Statistical Techniques for Transportation Engineering

Statistical Techniques for Transportation Engineering is written with a systematic approach in mind and covers a full range of data analysis topics, from the introductory level (basic probability, measures of dispersion, random variable, discrete and continuous distributions) through more generally used techniques (common statistical distributions, hypothesis testing), to advanced analysis and statistical modeling techniques (regression, AnoVa, and time series). The book also provides worked out examples and solved problems for a wide variety of transportation engineering challenges.

• Demonstrates how to effectively interpret, summarize, and report transportation data using appropriate statistical descriptors
• Teaches how to identify and apply appropriate analysis methods for transportation data
• Explains how to evaluate transportation proposals and schemes with statistical rigor

Civil Engineers, Transportation Engineers

Chapter 1. An Overview of Statistical Applications

• Abstract
• 1.1 Introduction
• 1.2 Probability Functions and Statistics
• 1.3 Applications of Normal Distribution
• 1.4 Confidence Bounds
• 1.5 Determination of Sample Size
• 1.6 Random Variables Summation
• 1.7 The Binomial Distributions
• 1.8 The Poisson Distribution
• 1.9 Testing of Hypothesis
• 1.10 Summary

Chapter 2. Preliminaries

• Abstract
• 2.1 Introduction
• 2.2 Basic Concepts
• 2.3 Tabulation of Data
• 2.4 Frequency Distribution
• 2.5 Cumulative Frequency Table
• 2.6 Measures of Central Tendency
• 2.7 Arithmetic Mean
• 2.8 Median
• 2.9 Mode
• 2.10 Geometric Mean
• 2.11 Harmonic Mean
• 2.12 Partition Values (Quartiles, Deciles, and Percentiles)
• 2.13 Measures of Dispersion
• 2.14 Range
• 2.15 Interquartile Range
• 2.16 Quartile Deviation
• 2.17 Mean Deviation
• 2.18 Standard Deviation

Chapter 3. Probability

• Abstract
• 3.1 Introduction
• 3.2 Classical Probability
• 3.3 Relative Frequency Approach of Probability
• 3.4 Symbolic Notation
• 3.5 Axiomatic Theory of Probability
• 3.6 Independent and Dependent Events
• 3.7 Conditional Probability
• 3.8 Multiplication Theorem on Probability
• 3.9 Baye’s Theorem

Chapter 4. Random Variables

• Abstract
• 4.1 Introduction
• 4.2 Discrete Random Variable
• 4.3 Probability Distribution for a Discrete Random Variable
• 4.4 Mean and Variance of a Discrete Distribution
• 4.5 Continuous Random Variable
• 4.6 Probability Density Function
• 4.7 Cumulative Distribution Function
• 4.8 Mean and Variance of a Continuous Random Variable
• 4.9 Joint Distributions
• 4.10 Conditional Probability Distribution
• 4.11 Independent Random Variables
• 4.12 Joint Probability Function of Continuous Random Variables
• 4.13 Joint Probability Distribution Function of Continuous Random Variables
• 4.14 Marginal Distribution Function
• 4.15 Conditional Probability Density Functions
• 4.16 Mathematical Expectation and Moments
• 4.17 Moments
• 4.18 Moment Generating Function
• 4.19 Properties of Moment Generating Function
• 4.20 Discrete Probability Distributions
• 4.21 Poisson Distribution
• 4.22 Discrete Uniform Distribution
• 4.23 The Negative Binomial and Geometric Distribution
• 4.24 Geometric Distribution
• 4.25 Continuous Probability Distributions
• 4.26 Normal Distribution
• 4.27 Characteristic Function
• 4.28 Gamma Distribution
• 4.29 Beta Distribution of First Kind
• 4.30 Weibull Distribution

Chapter 5. Curve Fitting

• Abstract
• 5.1 Introduction
• 5.2 The Method of Least Squares
• 5.3 The Least-Squares Line
• 5.4 Fitting a Parabola by the Method of Least Squares
• 5.5 Fitting the exponential curve of the form y=a ebx

