Edward A. McBean, PHD, is a Professor of Water Resources, Canada Research Chair in Water Supply Security in the School of Engineering at the University of Guelph. Dr. McBean is also University of Guelph Leadership Chair Professor.

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• Preface xiAuthor of the Book xiiiAcknowledgments xvAbout the Companion Website xvii1 Background to Risk Assessment and Management 11.1 The Case for Risk Assessment, Leading to Risk Management 11.2 The Need for Risk Quantification 31.3 Environmental Risk 51.4 A Measure of Quantifying Risk: Loss of Life Expectancy 51.5 Reliance on Environmental Data 61.5.1 Characteristics of Data 61.5.2 Indications of the Sources of Variability in Environmental Data 71.5.3 Independence of Successive Data Values 81.5.4 Uncertainties and Errors in Environmental Quality Data 91.6 Some Summary Indications of Approaches for Statistical Analyses 111.7 Overview of Book Content 121.8 References 121.9 Problems 13Part I Methodologies for Risk Characterization 152 Introduction to Risk Assessment 172.1 Challenges in Risk Assessment 172.2 Categories of Risk 192.3 De Minimis Risk 202.4 Toxicological Versus Epidemiological Data 222.5 Basics of Environmental Risk Assessment 232.6 Estimating Intake (Dose) 242.7 Calculating the Risk for Noncarcinogens 262.8 Calculating Risks for Carcinogens 312.8.1 Background to Classification System for Carcinogens 312.8.2 Calculating Risk from Carcinogens 312.8.3 Generalization to Allow Quantification of Exposure Assessment for Other Scenarios 352.8.3.1 Construction/Utility Worker 362.9 Ecological Risk Assessment 432.10 Issues of Uncertainties in Risk 482.11 References 482.12 Problems 493 Factors Influencing the Assessment and Management of Risk 553.1 Background for Some of the Issues Influencing Risk Assessment and Management 553.2 Issues of Perception Versus Reality in Risk Assessment 553.2.1 Influential Roles of the Public 553.2.2 Differences in Risk Characterization: Public Perception Versus the Reality of Risk 563.2.3 Characteristics of Risk Which Influence Risk Perception 603.2.3.1 People’s Behavior 613.2.4 Magnitudes and Consequences of Risk Influence People’s Willingness to Accept Risk 613.2.5 Examples of Trade]Offs Between Contributing Factors 623.2.5.1 Underestimation of Risk 633.2.5.2 The Influence of Voluntary and Involuntary Aspects of Risks 653.2.5.3 Dreadfulness of the Outcome 653.2.5.4 Visibility of the Hazard 653.2.5.5 Media Influences on Perception of Risks 653.3 Qualitative Risk Characterization and Probability–Impact Matrix Procedures 663.3.1 Introduction to Probability–Impact Matrix Procedures 663.3.2 Issues with the Risk Matrix Approach 693.4 Microbial Risk Assessment 693.5 References 743.6 Problems 754 Characteristics of Environmental Quality Data 794.1 Background to Data 794.2 Characteristics of Environmental Quality Data 804.2.1 Indications of the Sources of Variability in Environmental Data 804.2.2 Independence of Successive Data Values 814.2.3 Uncertainties and Errors in Environmental Quality Data 824.3 Some Summary Indications of Approaches for Statistical Analyses 844.4 Samples and Populations 854.5 Probability and Statistics 864.6 Graphical Data Descriptors 864.6.1 Histograms of Data 874.6.2 Probability Density Functions 874.6.3 Cumulative Distribution Functions 894.7 Summary Measures of the Distribution of Data 914.7.1 Measures of Central