A guide to the methodologies, typical mathematical notation, and assumptions used in risk assessment calculations
Risk Assessment describes the methodologies, the math, and assumptions needed in risk assessment calculations and explores the various statistical analysis procedures that are used for estimating the parameters employed in risk assessment approaches. The author - a noted expert in the field - outlines a logical step-by-step approach to assessment: Identify a hazard; Analyze the risk associated with that hazard; and Determine if the elimination, or control of the risk is warranted. The text puts the focus on assessing environmental risk and describes the basics used in hypothesis testing to determine when there are differences in environmental quality at various locations.
The author describes statistical techniques in approachable terms that are designed to be understandable to the non-statistician. The text downplays mathematical notation while offering clear explanations for the development of equations. It highlights applications with numerous examples of problems of censored data as they influence the use of alternative tests. In addition, the text focuses on both parametric and non-parametric procedures. This important resource:
- Describes in understandable terms the methodologies, typical mathematical notation, and assumptions used in risk assessment calculations
- Explores the fundamental calculation procedures and approaches for risk characterization
- Contains a wealth of example problems of interpretations of environmental monitoring results and shows how each procedure is used
- Includes problems at the end of each chapter that stress the fundamental concepts outlined
Written for senior undergraduate and graduate students and as a course text in engineering, Risk Assessment offers a guide to the fundamental calculation procedures and methodologies for characterizing risk in clear and accessible terms.
Table of Contents
Preface xi
Author of the Book xiii
Acknowledgments xv
About the Companion Website xvii
1 Background to Risk Assessment and Management 1
1.1 The Case for Risk Assessment, Leading to Risk Management 1
1.2 The Need for Risk Quantification 3
1.3 Environmental Risk 5
1.4 A Measure of Quantifying Risk: Loss of Life Expectancy 5
1.5 Reliance on Environmental Data 6
1.5.1 Characteristics of Data 6
1.5.2 Indications of the Sources of Variability in Environmental Data 7
1.5.3 Independence of Successive Data Values 8
1.5.4 Uncertainties and Errors in Environmental Quality Data 9
1.6 Some Summary Indications of Approaches for Statistical Analyses 11
1.7 Overview of Book Content 12
1.8 References 12
1.9 Problems 13
Part I Methodologies for Risk Characterization 15
2 Introduction to Risk Assessment 17
2.1 Challenges in Risk Assessment 17
2.2 Categories of Risk 19
2.3 De Minimis Risk 20
2.4 Toxicological Versus Epidemiological Data 22
2.5 Basics of Environmental Risk Assessment 23
2.6 Estimating Intake (Dose) 24
2.7 Calculating the Risk for Noncarcinogens 26
2.8 Calculating Risks for Carcinogens 31
2.8.1 Background to Classification System for Carcinogens 31
2.8.2 Calculating Risk from Carcinogens 31
2.8.3 Generalization to Allow Quantification of Exposure Assessment for Other Scenarios 35
2.8.3.1 Construction/Utility Worker 36
2.9 Ecological Risk Assessment 43
2.10 Issues of Uncertainties in Risk 48
2.11 References 48
2.12 Problems 49