Chapter 6. Correlation and Regression

• Abstract
• 6.1 Introduction
• 6.2 Correlation
• 6.3 Coefficient of Correlation
• 6.4 Methods of Finding Coefficient of Correlation
• 6.5 Scatter Diagram
• 6.6 Direct Method
• 6.7 Spearman’s Rank Correlation Coefficient
• 6.8 Calculation of r (Correlation Coefficient) (Karl Pearson’s Formula)
• 6.9 Regression
• 6.10 Regression Equation
• 6.11 Curve of Regression
• 6.12 Types of Regression
• 6.13 Regression Equations (Linear Fit)
• 6.14 Angle between Two Lines of Regression
• 6.15 Coefficient of Determination
• 6.16 Coefficient Nondetermination
• 6.17 Coefficient of Alienation
• 6.18 Multilinear Regression
• 6.19 Uses of Regression Analysis

Chapter 7. Sampling

• Abstract
• 7.1 Introduction
• 7.2 Population
• 7.3 Sample
• 7.4 Sampling
• 7.5 Random Sampling
• 7.6 Simple Random Sampling
• 7.7 Stratified Sampling
• 7.8 Systematic Sampling
• 7.9 Sample Size Determination
• 7.10 Sampling Distribution

Chapter 8. Hypothesis Testing

• Abstract
• 8.1 Introduction
• 8.2 Hypothesis
• 8.3 Hypothesis Testing
• 8.4 Types of Hypothesis
• 8.5 Computation of Test Statistic
• 8.6 Level of Significance
• 8.7 Critical Region
• 8.8 One-Tailed Test and Two-Tailed Test
• 8.9 Errors
• 8.10 Procedure for Hypothesis Testing
• 8.11 Important Tests of Hypothesis
• 8.12 Critical Values
• 8.13 Test of Significance—Large Samples
• 8.14 Test of Significance for Single Proportion
• 8.15 Testing of Significance for Difference of Proportions

Chapter 9. Chi-Square Distribution

• Abstract
• 9.1 Introduction
• 9.2 Contingency Table
• 9.3 Calculation of Expected Frequencies
• 9.4 Chi-Square Distribution
• 9.5 Mean and Variance of Chi-Square
• 9.6 Additive Property of Independent Chi-Square Variate
• 9.7 Degrees of Freedom
• 9.8 Conditions for Using Chi-Square Test
• 9.9 Uses of Chi-Square Test

Chapter 10. Test of Significance—Small Samples

• Abstract
• 10.1 Introduction
• 10.2 Moments About Mean
• 10.3 Properties of Probability Curve
• 10.4 Assumptions for t-Test
• 10.5 Uses of t-Distribution
• 10.6 Interval Estimate of Population Mean
• 10.7 Types of t-Test
• 10.8 Significant Values of t
• 10.9 Test of Significance of a Single Mean
• 10.10 Student’s t-Test for Difference of Means
• 10.11 Paired t-Test
• 10.12 F-Distribution

Chapter 11. ANOVA (Analysis of Variance)

• Abstract
• 11.1 Introduction
• 11.2 Assumptions
• 11.3 One-Way ANOVA
• 11.4 Working Rule

Chapter 12. Analysis of Time Series

• Abstract
• 12.1 Introduction
• 12.2 Purpose of Time Series Study
• 12.3 Editing of Data
• 12.4 Components of Time Series
• 12.5 Mathematical Model for a Time Series
• 12.6 Methods of Measuring Trend

Chapter 13. Index Numbers

• Abstract
• 13.1 Introduction
• 13.2 Definitions and Characteristics
• 13.3 Types of Index Numbers
• 13.4 Problems in the Construction of Index Numbers
• 13.5 Method of Constructing Index Numbers
• 13.6 Tests for Consistency of Index Numbers
• 13.7 Quantity Index Numbers
• 13.8 Consumer Price Index Number
• 13.9 Chain Base Method
• 13.10 Base Conversion
• 13.11 Splicing
• 13.12 Deflation