United States Office of Environmental EPA/240/R-02/005 Environmental Protection Information December 2002 Agency Washington, DC 20460 Guidance on Choosing a Sampling Design for Environmental Data Collection for Use in Developing a Quality Assurance Project Plan EPA QA/G-5S QualityQuality FOREWORD This document, Guidance for Choosing a Sampling Design for Environmental Data Collection (EPA QA/G-5S), will provide assistance in developing an effective QA Project Plan as described in Guidance for QA Project Plans (EPA QA/G-5) (EPA 1998b). QA Project Plans are one component of EPA’s Quality System. This guidance is different from most guidance in that it is not meant to be read in a linear or continuous fashion, but to be used as a resource or reference document. This guidance is a “tool-box” of statistical designs that can be examined for possible use as the QA Project Plan is being developed. EPA works every day to produce quality information products. The information used in these products are based on Agency processes to produce quality data, such as the quality system described in this document. Therefore, implementation of the activities described in this document is consistent with EPA’s Information Quality Guidelines and promotes the dissemination of quality technical, scientific, and policy information and decisions. This document provides guidance to EPA program managers, analysts, and planning teams on statistically based sampling schemes. It does not impose legally binding requirements and the methods described may not apply to a particular situation based on the circumstances. The Agency retains the discretion to adopt approaches on a case-by-case basis that may differ from the techniques described in this guidance. EPA may periodically revise this guidance without public notice. It is the intent of the Quality Staff to revise the document to include: new techniques, corrections, and suggestions for alternative techniques. Future versions of this document will include examples in depth that illustrate the strengths of each statistical design. This document is one of the U.S. Environmental Protection Agency Quality System Series documents. These documents describe the EPA policies and procedures for planning, implementing, and assessing the effectiveness of a Quality System. Questions regarding this document or other Quality System Series documents should be directed to the Quality Staff: U.S. Environmental Protection Agency Quality Staff (2811R) 1200 Pennsylvania Ave., NW Washington, D.C. 20460 Phone: (202) 564-6830 Fax: (202) 565-2441 E-mail: [email protected] Copies of EPA Quality System Series documents may be obtained from the Quality Staff or by downloading them from epa.gov/quality/index.html. Final EPA QA/G-5S i December 2002 Final EPA QA/G-5S ii December 2002 TABLE OF CONTENTS Page 1. INTRODUCTION ......................................................1 1.1 WHY IS SELECTING AN APPROPRIATE SAMPLING DESIGN IMPORTANT? ....................................................1 1.2 WHAT TYPES OF QUESTIONS WILL THIS GUIDANCE ADDRESS? .......2 1.3 WHO CAN BENEFIT FROM THIS DOCUMENT? .......................3 1.4 HOW DOES THIS DOCUMENT FIT INTO THE EPA QUALITY SYSTEM? ..4 1.5 WHAT SOFTWARE SUPPLEMENTS THIS GUIDANCE? .................5 1.6 WHAT ARE THE LIMITATIONS OR CAVEATS TO THIS DOCUMENT? ....5 1.7 HOW IS THIS DOCUMENT ORGANIZED? ............................6 2. OVERVIEW OF SAMPLING DESIGNS ....................................7 2.1 OVERVIEW ......................................................7 2.2 SAMPLING DESIGN CONCEPTS AND TERMS ........................8 2.3 PROBABILISTIC AND JUDGMENTAL SAMPLING DESIGNS ...........10 2.4 TYPES OF SAMPLING DESIGNS ...................................11 2.4.1 Judgmental Sampling .........................................12 2.4.2 Simple Random Sampling ......................................12 2.4.3 Stratified Sampling ...........................................13 2.4.4 Systematic and Grid Sampling ..................................13 2.4.5 Ranked Set Sampling .........................................14 2.4.6 Adaptive Cluster Sampling .....................................15 2.4.7 Composite Sampling .........................................15 3. THE SAMPLING DESIGN PROCESS ....................................17 3.1 OVERVIEW .....................................................17 3.2. INPUTS TO THE SAMPLING DESIGN PROCESS ......................17 3.3 STEPS IN THE SAMPLING DESIGN PROCESS .......................22 3.4 SELECTING A SAMPLING DESIGN .................................24 4. JUDGMENTAL SAMPLING ............................................27 4.1 OVERVIEW .....................................................27 4.2 APPLICATION ..................................................27 