Composite Sampling (eBook)

Acknowledgements 6
Contents 7
1 Introduction 12
2 Classifying Individual Samples into Oneof Two Categories 19
2.1 Introduction 19
2.2 Presence/Absence Measurements 21
2.2.1 Exhaustive Retesting 22
2.2.2 Sequential Retesting 25
2.2.3 Binary Split Retesting 28
2.2.4 Curtailed Exhaustive Retesting 33
2.2.5 Curtailed Sequential Retesting 37
2.2.6 Curtailed Binary Split Retesting 41
2.2.7 Entropy-Based Retesting 43
2.2.8 Exhaustive Retesting in the Presence of Classification Errors 48
2.2.9 Other Costs 50
2.3 Continuous Response Variables 51
2.3.1 Quantitatively Curtailed Exhaustive Retesting 55
2.3.2 Binary Split Retesting 56
2.3.3 Entropy-Based Retesting 59
2.4 Cost Analysis of Composite Sampling for Classification 59
2.4.1 Introduction 59
2.4.2 General Cost Expression 59
2.4.3 Effect of False Positives and False Negatives on Composite Sample Classification 60
2.4.4 Presence/Absence Measurements 61
2.4.5 Continuous Measurements 63
3 Identifying Extremely Large Observations 64
3.1 Introduction 64
3.2 Prediction of the Sample Maximum 65
3.3 The Sweep-Out Method to Identify the Sample Maximum 67
3.4 Extensive Search of Extreme Values 68
3.5 Application 69
3.6 Two-Way Composite Sampling Design 77
3.7 Illustrative Example 79
3.8 Analysis of Composite Sampling Data Using the Principle of Maximum Entropy 85
3.8.1 Introduction 85
3.8.2 Modeling Composite Sampling Using the Principle of Maximum Entropy 86
3.8.3 When Is the Maximum Entropy Model Reasonable in Practice? 87
4 Estimating Prevalence of a Trait 89
4.1 Introduction 89
4.2 The Maximum Likelihood Estimator 90
4.3 Alternative Estimators 92
4.4 Comparison Between p and p 93
4.5 Estimation of Prevalence in Presence of Measurement Error 93
5 A Bayesian Approach to the Classification Problem 95
5.1 Introduction 95
5.2 Bayesian Updating of p 98
5.3 Minimization of the Expected Relative Cost 101
5.4 Discussion 103
6 Inference on Mean and Variance 105
6.1 Introduction 105
6.2 Notation and Basic Results 106
6.2.1 Notation 106
6.2.2 Basic Results 107
6.3 Estimation Without Measurement Error 109
6.4 Estimation in the Presence of Measurement Error 111
6.5 Maintaining Precision While Reducing Cost 112
6.6 Estimation of 2x and 2 113
6.7 Estimation of Population Variance 114
6.8 Confidence Interval for the Population Mean 117
6.9 Tests of Hypotheses in the Population Mean 118
6.9.1 One-Sample Tests 118
6.9.2 Two-Sample Tests 119
6.10 Applications 120
6.10.1 Comparison of Arithmetic Averages of Soil pH Values with the pH Values of Composite Samples 120
6.10.2 Comparison of Random and Composite Sampling Methods for the Estimation of Fat Contents of Bulk Milk Supplies 120
6.10.3 Optimization of Sampling for the Determination of Mean Radium-226 Concentration in Surface Soil 121
7 Composite Sampling with Random Weights 123
7.1 Introduction 123
7.2 Expected Value, Variance, and Covariance of Bilinear Random Forms 124
7.3 Models for the Weights 126
7.3.1 Assumptions on the First Two Moments 127
7.3.2 Distributional Assumptions 127
7.4 The Model for Composite Sample Measurements 129
7.4.1 Subsampling a Composite Sample 129
7.4.2 Several Composite Samples 132
7.4.3 Subsampling of Several Composite Samples 133
7.4.4 Measurement Error 134
7.5 Applications 136
7.5.1 Sampling Frequency and Comparison of Graband Composite Sampling Programs for Effluents 136
7.5.2 Theoretical Comparison of Grab and Composite Sampling Programs 136
7.5.3 Grab vs. Composite Sampling: A Primer for the Manager and Engineer 137
