Experimental Statistics and Data Analysis for Mechanical and Aerospace Engineers
- Length: 608 pages
- Edition: 1
- Language: English
- Publisher: Chapman and Hall/CRC
- Publication Date: 2021-11-25
- ISBN-10: 0367555964
- ISBN-13: 9780367555962
- Sales Rank: #0 (See Top 100 Books)
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.
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 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 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 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 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 6.4. Study Problems for Chapter 6 7. Sampling Distribution of the Proportion 7.1. Sampling Distribution of a Proportion: Binomial Distribution 7.1.1. Bernoulli Process 7.1.2. Binomial Distribution 7.1.3. Binomial Probabilities in an Interval 7.1.4. Using the Symmetry of the Binomial Distribution 7.1.5. The Normal Approximation to the Binomial Distribution 7.1.6. Sampling with and without Replacement 7.1.7. The Hypergeometric Distribution 7.2. Summary 7.3. References 7.4. Study Problems for Chapter 7 8. Hypothesis Testing Using 1-Sample Statistics 8.1. Philosophy 8.1.1. Falsification 8.1.2. The Double-Negative: The Null Hypothesis 8.2. The Consequences of Being Wrong: 8.2.1. Type I Error Rate: 8.3. How Many Tails? Or Knowing Your Ass From the Hole in 8.3.1. Confidence Intervals for the One-sample Z-test 8.4. Summary of Z-test 8.5. One Sample 8.5.1. Guinness and the Invention of 8.5.2. The One-sample 8.6. Summary of Basic Hypothesis Testing 8.7. References 8.8. Study Problems for Chapter 8 9. 2-Sample Statistics 9.1. 2-sample 9.1.1. E(x) of x1 x2 Under the Null Hypothesis 9.1.2. 2sample 9.1.3. 2-sample 9.1.3.1. Assumption of Independence of Observations 9.1.3.2. Assumption of Normal Population Distribution(s) 9.1.3.3. Assumption of Homogeneity of Variance 9.2. Paired Sample 9.2.1. What Does the Paired-Sample 9.3. 2. Test of Independence: Testing the Independence of Proportions for Two or More Samples 9.3.1. Null and Alternative Hypotheses for Proportions 9.3.2. Assumptions of the 9.3.2.1. Independence 9.3.2.2. Cell Frequencies Greater Than 5 9.4. F-test of Equal Variances 9.4.1. Assumptions of the F-test 9.5. Summary of 2-sample Statistics 9.6. References 9.7. Study Problems for Chapter 9 10. Simple Linear Regression 10.1. Finding the Line of Best Fit 10.1.1. Goodness of Fit 10.1.1.1. R2: The Coe 10.1.2. When is a Linear Model NOT Appropriate? 10.2. Residual Analysis 10.2.1. Heteroscedasticity 10.3. Hypothesis Testing in Regression: 10.4. General Procedure for Performing Regression Analyses 10.5. Summary of Simple Linear Regression 10.6. References 10.7. Study Problems for Chapter 10 III. Applications of the General Linear Model 11. The General Linear Model: Regression with Multiple Predictors 11.1. Linear Algebra Approach to Regression 11.2. Calculus Approach to Regression 11.3. Fitting a Line 11.4. Expanding to Multiple Predictor Variables: Multiple Linear 11.4.1. Prediction 11.4.2. Extrapolation 11.4.3. Assumptions of Multiple Regression 11.4.4. Covariance and Correlation 11.4.5. Collinearity: Covariance Among Independent Variables 11.5. The General Linear Model 11.6. Extended Example 11.7. Summary 11.8. References 11.9. Chapter 11 Study Problems 12. The GLM with Categorical Independent Variables: The Analysis of Variance 12.1. The 2-sample 12.2. Expanding the 12.2.1. Residual Analysis 12.2.2. Multiple Comparisons: What to Do if You Find Significant Results 12.2.2.1. Dunn-Bonferroni Correction 12.2.2.2. Sche 12.2.3. Assumptions of the ANOVA 12.3. Extended Example 12.4. Summary 12.5. References 12.6. Study Problems for Chapter 12 13. The General Linear Model: Randomized Block Factorial ANOVA 13.1. It is All Just Regression 13.2. Randomized Block ANOVA 13.2.1. A Quick Note on Notation 13.2.2. Now Back to Analysis 13.2.3. Partial 13.2.3.1. E 13.3. Summary 13.4. References 13.5. Study Problems for Chapter 13 14. Factorial Analysis of Variance 14.1. Interactions as Additional Factors 14.1.1. Post Hoc Tests 14.1.2. Fixed vs. Random E 14.1.3. Assumptions of Factorial ANOVA 14.2. Nested Factors in ANOVA 14.3. Summary 14.4. References 14.5. Study Problems for Chapter 14 IV. Introduction to Computational Methods and Machine Learning 15. The Bootstrap 15.0.1. What It Means to Be 15.1. The Bootstrap Method 15.1.1. Basic Logic Computing a Bootstrap Confidence Interval 15.2. Empirical Distribution Function 15.3. Bootstrap Sampling Distribution of the Median 15.3.1. 2-sample Confidence Interval 15.4. Regression Coe 15.5. Summary 15.6. References 15.7. Study Problems for Chapter 15 16. Data Reduction: Principal Components Analysis 16.1. Data Reduction 16.1.1. Feature Elimination 16.1.2. Feature Extraction 16.2. PCA as a Projection 16.3. PCA as Matrix Factorization 16.3.1. Extended Example: Acoustics 16.4. Principal Components Regression 16.5. Dimension Reduction: Feature Elimination 16.5.1. The Scree Test 16.6. Summary 16.7. References 16.8. Study Problems for Chapter 16 Index
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