Tendency 914.7.2 Measures of the Dispersion of Data: Variance, Standard Deviation, and Range 944.7.3 Skewness 974.7.4 Kurtosis 984.7.5 Some Summary Comments 994.8 Further Summary Measures of the Distribution of Data 1004.8.1 Coefficient of Variation 1004.8.2 Standard Error of the Mean 1014.8.3 Standard Errors 1024.8.4 Summary Descriptors 1034.9 Conditional Probability and Bayes Theorem 1034.9.1 Basic Probability Concepts 1034.9.2 Bayes’ Theorem 1054.10 Summary 1064.11 References 1064.12 Problems 107Part II Characterization of Common Distributions 1095 The Normal or Gaussian Distribution 1115.1 Introduction 1115.2 The Mathematics of the Normal Distribution 1125.3 Tests for Normality 1155.3.1 Coefficient of Variation Test for Normality 1165.3.2 Skewness and Kurtosis Coefficient Tests for Normality 1195.3.3 Probability Plots 1195.3.4 The Chi]Square Goodness]of]Fit Test 1255.3.5 The Kolmogorov–Smirnov Goodness]of]Fit Test 1285.3.6 The Shapiro–Wilk W Test 1305.3.7 The Shapiro–Francia Test 1345.3.8 Data Transformations 1355.3.9 Summary of Goodness]of]Fit Tests 1355.4 The t]Distribution 1365.5 Extent of Use of the Normal Distribution 1365.6 Summary Comments 1365.7 References 1365.8 Problems 1376 The Lognormal Distribution 1416.1 Introduction 1416.2 Important Features of the Lognormal Distribution 1416.2.1 The Central Limit Theorem 1416.2.2 The Mathematics of the Lognormal Distribution 1426.2.3 Probability Paper 1456.3 Tests for Lognormality 1476.4 Generation of Lognormal Concentration Data 1486.5 References 1496.6 Problems 1507 Other Distributions Useful for Characterizing Environmental Quality Data 1537.1 Introduction 1537.2 The Poisson Distribution 1537.3 Extreme Value Distributions 1557.3.1 The Gumbel Distribution 1567.3.2 Log Pearson Type III Distribution 1587.4 References 1607.5 Problem 161Part III Hypothesis Testing of Environmental Quality 1638 Identification of System Changes and Outliers Using Control Charts 1658.1 Introduction 1658.2 Tolerance Intervals 1668.3 Confidence Intervals 1738.3.1 Confidence Limits Using the Normal Distribution (and the t]Distribution) 1738.3.2 Confidence Limits for Lognormally Distributed Data 1758.3.3 Distribution]Free or Nonparametric Confidence Limits 1758.4 Prediction Interval Characterizations 1768.4.1 The t]Distribution Prediction Intervals 1768.5 Detection of Data Outliers 1788.6 Summary of Approaches for Identifying Data Outliers 1868.7 References 1868.8 Problems 1869 Hypothesis Testing: Testing Statistical Significance of Differences Between Data for Single Constituents 1899.1 Introduction 1899.2 Details of Hypothesis Testing 1919.3 Steps for Significance Testing 1939.4 Student’s t]Test 1939.4.1 Development of the Equations 1939.4.1.1 Comparing One Sample with the Population Mean 1939.4.1.2 One]Sided Versus Two]Sided Tests 1989.4.1.3 Comparing Two Samples for Significance of Difference 1989.4.1.4 Assumptions Implicit in the t]Test 1999.4.2 Effect of Unequal Variances 2019.4.2.1 Pooled Variance 2049.4.3 Effect of Nonnormality on the Hypothesis Test 2079.4.4 Assumption of Independence 2089.4.5 Examples of t]Test Applications 2099.5 Acceptance and Rejection Regions 2119.6 Power of the Discrimination Tests 2139.6.1 Power of the t]Test 2159.7 Extensions of the t]Test 2169.7.1 Satterthwaite’s Modified t]Test 2169.7.2 Cochran’s Approximation to the Behrens–Fisher t]Test 2179.7.3 Paired t]Test 2189.7.4 Summary of Alternative