3 Factors Influencing the Assessment and Management of Risk 55
3.1 Background for Some of the Issues Influencing Risk Assessment and Management 55
3.2 Issues of Perception Versus Reality in Risk Assessment 55
3.2.1 Influential Roles of the Public 55
3.2.2 Differences in Risk Characterization: Public Perception Versus the Reality of Risk 56
3.2.3 Characteristics of Risk Which Influence Risk Perception 60
3.2.3.1 People’s Behavior 61
3.2.4 Magnitudes and Consequences of Risk Influence People’s Willingness to Accept Risk 61
3.2.5 Examples of TradeÂ]Offs Between Contributing Factors 62
3.2.5.1 Underestimation of Risk 63
3.2.5.2 The Influence of Voluntary and Involuntary Aspects of Risks 65
3.2.5.3 Dreadfulness of the Outcome 65
3.2.5.4 Visibility of the Hazard 65
3.2.5.5 Media Influences on Perception of Risks 65
3.3 Qualitative Risk Characterization and Probability-Impact Matrix Procedures 66
3.3.1 Introduction to Probability-Impact Matrix Procedures 66
3.3.2 Issues with the Risk Matrix Approach 69
3.4 Microbial Risk Assessment 69
3.5 References 74
3.6 Problems 75
4 Characteristics of Environmental Quality Data 79
4.1 Background to Data 79
4.2 Characteristics of Environmental Quality Data 80
4.2.1 Indications of the Sources of Variability in Environmental Data 80
4.2.2 Independence of Successive Data Values 81
4.2.3 Uncertainties and Errors in Environmental Quality Data 82
4.3 Some Summary Indications of Approaches for Statistical Analyses 84
4.4 Samples and Populations 85
4.5 Probability and Statistics 86
4.6 Graphical Data Descriptors 86
4.6.1 Histograms of Data 87
4.6.2 Probability Density Functions 87
4.6.3 Cumulative Distribution Functions 89
4.7 Summary Measures of the Distribution of Data 91
4.7.1 Measures of Central Tendency 91
4.7.2 Measures of the Dispersion of Data: Variance, Standard Deviation, and Range 94
4.7.3 Skewness 97
4.7.4 Kurtosis 98
4.7.5 Some Summary Comments 99
4.8 Further Summary Measures of the Distribution of Data 100
4.8.1 Coefficient of Variation 100
4.8.2 Standard Error of the Mean 101
4.8.3 Standard Errors 102
4.8.4 Summary Descriptors 103
4.9 Conditional Probability and Bayes Theorem 103
4.9.1 Basic Probability Concepts 103
4.9.2 Bayes’ Theorem 105
4.10 Summary 106
4.11 References 106
4.12 Problems 107
Part II Characterization of Common Distributions 109
5 The Normal or Gaussian Distribution 111
5.1 Introduction 111
5.2 The Mathematics of the Normal Distribution 112
5.3 Tests for Normality 115
5.3.1 Coefficient of Variation Test for Normality 116
5.3.2 Skewness and Kurtosis Coefficient Tests for Normality 119
5.3.3 Probability Plots 119
5.3.4 The ChiÂ]Square GoodnessÂ]ofÂ]Fit Test 125
5.3.5 The Kolmogorov-Smirnov GoodnessÂ]ofÂ]Fit Test 128
5.3.6 The Shapiro-Wilk W Test 130
5.3.7 The Shapiro-Francia Test 134
5.3.8 Data Transformations 135
5.3.9 Summary of GoodnessÂ]ofÂ]Fit Tests 135
5.4 The tÂ]Distribution 136
5.5 Extent of Use of the Normal Distribution 136
5.6 Summary Comments 136
5.7 References 136
5.8 Problems 137
6 The Lognormal Distribution 141
6.1 Introduction 141
6.2 Important Features of the Lognormal Distribution 141
6.2.1 The Central Limit Theorem 141
6.2.2 The Mathematics of the Lognormal Distribution 142
6.2.3 Probability Paper 145
6.3 Tests for Lognormality 147
6.4 Generation of Lognormal Concentration Data 148
6.5 References 149
6.6 Problems 150
7 Other Distributions Useful for Characterizing Environmental Quality Data 153
7.1 Introduction 153
7.2 The Poisson Distribution 153
