Composite Sampling

by Patil, Ganapati P.; Gore, Sharad D.; Taillie, Charles

• ISBN13: 9781441976277
• ISBN10: 1441976272
• Format: Hardcover
• Copyright: 2010-12-23
• Publisher: Springer Verlag

Summary

Sampling consists of selection, acquisition, and quantification of a part of the population. While selection and acquisition apply to physical sampling units of the population, quantification pertains only to the variable of interest, which is a particular characteristic of the sampling units. A sampling procedure is expected to provide a sample that is representative with respect to some specified criteria. Composite sampling, under idealized conditions, incurs no loss of information for estimating the population means. But an important limitation to the method has been the loss of information on individual sample values, such as, the extremely large value. In many of the situations where individual sample values are of interest or concern, composite sampling methods can be suitably modified to retrieve the information on individual sample values that may be lost due to compositing. This book presents statistical solutions to issues that arise in the context of applications of composite sampling.

Table of Contents

Introduction	p. 1
Classifying Individual Samples into One of Two Categories	p. 9
Introduction	p. 9
Presence/Absence Measurements	p. 11
Exhaustive Retesting	p. 12
Sequential Retesting	p. 15
Binary Split Retesting	p. 18
Curtailed Exhaustive Retesting	p. 23
Curtailed Sequential Retesting	p. 27
Curtailed Binary Split Retesting	p. 31
Entropy-Based Retesting	p. 33
Exhaustive Retesting in the Presence of Classification Errors	p. 38
Other Costs	p. 40
Continuous Response Variables	p. 41
Quantitatively Curtailed Exhaustive Retesting	p. 45
Binary Split Retesting	p. 46
Entropy-Based Retesting	p. 49
Cost Analysis of Composite Sampling for Classification	p. 49
Introduction	p. 49
General Cost Expression	p. 49
Effect of False Positives and False Negatives on Composite Sample Classification	p. 50
Presence/Absence Measurements	p. 51
Continuous Measurements	p. 53
Identifying Extremely Large Observations	p. 55
Introduction	p. 55
Prediction of the Sample Maximum	p. 56
The Sweep-Out Method to Identify the Sample Maximum	p. 58
Extensive Search of Extreme Values	p. 59
Application	p. 60
Two-Way Composite Sampling Design	p. 68
Illustrative Example	p. 70
Analysis of Composite Sampling Data Using the Principle of Maximum Entropy	p. 76
Introduction	p. 76
Modeling Composite Sampling Using the Principle of Maximum Entropy	p. 77
When Is the Maximum Entropy Model Reasonable in Practice?	p. 78
Estimating Prevalence of a Trait	p. 81
Introduction	p. 81
The Maximum Likelihood Estimator	p. 82
Alternative Estimators	p. 84
Comparison Between p and p	p. 85
Estimation of Prevalence in Presence of Measurement Error	p. 85
A Bayesian Approach to the Classification Problem	p. 87
Introduction	p. 87
Bayesian Updating of p	p. 90
Minimization of the Expected Relative Cost	p. 93
Discussion	p. 95
Inference on Mean and Variance	p. 97
Introduction	p. 97
Notation and Basic Results	p. 98
Notation	p. 98
Basic Results	p. 99
Estimation Without Measurement Error	p. 101
Estimation in the Presence of Measurement Error	p. 103
Maintaining Precision While Reducing Cost	p. 104
Estimation of ¿x2 and ¿¿2	p. 105
Estimation of Population Variance	p. 106
Confidence Interval for the Population Mean	p. 109
Tests of Hypotheses in the Population Mean	p. 110
One-Sample Tests	p. 110
Two-Sample Tests	p. 111
Applications	p. 112
Comparison of Arithmetic Averages of Soil pH Values with the pH Values of Composite Samples	p. 112
Comparison of Random and Composite Sampling Methods for the Estimation of Fat Contents of Bulk Milk Supplies	p. 112
Optimization of Sampling for the Determination of Mean Radium-226 Concentration in Surface Soil	p. 113
Composite Sampling with Random Weights	p. 115
Introduction	p. 115
Expected Value, Variance, and Covariance of Bilinear Random Forms	p. 116