Tests 2239.8 References 2239.9 Problems 22410 Multiple Comparisons Using Parametric Analyses 22710.1 Introduction 22710.2 Analysis of Variance (ANOVA) 22810.2.1 Development of the Null Hypothesis 22810.2.2 Multiple Comparisons and Statistical Power 22910.2.3 One]Way ANOVA and Two]Way Tests of ANOVA 22910.3 Testing for Homogeneity of Variance 23010.3.1 Box Plots 23010.3.2 Levene’s Test 23010.3.3 Bartlett’s Test 23210.4 ANOVA Procedure 23410.5 Two]Way ANOVA 23810.6 Iterations and Data Transformations 23810.7 Concerns with Multiple Comparisons 23910.8 Summary 23910.9 References 24010.10 Problems 24011 Testing Differences Between Monitoring Records When Censored Data Records Exist 24511.1 Introduction 24511.2 Alternative Types of Censoring 24611.3 Alternative Procedures for Statistical Analysis of Environmental Quality Datasets 25011.3.1 Simple Substitution Methods 25011.3.2 Test of Proportions 25111.3.3 Plotting Position Procedure 25311.3.4 Cohen’s Test 25411.3.5 Aitchison’s Method 25611.3.6 Maximum Likelihood Procedure 25811.4 Multiple Detection Limits 25911.5 References 25911.6 Problems 26012 Nonparametric Procedures 26312.1 Introduction 26312.2 Single Comparison Procedures 26412.2.1 Mann–Whitney Test 26412.2.1.1 Use of the Mann–Whitney Test to Test Equality of Variance 26612.2.2 Spearman’s Rank Correlation Coefficient 26612.2.3 Sign Test for Paired Observations 26712.3 Multiple Comparison Procedures 26812.3.1 Kruskal–Wallis Test (or Nonparametric ANOVA) 26812.3.2 Special Consideration of the Kruskal–Wallis Test 27112.4 References 27412.5 Problems 274Appendix A 277Index 309

Edward A. McBean, PHD, is a Professor of Water Resources, Canada Research Chair in Water Supply Security in the School of Engineering at the University of Guelph. Dr. McBean is also University of Guelph Leadership Chair Professor.

Select Guide Rating

• Preface xiAuthor of the Book xiiiAcknowledgments xvAbout the Companion Website xvii1 Background to Risk Assessment and Management 11.1 The Case for Risk Assessment, Leading to Risk Management 11.2 The Need for Risk Quantification 31.3 Environmental Risk 51.4 A Measure of Quantifying Risk: Loss of Life Expectancy 51.5 Reliance on Environmental Data 61.5.1 Characteristics of Data 61.5.2 Indications of the Sources of Variability in Environmental Data 71.5.3 Independence of Successive Data Values 81.5.4 Uncertainties and Errors in Environmental Quality Data 91.6 Some Summary Indications of Approaches for Statistical Analyses 111.7 Overview of Book Content 121.8 References 121.9 Problems 13Part I Methodologies for Risk Characterization 152 Introduction to Risk Assessment 172.1 Challenges in Risk Assessment 172.2 Categories of Risk 192.3 De Minimis Risk 202.4 Toxicological Versus Epidemiological Data 222.5 Basics of Environmental Risk Assessment 232.6 Estimating Intake (Dose) 242.7 Calculating the Risk for Noncarcinogens 262.8 Calculating Risks for Carcinogens 312.8.1 Background to Classification System for Carcinogens 312.8.2 Calculating Risk from Carcinogens 312.8.3 Generalization to Allow Quantification of Exposure Assessment for Other Scenarios 352.8.3.1 Construction/Utility Worker 362.9 Ecological Risk Assessment 432.10 Issues of Uncertainties in Risk 482.11 References 482.12 Problems 493 Factors Influencing the Assessment and Management of Risk 553.1 Background for Some of the Issues Influencing Risk Assessment and Management 