7.3 Extreme Value Distributions 155
7.3.1 The Gumbel Distribution 156
7.3.2 Log Pearson Type III Distribution 158
7.4 References 160
7.5 Problem 161
Part III Hypothesis Testing of Environmental Quality 163
8 Identification of System Changes and Outliers Using Control Charts 165
8.1 Introduction 165
8.2 Tolerance Intervals 166
8.3 Confidence Intervals 173
8.3.1 Confidence Limits Using the Normal Distribution (and the tÂ]Distribution) 173
8.3.2 Confidence Limits for Lognormally Distributed Data 175
8.3.3 DistributionÂ]Free or Nonparametric Confidence Limits 175
8.4 Prediction Interval Characterizations 176
8.4.1 The tÂ]Distribution Prediction Intervals 176
8.5 Detection of Data Outliers 178
8.6 Summary of Approaches for Identifying Data Outliers 186
8.7 References 186
8.8 Problems 186
9 Hypothesis Testing: Testing Statistical Significance of Differences Between Data for Single Constituents 189
9.1 Introduction 189
9.2 Details of Hypothesis Testing 191
9.3 Steps for Significance Testing 193
9.4 Student’s tÂ]Test 193
9.4.1 Development of the Equations 193
9.4.1.1 Comparing One Sample with the Population Mean 193
9.4.1.2 OneÂ]Sided Versus TwoÂ]Sided Tests 198
9.4.1.3 Comparing Two Samples for Significance of Difference 198
9.4.1.4 Assumptions Implicit in the tÂ]Test 199
9.4.2 Effect of Unequal Variances 201
9.4.2.1 Pooled Variance 204
9.4.3 Effect of Nonnormality on the Hypothesis Test 207
9.4.4 Assumption of Independence 208
9.4.5 Examples of tÂ]Test Applications 209
9.5 Acceptance and Rejection Regions 211
9.6 Power of the Discrimination Tests 213
9.6.1 Power of the tÂ]Test 215
9.7 Extensions of the tÂ]Test 216
9.7.1 Satterthwaite’s Modified tÂ]Test 216
9.7.2 Cochran’s Approximation to the Behrens-Fisher tÂ]Test 217
9.7.3 Paired tÂ]Test 218
9.7.4 Summary of Alternative Tests 223
9.8 References 223
9.9 Problems 224
10 Multiple Comparisons Using Parametric Analyses 227
10.1 Introduction 227
10.2 Analysis of Variance (ANOVA) 228
10.2.1 Development of the Null Hypothesis 228
10.2.2 Multiple Comparisons and Statistical Power 229
10.2.3 OneÂ]Way ANOVA and TwoÂ]Way Tests of ANOVA 229
10.3 Testing for Homogeneity of Variance 230
10.3.1 Box Plots 230
10.3.2 Levene’s Test 230
10.3.3 Bartlett’s Test 232
10.4 ANOVA Procedure 234
10.5 TwoÂ]Way ANOVA 238
10.6 Iterations and Data Transformations 238
10.7 Concerns with Multiple Comparisons 239
10.8 Summary 239
10.9 References 240
10.10 Problems 240
11 Testing Differences Between Monitoring Records When Censored Data Records Exist 245
11.1 Introduction 245
11.2 Alternative Types of Censoring 246
11.3 Alternative Procedures for Statistical Analysis of Environmental Quality Datasets 250
11.3.1 Simple Substitution Methods 250
11.3.2 Test of Proportions 251
11.3.3 Plotting Position Procedure 253
11.3.4 Cohen’s Test 254
11.3.5 Aitchison’s Method 256
11.3.6 Maximum Likelihood Procedure 258
11.4 Multiple Detection Limits 259
11.5 References 259
11.6 Problems 260
12 Nonparametric Procedures 263
12.1 Introduction 263
12.2 Single Comparison Procedures 264
12.2.1 Mann-Whitney Test 264
12.2.1.1 Use of the Mann-Whitney Test to Test Equality of Variance 266
12.2.2 Spearman’s Rank Correlation Coefficient 266
12.2.3 Sign Test for Paired Observations 267
12.3 Multiple Comparison Procedures 268
12.3.1 Kruskal-Wallis Test (or Nonparametric ANOVA) 268
12.3.2 Special Consideration of the Kruskal-Wallis Test 271
12.4 References 274
12.5 Problems 274
Appendix A 277
Index 309
