Experimental Statistics and Data Analysis for Mechanical and Aerospace Engineers (Advances in Applied Mathematics)

✍ Scribed by James A. Middleton

• Publisher: Chapman and Hall/CRC
• Year: 2021
• Tongue: English
• Leaves: 587
• Edition: 1
• Category: Library

✦ Synopsis

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. Introduction
2. Dealing with Variation
3. Types of Data
4. Introduction to Probability
5. Sampling Distribution of the Mean
6. The Ten Building Blocks of Experimental Design
7. Sampling Distribution of the Proportion
8. Hypothesis Testing Using the 1-sample Statistics
9. 2-sample Statistics
10. Simple Linear Regression
11. The General Linear Model: Regression with Multiple Predictors
12. The GLM with Categorical Independent Variables: The Analysis of Variance
13. The General Linear Model: Randomized Block Factorial ANOVA
14. Factorial Analysis of Variance
15. The Bootstrap
16. Data Reduction: Principal Components Analysis
Index

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.

✦ Table of 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
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