553.2 Issues of Perception Versus Reality in Risk Assessment 553.2.1 Influential Roles of the Public 553.2.2 Differences in Risk Characterization: Public Perception Versus the Reality of Risk 563.2.3 Characteristics of Risk Which Influence Risk Perception 603.2.3.1 People’s Behavior 613.2.4 Magnitudes and Consequences of Risk Influence People’s Willingness to Accept Risk 613.2.5 Examples of Trade]Offs Between Contributing Factors 623.2.5.1 Underestimation of Risk 633.2.5.2 The Influence of Voluntary and Involuntary Aspects of Risks 653.2.5.3 Dreadfulness of the Outcome 653.2.5.4 Visibility of the Hazard 653.2.5.5 Media Influences on Perception of Risks 653.3 Qualitative Risk Characterization and Probability–Impact Matrix Procedures 663.3.1 Introduction to Probability–Impact Matrix Procedures 663.3.2 Issues with the Risk Matrix Approach 693.4 Microbial Risk Assessment 693.5 References 743.6 Problems 754 Characteristics of Environmental Quality Data 794.1 Background to Data 794.2 Characteristics of Environmental Quality Data 804.2.1 Indications of the Sources of Variability in Environmental Data 804.2.2 Independence of Successive Data Values 814.2.3 Uncertainties and Errors in Environmental Quality Data 824.3 Some Summary Indications of Approaches for Statistical Analyses 844.4 Samples and Populations 854.5 Probability and Statistics 864.6 Graphical Data Descriptors 864.6.1 Histograms of Data 874.6.2 Probability Density Functions 874.6.3 Cumulative Distribution Functions 894.7 Summary Measures of the Distribution of Data 914.7.1 Measures of Central Tendency 914.7.2 Measures of the Dispersion of Data: Variance, Standard Deviation, and Range 944.7.3 Skewness 974.7.4 Kurtosis 984.7.5 Some Summary Comments 994.8 Further Summary Measures of the Distribution of Data 1004.8.1 Coefficient of Variation 1004.8.2 Standard Error of the Mean 1014.8.3 Standard Errors 1024.8.4 Summary Descriptors 1034.9 Conditional Probability and Bayes Theorem 1034.9.1 Basic Probability Concepts 1034.9.2 Bayes’ Theorem 1054.10 Summary 1064.11 References 1064.12 Problems 107Part II Characterization of Common Distributions 1095 The Normal or Gaussian Distribution 1115.1 Introduction 1115.2 The Mathematics of the Normal Distribution 1125.3 Tests for Normality 1155.3.1 Coefficient of Variation Test for Normality 1165.3.2 Skewness and Kurtosis Coefficient Tests for Normality 1195.3.3 Probability Plots 1195.3.4 The Chi]Square Goodness]of]Fit Test 1255.3.5 The Kolmogorov–Smirnov Goodness]of]Fit Test 1285.3.6 The Shapiro–Wilk W Test 1305.3.7 The Shapiro–Francia Test 1345.3.8 Data Transformations 1355.3.9 Summary of Goodness]of]Fit Tests 1355.4 The t]Distribution 1365.5 Extent of Use of the Normal Distribution 1365.6 Summary Comments 1365.7 References 1365.8 Problems 1376 The Lognormal Distribution 1416.1 Introduction 1416.2 Important Features of the Lognormal Distribution 1416.2.1 The Central Limit Theorem 1416.2.2 The Mathematics of the Lognormal Distribution 1426.2.3 Probability Paper 1456.3 Tests for Lognormality 1476.4 Generation of Lognormal Concentration Data 1486.5 References 1496.6 Problems 1507 Other Distributions Useful for Characterizing Environmental Quality Data 1537.1 Introduction 1537.2 The Poisson Distribution 1537.3 Extreme Value Distributions 1557.3.1 The Gumbel Distribution 1567.3.2 Log Pearson Type III Distribution 1587.4 References 1607.5 Problem 161Part III Hypothesis