Distributions 78 3.5.1 Normal Distribution 79 3.5.2 Exponential Distribution 84 3.5.3 Chi-Square Distribution 87 3.5.4 Student's I-Distribution 87 3.5.5 F-Distribulion 88 3.5.6 Weibull Distribution 88 3.5.7 Gamma Distribution 88 3.5.8 Log-Normal Distribution 90 3.6 Experimental Distributions 92 Problems 105 4. Descriptive Statistics 122 4.1 Introduction 122 4.2 Measures of Location 123 4.3 Measures of Variability 125 Problems 129 5. Expected Values and Moments 130 5.1 Introduction 130 5.2 Discrete Distributions 131 5.3 Continuous Distributions 133 5.4 Joint Distributions and Independence of Random Variables 134 5.5 Moments 137 5.6 Examples 138 Problems 141 6. Statistical Inference: Estimation 144 6.1 Introduction 144 6.2 Statistical Estimation 144 6.3 Point Estimates 145 6.4 Interval Estimates 147 6.5 Chi-Square Distributions 149 6.6 The t-Distribution 150 6.7 The F-Distribution 152 6.8 Estimation of the Mean 153 6.9 Comparison of Two Means 158 6.10 Estimation Involving Paired Observations 163 6.11 Variance 165 6.12 Estimation of a Variance 165 6.13 Comparison of Two Variances 167 6.14 Estimation of a Proportion P 169 6.15 Comparison of Two Proportions 172 Problems 174 Reference 183 7. Statistical Inference: Hypothesis Testing 184 7.1 Introduction 184 7.2 Types of Errors 185 7.3 Testing of Hypotheses 186 7.4 One-Tailed and Two-Tailed Tests 186 7.5 Tests Concerning the Mean 190 7.5.1 Parametric Methods for the Mean (Variance Is Known) 190 7.5.2 Parametric Methods for the Mean (Variance Is Unknown) 192 7.5.3 Nonparametric Methods for the Mean 194 7.6 Parametric Tests on the Difference of Two Means 198 7.6.1 Wilcoxon Rank-Sum Test 206 7.7 Paired t-Test 207 7.7.1 Parametric Test for Paired Observations 207 7.7.2 Wilcoxon Signed-Ranks Test for Paired Data 209 7.8 Testing a Proportion P 210 7.9 Testing the Difference of Two Proportions 211 7.10 Tests Concerning the Variance 212 7.11 Goodness-of-Fit Tests 214 7.12 Contingency Tests 217 7.13 Bartlett's Test for Equality of Variances 219 7.14 Testing the Equality of Variances 222 Problems 224 References 243 8. Analysis of Variance 244 8.1 Introduction 244 8.2 General Linear Model 246 8.3 One-Way Analysis of Variance 247 8.3.1 Pooled Variance Estimates 247 8.3.2 Variance of Group Means 248 8.3.3 Model for One-Way Analysis of Variance 250 8.3.4 Unequal Observations in One-Way Analysis of Variance 256 8.3.5 Subsampling in One-Way Analysis of Variance 259 8.4 Two-Way and Three-Way Analysis of Variance 263 8.4.1 Model for Two-Way Analysis of Variance 263 8.4.2 Interaction 269 8.4.3 Assumptions in Two-Way Analysis of Variance 271 8.4.4 Model for Three-Way Analysis of Variance 276 8.5 Confidence Intervals and Tests of Hypotheses 281 8.6 Multiple Comparisons Among Treatment Means 285 8.7 Nonparametric Methods in Analysis of Variance 290 8.7.1 Kruskal-Wallis Test 291 Problems 292 References 315 9. Regression Analysis 316 9.1 Introduction 316 9.2 Simple Linear Regression 316 9.2.1 Interval Estimation in Simple Linear Regression 324 9.2.2 Hypothesis Testing in Simple Linear Regression 328 9.2.3 Inverse Prediction in Simple Linear Regression 330 9.2.4 Analysis of Variance in Simple Linear Regression 331 9.2.5 Lack of Fit 335 9.2.6 Regression Through a Point 338 9.3 Testing Equality of Slopes 339 9.4 Multiple Linear Regression 342 9.5 Polynomial Regression 350 9.6 Transformation of Data in Regression Analysis 364 9.6.1 Propogation of Error 365 9.6.2 On Transforming the Data 365 9.6.3 Useful Transformations 366 9.7 Nonlinear Regression 381 9.8 Correlation Analysis 392 9.8.1 Correlation in Simple Linear Regression 392 9.8.2 Correlation in Multiple Linear Regression 395 9.9 Stepwise Regression 399 Problems 412 References 445 10 Statistical Process Control and Reliability 448 10.1 Introduction 448 10.2 Control Charts 449 10.3 Statistical Process Control 453 10.4 Other Quality-Control Procedures 474 10.5 Acceptance Sampling 475 10.6 Reliability 477 10.6.1 Reliability of Series and Parallel Systems 481 Problems 484 References 491 11. Experimental Design 492 11.1 Introduction 492 11.2 Random Sequencing in Experimental Designs 502 11.3 Sources of Error 505 11.4 Completely Randomized Designs 505 11.4.1 Analysis of Variance 506 11.4.2 Two-Way Analysis of Variance 509 11.4.3 Two-Way Analysis of Variance with Subsampling 509 11.4.4 Three-Way Analysis of Variance 510 11.4.5 Four-Way Analysis of Variance 514 11.4.6 Nested Designs 517 11.5 Randomized Complete Block Design 521 11.5.1 Analysis of Variance, RCB 522 11.5.2 Missing Data, RCB 523 11.5.3 Paired Observations, RCB 526 11.5.4 Subsampling in a Randomized Complete Block Design 527 11.5.5 Nonparametric Methods and Randomized Complete Blocks 532 11.6 Latin Square Designs 533 11.6.1 Analysis of Variance for the Latin Square 535 11.6.2 Missing Data, LS 539 11.7 