TRANSPORTATION STATISTICS AND MICROSIMULATION
CHAPTER ? OVERVIEW: THE ROLE OF STATISTICS IN TRANSPORTATION ENGINEERING 1 1 WHAT IS ENGINEERING? 1 2 WHAT IS TRANSPORTATION ENGINEERING? 1 3 GOAL OF THE TEXTBOOK 1 4 OVERVIEW OF THE TEXTBOOK 1 5 WHO IS THE AUDIENCE FOR THIS TEXTBOOK? 1 6 RELAX—EVERYTHING IS FINE REFERENCES CHAPTER ? GRAPHICAL METHODS FOR DISPLAYING DATA 2 1 INTRODUCTION 2 2 HISTOGRAM 2 3 BOX AND WHISKER PLOT 2 4 QUANTILE PLOT 2 5 SCATTER PLOT 2 6 PARALLEL PLOT 2 7 TIME SERIES PLOT 2 8 QUALITY CONTROL PLOTS 2 9 CONCLUDING REMARKS HOMEWORK PROBLEMS CHAPTER ? NUMERICAL SUMMARY MEASURES 3 1 INTRODUCTION 3 2 MEASURES OF CENTRAL TENDENCY MEAN MEDIAN TRIMMED MEAN MODE PROPORTION 3 3 MEASURES OF RELATIVE STANDING PERCENTILE QUARTILE 3 4 MEASURES OF VARIABILITY RANGE VARIANCE STANDARD DEVIATION INTERQUARTILE RANGE COEFFICIENT OF VARIATION 3 5 MEASURES OF ASSOCIATION PEARSON’S SAMPLE CORRELATION COEFFICIENT SPEARMAN’S RANK CORRELATION COEFFICIENT 3 6 CONCLUDING REMARKS CHAPTER ? PROBABILITY AND RANDOM VARIABLES 4 1 INTRODUCTION 4 2 SAMPLE SPACES AND EVENTS 4 3 INTERPRETATION OF PROBABILITY 4 4 RANDOM VARIABLE FUNCTIONS OF A RANDOM VARIABLE 4 5 EXPECTATIONS OF RANDOM VARIABLES EXPECTED VALUES ARE LINEAR 4 6 COVARIANCES AND CORRELATION OF RANDOM VARIABLES 4 7 COMPUTING EXPECTED VALUES OF FUNCTIONS OF RANDOM VARIABLES 4 8 CONDITIONAL PROBABILITY 4 9 BAYES’ THEOREM 4 10 CONCLUDING REMARKS CHAPTER ? COMMON PROBABILITY DISTRIBUTIONS 5 1 INTRODUCTION 5 2 DISCRETE DISTRIBUTIONS BINOMIAL DISTRIBUTION POISSON DISTRIBUTION NEGATIVE BINOMIAL DISTRIBUTION 5 3 CONTINUOUS DISTRIBUTIONS NORMAL DISTRIBUTION T-DISTRIBUTION LOGNORMAL DISTRIBUTION EXPONENTIAL DISTRIBUTION GAMMA DISTRIBUTION CHI-SQUARE DISTRIBUTION F-DISTRIBUTION BETA DISTRIBUTION 5 4 CONCLUDING REMARKS APPENDIX: TABLE OF THE MOST POPULAR DISTRIBUTIONS IN TRANSPORTATION ENGINEERING CHAPTER ? SAMPLING DISTRIBUTIONS 6 1 INTRODUCTION 6 2 RANDOM SAMPLING 6 3 SAMPLING DISTRIBUTION OF A SAMPLE MEAN 6 4 SAMPLING DISTRIBUTION OF A SAMPLE VARIANCE 6 5 SAMPLING DISTRIBUTION OF A SAMPLE PROPORTION 6 6 CONCLUDING REMARKS CHAPTER ? INFERENCES: HYPOTHESIS TESTING AND INTERVAL ESTIMATION 7 1 INTRODUCTION 7 2 FUNDAMENTALS OF HYPOTHESIS TESTING 7 3 INFERENCES ON A SINGLE POPULATION MEAN HYPOTHESIS TESTS ABOUT