Testing of Environmental Quality 1638 Identification of System Changes and Outliers Using Control Charts 1658.1 Introduction 1658.2 Tolerance Intervals 1668.3 Confidence Intervals 1738.3.1 Confidence Limits Using the Normal Distribution (and the t]Distribution) 1738.3.2 Confidence Limits for Lognormally Distributed Data 1758.3.3 Distribution]Free or Nonparametric Confidence Limits 1758.4 Prediction Interval Characterizations 1768.4.1 The t]Distribution Prediction Intervals 1768.5 Detection of Data Outliers 1788.6 Summary of Approaches for Identifying Data Outliers 1868.7 References 1868.8 Problems 1869 Hypothesis Testing: Testing Statistical Significance of Differences Between Data for Single Constituents 1899.1 Introduction 1899.2 Details of Hypothesis Testing 1919.3 Steps for Significance Testing 1939.4 Student’s t]Test 1939.4.1 Development of the Equations 1939.4.1.1 Comparing One Sample with the Population Mean 1939.4.1.2 One]Sided Versus Two]Sided Tests 1989.4.1.3 Comparing Two Samples for Significance of Difference 1989.4.1.4 Assumptions Implicit in the t]Test 1999.4.2 Effect of Unequal Variances 2019.4.2.1 Pooled Variance 2049.4.3 Effect of Nonnormality on the Hypothesis Test 2079.4.4 Assumption of Independence 2089.4.5 Examples of t]Test Applications 2099.5 Acceptance and Rejection Regions 2119.6 Power of the Discrimination Tests 2139.6.1 Power of the t]Test 2159.7 Extensions of the t]Test 2169.7.1 Satterthwaite’s Modified t]Test 2169.7.2 Cochran’s Approximation to the Behrens–Fisher t]Test 2179.7.3 Paired t]Test 2189.7.4 Summary of Alternative Tests 2239.8 References 2239.9 Problems 22410 Multiple Comparisons Using Parametric Analyses 22710.1 Introduction 22710.2 Analysis of Variance (ANOVA) 22810.2.1 Development of the Null Hypothesis 22810.2.2 Multiple Comparisons and Statistical Power 22910.2.3 One]Way ANOVA and Two]Way Tests of ANOVA 22910.3 Testing for Homogeneity of Variance 23010.3.1 Box Plots 23010.3.2 Levene’s Test 23010.3.3 Bartlett’s Test 23210.4 ANOVA Procedure 23410.5 Two]Way ANOVA 23810.6 Iterations and Data Transformations 23810.7 Concerns with Multiple Comparisons 23910.8 Summary 23910.9 References 24010.10 Problems 24011 Testing Differences Between Monitoring Records When Censored Data Records Exist 24511.1 Introduction 24511.2 Alternative Types of Censoring 24611.3 Alternative Procedures for Statistical Analysis of Environmental Quality Datasets 25011.3.1 Simple Substitution Methods 25011.3.2 Test of Proportions 25111.3.3 Plotting Position Procedure 25311.3.4 Cohen’s Test 25411.3.5 Aitchison’s Method 25611.3.6 Maximum Likelihood Procedure 25811.4 Multiple Detection Limits 25911.5 References 25911.6 Problems 26012 Nonparametric Procedures 26312.1 Introduction 26312.2 Single Comparison Procedures 26412.2.1 Mann–Whitney Test 26412.2.1.1 Use of the Mann–Whitney Test to Test Equality of Variance 26612.2.2 Spearman’s Rank Correlation Coefficient 26612.2.3 Sign Test for Paired Observations 26712.3 Multiple Comparison Procedures 26812.3.1 Kruskal–Wallis Test (or Nonparametric ANOVA) 26812.3.2 Special Consideration of the Kruskal–Wallis Test 27112.4 References 27412.5 Problems 274Appendix A 277Index 309

Edward A. McBean, PHD, is a Professor of Water Resources, Canada Research Chair in Water Supply Security in the School of Engineering at the University of Guelph. Dr. McBean is also University of Guelph Leadership Chair Professor.

