Table of Contents

Overview: The Role of Statistics in Transportation Engineering
What Is Engineering?
What Is Transportation Engineering?
Goal of the Textbook
Overview of the Textbook
Who Is the Audience for This Textbook?
Relax—Everything Is Fine

Graphical Methods for Displaying Data
Introduction
Histogram
Box and Whisker Plot
Quantile Plot
Scatter Plot
Parallel Plot
Time Series Plot
Quality Control Plots
Concluding Remarks

Numerical Summary Measures
Introduction
Measures of Central Tendency
Measures of Relative Standing
Measures of Variability
Measures of Association
Concluding Remarks

Probability and Random Variables
Introduction
Sample Spaces and Events
Interpretation of Probability
Random Variable
Expectations of Random Variables
Covariances and Correlation of Random Variables
Computing Expected Values of Functions of Random Variables
Conditional Probability
Bayes’ Theorem
Concluding Remarks

Common Probability Distributions
Introduction
Discrete Distributions
Continuous Distributions
Concluding Remarks
Appendix: Table of the Most Popular Distributions in Transportation Engineering

Sampling Distributions
Introduction
Random Sampling
Sampling Distribution of a Sample Mean
Sampling Distribution of a Sample Variance
Sampling Distribution of a Sample Proportion
Concluding Remarks

Inferences: Hypothesis Testing and Interval Estimation
Introduction
Fundamentals of Hypothesis Testing
Inferences on a Single Population Mean
Inferences about Two Population Means
Inferences about One Population Variance
Inferences about Two Population Variances
Concluding Remarks
Appendix: Welch (1938) Degrees of Freedom for the Unequal Variance t-Test

Other Inferential Procedures: ANOVA and Distribution-Free Tests
Introduction
Comparisons of More than Two
Population Means
Multiple Comparisons
One- and Multiway ANOVA
Assumptions for ANOVA
Distribution-Free Tests
Conclusions

Inferences Concerning Categorical Data
Introduction
Tests and Confidence Intervals for a Single Proportion
Tests and Confidence Intervals for Two Proportions
Chi-Square Tests Concerning More Than Two Population Proportions
The Chi-Square Goodness-of-Fit Test for Checking Distributional Assumptions
Conclusions

Linear Regression
Introduction
Simple Linear Regression
Transformations
Understanding and Calculating R²
Verifying the Main Assumptions in Linear Regression
Comparing Two Regression Lines at a Point and Comparing Two Regression Parameters
The Regression Discontinuity Design (RDD)
Multiple Linear Regression
Variable Selection for Regression Models
Additional Collinearity Issues
Concluding Remarks

Regression Models for Count Data
Introduction
Poisson Regression Model
Overdispersion
Assessing Goodness of Fit of Poisson Regression Models
Negative Binomial Regression Model
Concluding Remarks
Appendix: Maximum Likelihood Estimation

Experimental Design
Introduction
Comparison of Direct Observation and Designed Experiments
Motivation for Experimentation
A Three-Factor, Two Levels per Factor Experiment
Factorial Experiments
Fractional Factorial Experiments
Screening Designs
D-Optimal and I-Optimal Designs
Sample Size Determination
Field and Quasi-Experiments
Concluding Remarks
Appendix: Choice Modeling of Experiments

Cross-Validation, Jackknife, and Bootstrap Methods for Obtaining Standard Errors
Introduction
Methods for Standard Error Estimation When a Closed-Form Formula Is Not Available
Cross-Validation
The Jackknife Method for Obtaining Standard Errors
Bootstrapping
Concluding Remarks

Bayesian Approaches to Transportation Data Analysis
Introduction
Fundamentals of Bayesian Statistics
Bayesian Inference
Concluding Remarks

Microsimulation
Introduction
Overview of Traffic Microsimulation Models
Analyzing Microsimulation Output
Performance Measures
Concluding Remarks

Appendix: Soft Modeling and Nonparametric Model Building

Homework Problems and References appear at the end of each chapter.