Statistical Techniques for Transportation Engineering

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 e^bx

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