Table of Contents

CHAPTER 1 INTRODUCTION

What Is This Book About? Units, Physical Constants and Their Uncertainties, Dimensionless Quantities, Software

CHAPTER 2 ASPECTS OF R *

Getting R, Using R, Getting Help, Libraries and Packages, Variables, Vectors, Arithmetic, Data Frames, Exporting Data, Importing Data, Internal Mathematical Functions, Writing Your Own Functions, Plotting Mathematical Functions, Loops, Making Decisions, Scripts, Reading Data from Websites, Matrices and Linear Algebra, Some Useful Functions and Operations

CHAPTER 3 STATISTICS *

Populations and Samples, Mean, Median, Standard Deviation, and Variance of a Sample, Covariance and Correlation, Visualizing Data Histograms, Box Plots, Plotting Data Sets, Some Plotting Parameters and Commands Estimating Population Statistics Confidence Interval for the Population Mean Using Student's t Variables, Confidence Interval for the Population Variance Using Chi-Square Variables, Confidence Interval Interpretation Comparing the Means of Two Samples, Testing Data for Normality, Outlier Identification, Modified Thompson Technique, Chauvenet's Criterion *

CHAPTER 4 CURVE FITS *

Linear Regression, Nonlinear Regression, Kernel Smoothing

CHAPTER 5 UNCERTAINTY OF A MEASURED QUANTITY *

What Is Uncertainty? Random Variables, Measurement Uncertainties, Elemental Systematic Errors, Normal Distributions, Uniform Distributions, Triangular Distributions

CHAPTER 6 UNCERTAINTY OF A RESULT CALCULATED USING EXPERIMENTAL DATA *

Taylor Series Approach. Coverage Factors, The Kline-McClintock Equation, Balance Checks

CHAPTER 7 TAYLOR SERIES UNCERTAINTY OF A LINEAR REGRESSION CURVE FIT

Curve-fit Expressions, Cases to Consider: Case 1: No Errors and No Correlations, Case 2: Random Errors Only, Case 3: Random and Systematic Errors *

General Linear Regression Theory, Uncertainties in Regression Coefficients, Evaluating Uncertainties with Built-in R functions *

CHAPTER 8 MONTE CARLO METHODS *

Overall Monte Carlo Approach, Random Number Generation, Accept/Reject Method, Inverse-cdf Method *Random Sampling, Uncertainty of a Measured Variable, Bootstrapping with Internal Functions in R, Monte Carlo Convergence Criteria, Uncertainty of a Result Calculated Using Experimental Data, Uncertainty Bands for Linear Regression Curve Fits, Uncertainty Bands for a Curve Fit with Kernel Smoothing *

CHAPTER 9 THE BAYESIAN APPROACH *

Bayes Theorem for Probability Density Functions; Bayesian Estimation of the Mean and Standard Deviation of a Normal Population *

APPENDIX PROBABILITY DENSITY FUNCTIONS *

Univariate pdfs Normal Distribution, Uniform Distribution, Triangular Distribution, Student's t Distribution, Chi-Square Distribution Multivariate pdfs, Marginal Distributions, References

About the Author

Benjamin D. Shaw is a professor in the Mechanical and Aerospace Engineering Department at the University of California, Davis. His research interests are primarily in experimental and theoretical aspects of combustion. Along with other courses, he has taught undergraduate and graduate courses on engineering experimentation and uncertainty analysis. He has published widely in archival journals and became an ASME Fellow in 2003.