Greco-Latin Square 541 11.8 Factorial Experiments 542 11.8.1 Main Effects 543 11.8.2 Confounding 546 11.9 Other Designs 549 11.9.1 Split-Plot Designs 549 11.9.2 Incomplete Block Designs 552 11.10 Design Efficiency 555 11.11 Analysis Of Covariance 556 Problems 562 References 584 Appendix A: Introduction to SAS 586 Appendix B: Tables of Statistical Functions 592 Table I: Binomial Cumulative Distribution 592 Table II: Poisson Cumulative Distribution 601 Table Ill: Standard Normal Cumulative Distribution 607 Table IV: Cumulative t-Distribution 615 Table V: Cumulative Chi-Square (x2) 617 Table VI: Cumulative F-Distribution 622 Table VII: Percentiles of the Wilcoxon Signed-Ranks Test Statistic8 647 Table VIII: Percentiles of the Wilcoxon Rank-Sum Statistic 651 Table IX: Percentiles of the Kruskal-Wallis Test Statistic for 654 Appendix C: Answers to Selected Problems 656 Index 664 Content: Cover Half Title Title Page Copyright Page Preface Contents List of Worked Examples List of Tables 1. lntroduction 2.2 Definition of Probability 2.3 Possible Ways for Events to Occur 2.3.1 Permutations 2.3.2 Combinations 2.4 Probability Computation Rules 2.4.1 Applications 2.5 A Posteriori Probability Problems References 3. Distributions 3.1 Introduction 3.2 Definitions 3.3 Theoretical Distributions 3.4 Discrete Distributions 3.4.1 Binomial Distribution 3.4.2 Poisson Distribution 3.4.3 Negative Binomial Distribution 3.4.4 Hypergeometric Distribution 3.5 Continuous Distributions3.5.1 Normal Distribution 3.5.2 Exponential Distribution 3.5.3 Chi-Square Distribution 3.5.4 Student's I-Distribution 3.5.5 F-Distribulion 3.5.6 Weibull Distribution 3.5.7 Gamma Distribution 3.5.8 Log-Normal Distribution 3.6 Experimental Distributions Problems 4. Descriptive Statistics 4.1 Introduction 4.2 Measures of Location 4.3 Measures of Variability Problems 5. Expected Values and Moments 5.1 Introduction 5.2 Discrete Distributions 5.3 Continuous Distributions 5.4 Joint Distributions and Independence of Random Variables 5.5 Moments 5.6 ExamplesProblems 6. Statistical Inference: Estimation 6.1 Introduction 6.2 Statistical Estimation 6.3 Point Estimates 6.4 Interval Estimates 6.5 Chi-Square Distributions 6.6 The t-Distribution 6.7 The F-Distribution 6.8 Estimation of the Mean 6.9 Comparison of Two Means 6.10 Estimation Involving Paired Observations 6.11 Variance 6.12 Estimation of a Variance 6.13 Comparison of Two Variances 6.14 Estimation of a Proportion P 6.15 Comparison of Two Proportions Problems Reference 7. Statistical Inference: Hypothesis Testing 7.1 Introduction 7.2 Types of Errors 7.3 Testing of Hypotheses7.4 One-Tailed and Two-Tailed Tests 7.5 Tests Concerning the Mean 7.5.1 Parametric Methods for the Mean (Variance Is Known) 7.5.2 Parametric Methods for the Mean (Variance Is Unknown) 7.5.3 Nonparametric Methods for the Mean 7.6 Parametric Tests on the Difference of Two Means 7.6.1 Wilcoxon Rank-Sum Test 7.7 Paired t-Test 7.7.1 Parametric Test for Paired Observations 7.7.2 Wilcoxon Signed-Ranks Test for Paired Data 7.8 Testing a Proportion P 7.9 Testing the Difference of Two Proportions 7.10 Tests Concerning the Variance 7.11 Goodness-of-Fit Tests 7.12 Contingency Tests7.13 Bartlett's Test for Equality of Variances 7.14 Testing the Equality of Variances Problems References 8. Analysis of Variance 8.1 Introduction 8.2 General Linear Model 8.3 One-Way Analysis of Variance 8.3.1 Pooled Variance Estimates 8.3.2 Variance of Group Means 8.3.3 Model for One-Way Analysis of Variance 8.3.4 Unequal Observations in One-Way Analysis of Variance 8.3.5 Subsampling in One-Way Analysis of Variance 8.4 Two-Way and Three-Way Analysis of Variance 8.4.1 Model for Two-Way Analysis of Variance 8.4.2 Interaction Requiring no previous statistical training, the Third Edition of this authoritative, practical text details the fundamentals of applied statistics and experimental design - presenting a unified approach to data handling that emphasizes the analysis of variance, regression analysis, and the use of Statistical Analysis System (SAS) computer programs. Keeping abstract theorizing to a minimum, Statistical Methods for Engineers and Scientists, Third Edition integrates a broad range of essential topics ... discusses modern nonparametric methods ... contains information on statistical process control and reliability ... supplies fault and event trees ... furnishes numerous additional end-of-chapter problems and worked examples ... evaluates the relative advantages and limitations of the most widely used experimental designs ... and more. Details the fundamentals of applied statistics and experimental design. This book presents a unified approach to data handling that emphasizes the analysis of variance, regression analysis and the use of Statistical Analysis System computer programs.