A POPULATION MEAN 7 3 1 1 Z-TEST 7 3 1 2 T-TEST INTERVAL ESTIMATES FOR A POPULATION MEAN 7 3 2 1 BIAS-ADJUSTED CONFIDENCE INTERVALS 7 4 INFERENCES ABOUT TWO POPULATION MEANS HYPOTHESIS TESTS ABOUT EQUALITY OF TWO POPULATION MEANS 7 4 1 1 PAIRED T-TEST 7 4 1 2 POOLED T-TEST 7 4 1 3 UNEQUAL VARIANCE T-TEST INTERVAL ESTIMATES AND BIAS ADJUSTMENT FOR DIFFERENCE OF TWO POPULATION MEANS 7 5 INFERENCES ABOUT ONE POPULATION VARIANCE 7 6 INFERENCES ABOUT TWO POPULATION VARIANCES CONFIDENCE INTERVALS FOR THE RATIO OF TWO VARIANCES BIAS-CORRECTED CONFIDENCE INTERVAL FOR THE RATIO OF TWO VARIANCES ONE-SIDED TESTS 7 7 CONCLUDING REMARKS APPENDIX: WELCH (1938) DEGREES OF FREEDOM FOR THE UNEQUAL VARIANCE T-TEST CHAPTER ? OTHER INFERENTIAL PROCEDURES: ANOVA AND DISTRIBUTION-FREE TESTS 8 1 INTRODUCTION 8 2 COMPARISONS OF MORE THAN TWO POPULATION MEANS 8 3 MULTIPLE COMPARISONS 8 4 ONE- AND MULTIWAY ANOVA 8 5 ASSUMPTIONS FOR ANOVA 8 6 DISTRIBUTION-FREE TESTS 8 6 1 THE KOLMOGOROV–SMIRNOV GOODNESS-OF- FIT TEST THE KRUSKAL–WALLIS APPROACH TO ANOVA 8 7 CONCLUSIONS CHAPTER ? INFERENCES CONCERNING CATEGORICAL DATA 9 1 INTRODUCTION 9 2 TESTS AND CONFIDENCE INTERVALS FOR A SINGLE PROPORTION 9 3 TESTS AND CONFIDENCE INTERVALS FOR TWO PROPORTIONS 9 4 CHI-SQUARE TESTS CONCERNING MORE THAN TWO POPULATION PROPORTIONS CHI-SQUARE TEST FOR UNIVARIATE CATEGORICAL DATA TESTS FOR INDEPENDENCE OF TWO CATEGORICAL VARIABLES TESTS FOR HOMOGENEITY OF TWO OR MORE POPULATIONS 9 5 THE CHI-SQUARE GOODNESS-OF-FIT TEST FOR CHECKING DISTRIBUTIONAL ASSUMPTIONS 9 6 CONCLUSIONS CHAPTER 0 ? LINEAR REGRESSION 10 1 INTRODUCTION 10 2 SIMPLE LINEAR REGRESSION CORRELATION COEFFICIENT FITTING A STRAIGHT LINE 10 2 2 1 ESTIMATING SLOPE AND INTERCEPT 10 2 2 2 INFERENCES ON SLOPE AND INTERCEPT PREDICTION 10 3 TRANSFORMATIONS 10 5 VERIFYING THE MAIN ASSUMPTIONS IN LINEAR REGRESSION 10 6 COMPARING TWO REGRESSION LINES AT A POINT AND COMPARING TWO REGRESSION PARAMETERS 10 7 THE REGRESSION DISCONTINUITY DESIGN (RDD) 10 8 MULTIPLE LINEAR REGRESSION CONFIDENCE INTERVALS ON REGRESSION PARAMETERS 10 8 1 1 EXTRAPOLATION 10 9 VARIABLE SELECTION FOR REGRESSION MODELS 10 10 ADDITIONAL COLLINEARITY ISSUES 10 11 CONCLUDING REMARKS CHAPTER 1 ? REGRESSION MODELS FOR COUNT DATA 11 1 INTRODUCTION 11 2 POISSON REGRESSION