Select Guide Rating

• Preface xiAuthor of the Book xiiiAcknowledgments xvAbout the Companion Website xvii1 Background to Risk Assessment and Management 11.1 The Case for Risk Assessment, Leading to Risk Management 11.2 The Need for Risk Quantification 31.3 Environmental Risk 51.4 A Measure of Quantifying Risk: Loss of Life Expectancy 51.5 Reliance on Environmental Data 61.5.1 Characteristics of Data 61.5.2 Indications of the Sources of Variability in Environmental Data 71.5.3 Independence of Successive Data Values 81.5.4 Uncertainties and Errors in Environmental Quality Data 91.6 Some Summary Indications of Approaches for Statistical Analyses 111.7 Overview of Book Content 121.8 References 121.9 Problems 13Part I Methodologies for Risk Characterization 152 Introduction to Risk Assessment 172.1 Challenges in Risk Assessment 172.2 Categories of Risk 192.3 De Minimis Risk 202.4 Toxicological Versus Epidemiological Data 222.5 Basics of Environmental Risk Assessment 232.6 Estimating Intake (Dose) 242.7 Calculating the Risk for Noncarcinogens 262.8 Calculating Risks for Carcinogens 312.8.1 Background to Classification System for Carcinogens 312.8.2 Calculating Risk from Carcinogens 312.8.3 Generalization to Allow Quantification of Exposure Assessment for Other Scenarios 352.8.3.1 Construction/Utility Worker 362.9 Ecological Risk Assessment 432.10 Issues of Uncertainties in Risk 482.11 References 482.12 Problems 493 Factors Influencing the Assessment and Management of Risk 553.1 Background for Some of the Issues Influencing Risk Assessment and Management 553.2 Issues of Perception Versus Reality in Risk Assessment 553.2.1 Influential Roles of the Public 553.2.2 Differences in Risk Characterization: Public Perception Versus the Reality of Risk 563.2.3 Characteristics of Risk Which Influence Risk Perception 603.2.3.1 People’s Behavior 613.2.4 Magnitudes and Consequences of Risk Influence People’s Willingness to Accept Risk 613.2.5 Examples of Trade]Offs Between Contributing Factors 623.2.5.1 Underestimation of Risk 633.2.5.2 The Influence of Voluntary and Involuntary Aspects of Risks 653.2.5.3 Dreadfulness of the Outcome 653.2.5.4 Visibility of the Hazard 653.2.5.5 Media Influences on Perception of Risks 653.3 Qualitative Risk Characterization and Probability–Impact Matrix Procedures 663.3.1 Introduction to Probability–Impact Matrix Procedures 663.3.2 Issues with the Risk Matrix Approach 693.4 Microbial Risk Assessment 693.5 References 743.6 Problems 754 Characteristics of Environmental Quality Data 794.1 Background to Data 794.2 Characteristics of Environmental Quality Data 804.2.1 Indications of the Sources of Variability in Environmental Data 804.2.2 Independence of Successive Data Values 814.2.3 Uncertainties and Errors in Environmental Quality Data 824.3 Some Summary Indications of Approaches for Statistical Analyses 844.4 Samples and Populations 854.5 Probability and Statistics 864.6 Graphical Data Descriptors 864.6.1 Histograms of Data 874.6.2 Probability Density Functions 874.6.3 Cumulative Distribution Functions 894.7 Summary Measures of the Distribution of Data 914.7.1 Measures of Central Tendency 914.7.2 Measures of the Dispersion of Data: Variance, Standard Deviation, and Range 944.7.3 Skewness 974.7.4 Kurtosis 984.7.5 Some Summary Comments 994.8 Further Summary Measures of the Distribution of Data 1004.8.1 Coefficient of Variation 1004.8.2 Standard Error of the Mean 1014.8.3 Standard Errors 1024.8.4 Summary Descriptors 1034.9 Conditional Probability and Bayes Theorem 1034.9.1 Basic Probability Concepts 1034.9.2 Bayes’ Theorem 1054.10 Summary 1064.11 References 1064.12 Problems 107Part II Characterization of Common Distributions 1095 The Normal or Gaussian Distribution 1115.1 Introduction 1115.2 The Mathematics of the Normal Distribution 1125.3 Tests for Normality 1155.3.1 Coefficient of Variation Test for Normality 1165.3.2 Skewness and Kurtosis Coefficient Tests for Normality 1195.3.3 Probability Plots 1195.3.4 The Chi]Square Goodness]of]Fit Test 1255.3.5 The Kolmogorov–Smirnov Goodness]of]Fit Test 