4.3 BENEFITS ......................................................28 4.4 LIMITATIONS ...................................................28 4.5 IMPLEMENTATION ..............................................28 4.6 RELATIONSHIP TO OTHER SAMPLING DESIGNS ....................29 Final EPA QA/G-5S iii December 2002 Page 4.7 EXAMPLES OF SUCCESSFUL USE .................................30 4.8 EXAMPLES OF UNSUCCESSFUL USE ..............................31 5. SIMPLE RANDOM SAMPLING .........................................33 5.1 OVERVIEW .....................................................33 5.2 APPLICATION ..................................................33 5.3 BENEFITS ......................................................34 5.4 LIMITATIONS ...................................................34 5.5 IMPLEMENTATION ..............................................35 5.6 RELATIONSHIP TO OTHER SAMPLING DESIGNS ....................39 5.7 EXAMPLES .....................................................40 APPENDIX 5. SAMPLE SIZE TABLES .....................................44 6. STRATIFIED SAMPLING ..............................................51 6.1 OVERVIEW .....................................................51 6.2 APPLICATION ..................................................51 6.3 BENEFITS ......................................................52 6.4 LIMITATIONS ...................................................53 6.5 IMPLEMENTATION ..............................................53 6.6 RELATIONSHIP TO OTHER SAMPLING DESIGNS ....................54 6.7 EXAMPLE ......................................................55 APPENDIX 6-A. FORMULAE FOR ESTIMATING SAMPLE SIZE ..............57 APPENDIX 6-B. DALENIUS-HODGES PROCEDURE ........................59 APPENDIX 6-C. CALCULATING THE MEAN AND STANDARD ERROR ........60 7. SYSTEMATIC/GRID SAMPLING .......................................63 7.1 OVERVIEW .....................................................63 7.2 APPLICATION ..................................................64 7.3 BENEFITS ......................................................67 7.4 LIMITATIONS ...................................................68 7.5 IMPLEMENTATION ..............................................69 7.6 RELATIONSHIP TO OTHER SAMPLING DESIGNS ....................71 7.7 EXAMPLES .....................................................72 8. RANKED SET SAMPLING .............................................77 8.1 OVERVIEW .....................................................77 8.2 APPLICATION ..................................................80 8.3 BENEFITS ......................................................80 8.4 LIMITATIONS ...................................................82 Final EPA QA/G-5S iv December 2002 Page 8.5 IMPLEMENTATION ..............................................83 8.6 EXAMPLES ....................................................84 APPENDIX 8-A. USING RANKED SET SAMPLING .........................87 9. ADAPTIVE CLUSTER SAMPLING .....................................103 9.1 OVERVIEW ....................................................103 9.2 APPLICATION .................................................103 9.3 BENEFITS .....................................................104 9.4 LIMITATIONS ..................................................104 9.5 IMPLEMENTATION .............................................106 9.6 RELATIONSHIP TO OTHER SAMPLING DESIGNS ...................108 9.7 EXAMPLE .....................................................109 APPENDIX 9-A. ESTIMATORS OF MEAN AND VARIANCE .................111 10. COMPOSITE SAMPLING .............................................119 10.1 OVERVIEW ....................................................119 10.2 COMPOSITE SAMPLING FOR ESTIMATING A MEAN ................122 10.2.1 Overview .................................................122 10.2.2 Application ...............................................124 10.2.3 Benefits ..................................................125 10.2.4 Limitations ................................................125 10.2.5 Implementation .............................................127 10.2.6 Relationship to Other Sampling Designs ..........................130 10.2.7 Examples .................................................133 10.3 COMPOSITE SAMPLING FOR ESTIMATING A POPULATION PROPORTION ..................................................133 10.3.1 Overview .................................................133 10.3.2 Application ...............................................134 10.3.3 Benefits ..................................................135 10.3.4 Limitations ................................................135 10.3.5 Implementation .............................................135 10.3.6 Relationship to Other Sampling Designs