7.5.4 Composite Samples Overestimate Waste Loads 137
7.5.5 Composite Samples for Foliar Analysis 140
7.5.6 Lateral Variability of Forest Floor Properties Under Second-Growth Douglas-Fir Stands and the Usefulness of Composite SamplingTechniques 141
8 A Linear Model for Estimation with Composite Sample Data 143
8.1 Introduction 143
8.2 Motivation for a Unified Model 144
8.3 The Model 145
8.4 Discussion of the Assumptions 147
8.4.1 The Structural/Sampling Submodel 147
8.4.2 The Compositing/Subsampling Submodel 148
8.4.3 The Structure of the Matrices W, MW, and W 148
8.5 Moments of x and y 154
8.6 Complex Sampling Schemes Before Compositing 154
8.6.1 Segmented Populations 155
8.6.2 Estimating the Mean in Segmented Populations 155
8.6.3 Estimating Variance Components in Segmented Populations 158
8.7 Estimating the Effect of a Binary Factor 161
8.7.1 Fully Segregated Composites 165
8.7.2 Fully Confounded Composites 169
8.8 Elementary Matrices and Kronecker Products 172
8.8.1 Decomposition of Block Matrices 173
8.9 Expectation and Dispersion Matrix When Both W and x Are Random 176
8.9.1 The Expectation of Wx 176
8.9.2 Variance/Covariance Matrix of Wx 180
9 Composite Sampling for Site Characterization and Cleanup Evaluation 182
9.1 Data Quality Objectives 182
9.2 Optimal Composite Designs 185
9.2.1 Cost of a Sampling Program 186
9.2.2 Optimal Allocation of Resources 186
9.2.3 Power of a Test and Determination of Sample Size 187
9.2.4 Algorithms for Determination of Sample Size 188
10 Spatial Structures of Site Characteristics and Composite Sampling 190
10.1 Introduction 190
10.2 Models for Spatial Processes 190
10.2.1 Composite Sampling 194
10.3 Application to Two Superfund Sites 197
10.3.1 The Two Sites 197
10.3.2 Methods 198
10.3.3 Results 199
10.3.4 Discussion 202
10.4 Compositing by Spatial Contiguity 205
10.4.1 Introduction 205
10.4.2 Retesting Strategies 206
10.4.3 Composite Sample-Forming Schemes 207
10.5 Compositing of Ranked Set Samples 208
10.5.1 Ranked Set Sampling 208
10.5.2 Relative Precision of the RSS Estimatorof a Population Mean Relative to Its SRS Estimator 211
10.5.3 Unequal Allocation of Sample Sizes 212
10.5.4 Formation of Homogeneous Composite Samples 213
11 Composite Sampling of Soils and Sediments 215
11.1 Detection of Contamination 215
11.1.1 Detecting PCB Spills 215
11.1.2 Compositing Strategy for Analysis of Samples 217
11.2 Estimation of the Average Level of Contamination 219
11.2.1 Estimation of the Average PCB Concentrationon the Spill Area 219
11.2.2 Onsite Surface Soil Sampling for PCBat the Armagh Site 220
11.2.3 The Armagh Site 221
11.2.4 Simulating Composite Samples 224
11.2.5 Locating Individual Samples with High PCB Concentrations 227
11.3 Estimation of Trace Metal Storage in Lake St. Clair Post-settlement Sediments Using Composite Samples 228
12 Composite Sampling of Liquids and Fluids 232
12.1 Comparison of Random and Composite Sampling Methodsfor the Estimation of Fat Content of Bulk Milk Supplies 232
12.1.1 Experiment 232
12.1.2 Estimation Methods 233
12.1.3 Results 233
12.1.4 Composite Compared with Yield-Weighted Estimate of Fat Percentage 234
12.2 Composite Sampling of Highway Runoff 234
12.3 Composite Samples Overestimate Waste Loads 237
13 Composite Sampling and Indoor Air Pollution 240
13.1 Household Dust Samples 240
14 Composite Sampling and Bioaccumulation 243
14.1 Example: National Human Adipose Tissue Survey 245
14.2 Results from the Analysis of 1987 NHATS Data 245
Glossary and Terminology 247
Bibliography 253
Index 271