| Description |
1 online resource : illustrations (black and white) |
| Series |
Advances in applied mathematics |
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Advances in applied mathematics.
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| Contents |
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- List of Figures -- List of Tables -- Symbols -- I -- 1. Introduction -- 1.1. Approach of This Book -- 1.1.1. Data Modeling -- 1.1.2. Building an Empirical Mindset -- 1.2. The Role of Data -- 1.3. References -- 1.4. Chapter 1 Study Problems -- 2. Dealing with Variation -- 2.1. Measurement -- 2.1.1. Natural Variation -- 2.1.1.1. Shape of Data -- 2.2. Distribution -- 2.2.1. Histogram -- 2.2.1.1. How to Draw a Histogram -- 2.2.1.2. Comparing Histograms |
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2.3. Accuracy and Precision of Measurements -- 2.3.1. Accuracy-Systematic Error -- 2.3.1.1. Sources of Systematic Error -- 2.3.2. Precision-Random Error -- 2.4. Continuous Versus Discrete Data -- 2.4.1. Discrete Random Variables -- 2.4.2. Continuous Random Variables -- 2.5. Law of Large Numbers -- 2.6. Central Limit Theorem -- 2.7. Representativeness -- 2.7.1. "Simple" Random Sampling -- 2.8. References -- 2.9. Chapter 2 Study Problems -- 3. Types of Data -- 3.1. Scales of Measure -- 3.1.1. Nominal Data -- 3.1.2. Ordinal Data -- 3.1.3. Interval Data -- 3.1.4. Ratio Data |
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3.2. Population Parameters and Sample Statistics -- 3.2.1. Parameters -- 3.2.1.1. Population Parameters -- 3.2.1.2. What Are the Important Sample Statistics That Model Population Parameters? -- 3.2.1.3. Nominal Data: -- 3.2.1.4. Symmetry of the Binomial Distribution -- 3.2.1.5. Ordinal Data: -- 3.2.1.6. Interval -- 3.3. The Sample Mean and Standard Deviation as Robust Estimators -- 3.4. References -- 3.5. Study Problems for Chapter 3 -- 4. Introduction to Probability -- 4.1. Simple Probability -- 4.2. Conditional Probability -- 4.3. Moments of a Distribution -- 4.3.1. The Mean as a Moment |
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4.3.2. The Variance as a Moment -- 4.3.3. Summary: Bringing Probability, Moments, and Sample Statistics -- 4.4. Probability Density Function and Cumulative Distribution -- 4.5. Summary of Probability -- 4.6. Study Problems for Chapter 4 -- 5. The Sampling Distribution of the Mean -- 5.1. The General Logic of the Sampling Distribution -- 5.2. Sampling Distribution of the Mean -- 5.3. The Standard Normal Distribution -- 5.3.1. Probability Density of the Standard Normal Distribution -- 5.3.2. Now Let's Do Some Real Stats with the Normal Distribution! -- 5.3.3. The Z-test -- 5.4. Summary |
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5.5. References -- 5.6. Study Problems for Chapter 5 -- II. Testing Hypotheses -- 6. The Ten Building Blocks of Experimental Design -- 6.0.1. Notation -- 6.1. Basic Experimental Designs -- 6.1.1. One-shot Case Study -- 6.1.2. One-sample, Pre-post Design -- 6.1.3. Static Sample Comparison -- 6.1.4. Random Sample Design -- 6.1.5. Pre-post Randomized Sample -- 6.1.6. Factorial Designs -- 6.1.7. Randomized Block Factorial Designs -- 6.1.8. One-shot Repeated Measures -- 6.1.9. Randomized Factors Repeated Measures -- 6.1.10. Ex-post-facto -- 6.1.11. Time Series -- 6.2. Summary -- 6.3. References |
| Summary |
This book develops foundational concepts in probability and statistics with primary applications in mechanical and aerospace engineering. It develops the mindset a data analyst must have to interpret an ill-defined problem, operationalize it, collect or interpret data, and use this evidence to make decisions that can improve the quality of engineered products and systems. It was designed utilizing the latest research in statistics learning and in engagement teaching practices The author's focus is on developing students' conceptual understanding of statistical theory with the goal of effective design and conduct of experiments. Engineering statistics is primarily a form of data modeling. Emphasis is placed on modelling variation in observations, characterizing its distribution, and making inferences with regards to quality assurance and control. Fitting multivariate models, experimental design and hypothesis testing are all critical skills developed. All topics are developed utilizing real data from engineering projects, simulations, and laboratory experiences. In other words, we begin with data, we end with models. The key features are: Realistic contexts situating the learning of the statistics in actual engineering practice. A balance of rigorous mathematics, conceptual scaffolding, and real, messy data, to ensure that students learn the important concepts and can apply them in practice. The consistency of text, lecture notes, data sets, and simulations yield a coherent set of instructional resources for the instructor and a coherent set of learning experiences for the students. MatLab is used as a computational tool. Other tools are easily substituted. Table of Contents 1. Introduction2. Dealing with Variation3. Types of Data4. Introduction to Probability5. Sampling Distribution of the Mean6. The Ten Building Blocks of Experimental Design7. Sampling Distribution of the Proportion8. Hypothesis Testing Using the 1-sample Statistics9. 2-sample Statistics10. Simple Linear Regression11. The General Linear Model: Regression with Multiple Predictors12. The GLM with Categorical Independent Variables: The Analysis of Variance13. The General Linear Model: Randomized Block Factorial ANOVA14. Factorial Analysis of Variance15. The Bootstrap16. Data Reduction: Principal Components AnalysisIndex Author Biography James A. Middleton is Professor of Mechanical and Aerospace Engineering and former Director of the Center for Research on Education in Science, Mathematics, Engineering, and Technology at Arizona State University. Previously, he held the Elmhurst Energy Chair in STEM education at the University of Birmingham in the UK. He received his Ph. D. from the University of Wisconsin-Madison. He has been Senior co-Chair of the Special Interest Group for Mathematics Education in the American Educational Research Association, and as Chair of the National Council of Teachers of Mathematics' Research Committee. He has been a consultant for the College Board, the Rand Corporation, the National Academies, the American Statistical Association, the IEEE, and numerous school systems around the United States, the UK, and Australia. He has garnered over $30 million in grants to study and improve mathematics education in urban schools |
| Notes |
"A Chapman & Hall book." |
| Bibliography |
Includes bibliographical references |
| Notes |
James A. Middleton is Professor of Mechanical and Aerospace Engineering and former Director of the Center for Research on Education in Science, Mathematics, Engineering, and Technology at Arizona State University. Previously, he held the Elmhurst Energy Chair in STEM education at the University of Birmingham in the UK. He received his Ph. D. from the University of Wisconsin-Madison. He has been Senior co-Chair of the Special Interest Group for Mathematics Education in the American Educational Research Association, and as Chair of the National Council of Teachers of Mathematics' Research Committee. He has been a consultant for the College Board, the Rand Corporation, the National Academies, the American Statistical Association, the IEEE, and numerous school systems around the United States, the UK, and Australia. He has garnered over $30 million in grants to study and improve mathematics education in urban schools |
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Online resource; title from digital title page (viewed on December 22, 2021) |
| Subject |
Engineering -- Statistical methods.
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Engineering -- Data processing.
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MATHEMATICS -- Probability & Statistics -- General.
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SCIENCE -- Applied Sciences.
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Engineering -- Data processing
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Engineering -- Statistical methods
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| Form |
Electronic book
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| ISBN |
9781003094227 |
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1003094228 |
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9781000469615 |
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1000469611 |
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9781000469622 |
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100046962X |
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