MODEL 11 3 OVERDISPERSION 11 4 ASSESSING GOODNESS OF FIT OF POISSON REGRESSION MODELS 11 5 NEGATIVE BINOMIAL REGRESSION MODEL 11 6 CONCLUDING REMARKS APPENDIX: MAXIMUM LIKELIHOOD ESTIMATION CHAPTER 2 ? EXPERIMENTAL DESIGN 12 1 INTRODUCTION 12 2 COMPARISON OF DIRECT OBSERVATION AND DESIGNED EXPERIMENTS 12 3 MOTIVATION FOR EXPERIMENTATION THE GOOD EXPERIMENT THE POOR EXPERIMENT 12 4 A THREE-FACTOR, TWO LEVELS PER FACTOR EXPERIMENT A COMMON FALLACY: CHANGING ONE FACTOR AT A TIME EXPERIMENTS 12 5 FACTORIAL EXPERIMENTS 12 6 FRACTIONAL FACTORIAL EXPERIMENTS 12 7 SCREENING DESIGNS 12 8 D-OPTIMAL AND I-OPTIMAL DESIGNS 12 9 SAMPLE SIZE DETERMINATION 12 10 FIELD AND QUASI-EXPERIMENTS 12 11 CONCLUDING REMARKS APPENDIX: CHOICE MODELING OF EXPERIMENTS CHAPTER 3 ? CROSS-VALIDATION, JACKKNIFE, AND BOOTSTRAP METHODS FOR OBTAINING STANDARD ERRORS 13 1 INTRODUCTION 13 2 METHODS FOR STANDARD ERROR ESTIMATION WHEN A CLOSED-FORM FORMULA IS NOT AVAILABLE 13 3 CROSS-VALIDATION 13 4 THE JACKKNIFE METHOD FOR OBTAINING STANDARD ERRORS 13 5 BOOTSTRAPPING 13 6 CONCLUDING REMARKS CHAPTER 4 ? BAYESIAN APPROACHES TO TRANSPORTATION DATA ANALYSIS 14 1 INTRODUCTION 14 2 FUNDAMENTALS OF BAYESIAN STATISTICS 14 3 BAYESIAN INFERENCE CONJUGATE PRIORS 14 3 1 1 FOR POISSON LIKELIHOOD 14 3 1 2 FOR BINOMIAL LIKELIHOOD 14 3 1 3 FOR NORMAL LIKELIHOOD POINT ESTIMATION UNCERTAINTY ESTIMATION 14 3 3 1 POSTERIOR STANDARD DEVIATION 14 3 3 2 CREDIBLE INTERVALS 14 4 CONCLUDING REMARKS CHAPTER 5 ? MICROSIMULATION 15 1 INTRODUCTION 15 2 OVERVIEW OF TRAFFIC MICROSIMULATION MODELS 15 3 ANALYZING MICROSIMULATION OUTPUT MODEL CALIBRATION VALIDATION AND VERIFICATION AGGREGATE GOODNESS-OF-FIT MEASUREMENTS STATISTICAL ANALYSIS OF MICROSIMULATION OUTPUT IDENTIFYING THE STATISTICALLY OPTIMAL NUMBER OF SIMULATION RUNS MICROSIMULATION CALIBRATION COMPUTER-BASED MICROSIMULATION CALIBRATION ABSOLUTE VS RELATIVE MODEL ACCURACY 15 4 PERFORMANCE MEASURES OVERVIEW OF PERFORMANCE MEASURES COMMON PERFORMANCE MEASURES USED IN SIMULATION ANALYSIS TRAVEL TIME TOTAL DELAY QUEUE LENGTH (OVERSATURATION) NUMBER OF VEHICLES COMPLETING SIMULATION PERCENTAGE OF CORRIDOR (OD MOVEMENTS) CONGESTED (PCC) MEASURE TRAVEL TIME VARIABILITY LEVEL OF SERVICE 15 4 10 TRAVEL RATE 15 4 11 PERFORMANCE INDICES 15 5 CONCLUDING REMARKS