1285.3.6 The Shapiro–Wilk W Test 1305.3.7 The Shapiro–Francia Test 1345.3.8 Data Transformations 1355.3.9 Summary of Goodness]of]Fit Tests 1355.4 The t]Distribution 1365.5 Extent of Use of the Normal Distribution 1365.6 Summary Comments 1365.7 References 1365.8 Problems 1376 The Lognormal Distribution 1416.1 Introduction 1416.2 Important Features of the Lognormal Distribution 1416.2.1 The Central Limit Theorem 1416.2.2 The Mathematics of the Lognormal Distribution 1426.2.3 Probability Paper 1456.3 Tests for Lognormality 1476.4 Generation of Lognormal Concentration Data 1486.5 References 1496.6 Problems 1507 Other Distributions Useful for Characterizing Environmental Quality Data 1537.1 Introduction 1537.2 The Poisson Distribution 1537.3 Extreme Value Distributions 1557.3.1 The Gumbel Distribution 1567.3.2 Log Pearson Type III Distribution 1587.4 References 1607.5 Problem 161Part III Hypothesis Testing of Environmental Quality 1638 Identification of System Changes and Outliers Using Control Charts 1658.1 Introduction 1658.2 Tolerance Intervals 1668.3 Confidence Intervals 1738.3.1 Confidence Limits Using the Normal Distribution (and the t]Distribution) 1738.3.2 Confidence Limits for Lognormally Distributed Data 1758.3.3 Distribution]Free or Nonparametric Confidence Limits 1758.4 Prediction Interval Characterizations 1768.4.1 The t]Distribution Prediction Intervals 1768.5 Detection of Data Outliers 1788.6 Summary of Approaches for Identifying Data Outliers 1868.7 References 1868.8 Problems 1869 Hypothesis Testing: Testing Statistical Significance of Differences Between Data for Single Constituents 1899.1 Introduction 1899.2 Details of Hypothesis Testing 1919.3 Steps for Significance Testing 1939.4 Student’s t]Test 1939.4.1 Development of the Equations 1939.4.1.1 Comparing One Sample with the Population Mean 1939.4.1.2 One]Sided Versus Two]Sided Tests 1989.4.1.3 Comparing Two Samples for Significance of Difference 1989.4.1.4 Assumptions Implicit in the t]Test 1999.4.2 Effect of Unequal Variances 2019.4.2.1 Pooled Variance 2049.4.3 Effect of Nonnormality on the Hypothesis Test 2079.4.4 Assumption of Independence 2089.4.5 Examples of t]Test Applications 2099.5 Acceptance and Rejection Regions 2119.6 Power of the Discrimination Tests 2139.6.1 Power of the t]Test 2159.7 Extensions of the t]Test 2169.7.1 Satterthwaite’s Modified t]Test 2169.7.2 Cochran’s Approximation to the Behrens–Fisher t]Test 2179.7.3 Paired t]Test 2189.7.4 Summary of Alternative Tests 2239.8 References 2239.9 Problems 22410 Multiple Comparisons Using Parametric Analyses 22710.1 Introduction 22710.2 Analysis of Variance (ANOVA) 22810.2.1 Development of the Null Hypothesis 22810.2.2 Multiple Comparisons and Statistical Power 22910.2.3 One]Way ANOVA and Two]Way Tests of ANOVA 22910.3 Testing for Homogeneity of Variance 23010.3.1 Box Plots 23010.3.2 Levene’s Test 23010.3.3 Bartlett’s Test 23210.4 ANOVA Procedure 23410.5 Two]Way ANOVA 23810.6 Iterations and Data Transformations 23810.7 Concerns with Multiple Comparisons 23910.8 Summary 23910.9 References 24010.10 Problems 24011 Testing Differences Between Monitoring Records When Censored Data Records Exist 24511.1 Introduction 24511.2 Alternative Types of Censoring 24611.3 Alternative Procedures for Statistical Analysis of Environmental Quality Datasets 25011.3.1 Simple Substitution Methods 25011.3.2 Test of Proportions 25111.3.3 Plotting Position Procedure 25311.3.4 Cohen’s Test 25411.3.5 Aitchison’s Method 25611.3.6 Maximum Likelihood Procedure 25811.4 Multiple Detection Limits 25911.5 References 25911.6 Problems 26012 Nonparametric Procedures 26312.1 Introduction 26312.2 Single Comparison Procedures 26412.2.1 Mann–Whitney Test 26412.2.1.1 Use of the Mann–Whitney Test to Test Equality of Variance 26612.2.2 Spearman’s Rank Correlation Coefficient 26612.2.3 Sign Test for Paired Observations 26712.3 Multiple Comparison Procedures 26812.3.1 Kruskal–Wallis Test (or Nonparametric ANOVA) 26812.3.2 Special Consideration of the Kruskal–Wallis Test 27112.4 References 27412.5 Problems 274Appendix A 277Index 309