Table of Contents
TABLE OF CONTENTS
CHAPTER 1 INTRODUCTION *
What Is This Book About? *
Units *
Physical Constants and Their Uncertainties *
Dimensionless Quantities *
Software *
Topics Covered *
References *
Problems *
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 *
Data Frames *
Vectors *
Probability and Statistics *
Plotting *
Matrices and Linear Algebra *
Data/Functions/Libraries/Packages *
Various *
References *
Problems *
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 *
References *
Problems *
CHAPTER 4 CURVE FITS *
Linear Regression *
Nonlinear Regression *
Kernel Smoothing *
References *
Problems *
CHAPTER 5 UNCERTAINTY OF A MEASURED QUANTITY *
What Is Uncertainty? *
Random Variables *
Measurement Uncertainties *
Elemental Systematic Errors *
Normal Distributions *
Uniform Distributions *
Triangular Distributions *
Coverage Factors *
References *
Problems *
CHAPTER 6 UNCERTAINTY OF A RESULT CALCULATED USING EXPERIMENTAL DATA *
Taylor Series Approach *
Coverage Factors *
The Kline-McClintock Equation *
Balance Checks *
References *
Problems *
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 *
References *
Problems *
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 *
References *
Problems *
CHAPTER 9 THE BAYESIAN APPROACH *
Bayes Theorem for Probability Density Functions *
Bayesian Estimation of the Mean and Standard Deviation of a Normal Population *
References *
Problems *
APPENDIX PROBABILITY DENSITY FUNCTIONS *
Univariate pdfs *
Normal Distribution *
Uniform Distribution *
Triangular Distribution *
Student's t Distribution *
Chi-Square Distribution *
Multivariate pdfs *
Marginal Distributions *
References *