Models for the Weights	p. 118
Assumptions on the First Two Moments	p. 119
Distributional Assumptions	p. 119
The Model for Composite Sample Measurements	p. 121
Subsampling a Composite Sample	p. 121
Several Composite Samples	p. 124
Subsampling of Several Composite Samples	p. 125
Measurement Error	p. 126
Applications	p. 128
Sampling Frequency and Comparison of Grab and Composite Sampling Programs for Effluents	p. 128
Theoretical Comparison of Grab and Composite Sampling Programs	p. 128
Grab vs. Composite Sampling: A Primer for the Manager and Engineer	p. 129
Composite Samples Overestimate Waste Loads	p. 129
Composite Samples for Foliar Analysis	p. 132
Lateral Variability of Forest Floor Properties Under Second-Growth Douglas-Fir Stands and the Usefulness of Composite Sampling Techniques	p. 133
A Linear Model for Estimation with Composite Sample Data	p. 135
Introduction	p. 135
Motivation for a Unified Model	p. 136
The Model	p. 137
Discussion of the Assumptions	p. 139
The Structural/Sampling Submodel	p. 139
The Compositing/Subsampling Submodel	p. 140
The Structure of the Matrices W, Mw, and ¿w	p. 140
Moments of x and y	p. 146
Complex Sampling Schemes Before Compositing	p. 146
Segmented Populations	p. 147
Estimating the Mean in Segmented Populations	p. 147
Estimating Variance Components in Segmented Populations	p. 150
Estimating the Effect of a Binary Factor	p. 153
Fully Segregated Composites	p. 157
Fully Confounded Composities	p. 161
Elementary Matrices and Kronecker Products	p. 164
Decomposition of Block Matrices	p. 165
Expectation and Dispersion Matrix When Both W and x Are Random	p. 168
The Expectation of W x	p. 168
Variance/Covariance Matrix of W x	p. 172
Composite Sampling for Site Characterization and Cleanup Evaluation	p. 175
Data Quality Objectives	p. 175
Optimal Composite Designs	p. 178
Cost of a Sampling Program	p. 179
Optimal Allocation of Resources	p. 179
Power of a Test and Determination of Sample Size	p. 180
Algorithms for Determination of Sample Size	p. 181
Spatial Structures of Site Characteristics and Composite Sampling	p. 183
Introduction	p. 183
Models for Spatial Processes	p. 183
Composite Sampling	p. 187
Application to Two Superfund Sites	p. 190
The Two Sites	p. 190
Methods	p. 191
Results	p. 192
Discussion	p. 195
Compositing by Spatial Contiguity	p. 198
Introduction	p. 198
Retesting Strategies	p. 199
Composite Sample-Forming Schemes	p. 200
Compositing of Ranked Set Samples	p. 201
Ranked Set Sampling	p. 201
Relative Precision of the RSS Estimator of a Population Mean Relative to Its SRS Estimator	p. 204
Unequal Allocation of Sample Sizes	p. 205
Formation of Homogeneous Composite Samples	p. 206
Composite Sampling of Soils and Sediments	p. 209
Detection of Contamination	p. 209
Detecting PCB Spills	p. 209
Compositing Strategy for Analysis of Samples	p. 211
Estimation of the Average Level of Contamination	p. 213
Estimation of the Average PCB Concentration on the Spill Area	p. 213
Onsite Surface Soil Sampling for PCB at the Armagh Site	p. 214
The Armagh Site	p. 215
Simulating Composite Samples	p. 218
Locating Individual Samples with High PCB Concentrations	p. 221
Estimation of Trace Metal Storage in Lake St. Clair Post-settlement Sediments Using Composite Samples	p. 222
Composite Sampling of Liquids and Fluids	p. 227
Comparison of Random and Composite Sampling Methods for the Estimation of Fat Content of Bulk Milk Supplies	p. 227
Experiment	p. 227
Estimation Methods	p. 228
Results	p. 228
Composite Compared with Yield-Weighted Estimate of Fat Percentage	p. 229
Composite Sampling of Highway Runoff	p. 229
Composite Samples Overestimate Waste Loads	p. 232
Composite Sampling and Indoor Air Pollution	p. 235
Household Dust Samples	p. 235
Composite Sampling and Bioaccumulation	p. 239
Example: National Human Adipose Tissue Survey	p. 241
Results from the Analysis of 1987 NHATS Data	p. 241
Glossary and Terminology	p. 243
Bibliography	p. 249
Index	p. 267
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