Sampling Techniques

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ISBN: 9780471162407 | 047116240X
Cover: Paperback
Copyright: 1/16/1991

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Clearly demonstrates a wide range of sampling methods now in use by governments, in business, market and operations research, social science, medicine, public health, agriculture, and accounting. Gives proofs of all the theoretical results used in modern sampling practice. New topics in this edition include the approximate methods developed for the problem of attaching standard errors or confidence limits to nonlinear estimates made from the results of surveys with complex plans.

CHAPTER 1 INTRODUCTION

(17)

1.1 Advantages of the Sampling Method

(1)

1.2 Some Uses of Sample Surveys

(2)

1.3 The Principal Steps in a Sample Survey

(4)

1.4 The Role of Sampling Theory

(1)

1.5 Probability Sampling

(1)

1.6 Alternatives to Probability Sampling

(1)

1.7 Use of the Normal Distribution

(1)

1.8 Bias and Its Effects

(3)

1.9 The Mean Square Error

(1)

Exercises

(2)

CHAPTER 2 SIMPLE RANDOM SAMPLING

(32)

2.1 Simple Random Sampling

(1)

2.2 Selection of a Simple Random Sample

(1)

2.3 Definitions and Notation

(1)

2.4 Properties of the Estimates

(2)

2.5 Variances of the Estimates

(1)

2.6 The Finite Population Correction

(1)

2.7 Estimation of the Standard Error from a Sample

(2)

2.8 Confidence Limits

(1)

2.9 An Alternative Method of Proof

(1)

2.10 Random Sampling with Replacement

(1)

2.11 Estimation of a Ratio

(4)

2.12 Estimates of Means Over Subpopulations

(1)

2.13 Estimates of Totals Over Subpopulations

(4)

2.14 Comparisons Between Domain Means

(1)

2.15 Validity of the Normal Approximation

(5)

2.16 Linear Estimators of the Population Mean

(1)

Exercises

(5)

CHAPTER 3 SAMPLING PROPORTIONS AND PERCENTAGES

(22)

3.1 Qualitative Characteristics

(1)

3.2 Variances of the Sample Estimates

(3)

3.3 The Effect of Pon the Standard Errors

(2)

3.4 The Binomial Distribution

(1)

3.5 The Hypergeometric Distribution

(2)

3.6 Confidence Limits

(3)

3.7 Classification into More than Two Classes

(1)

3.8 Confidence Limits with More than Two Classes

(1)

3.9 The Conditional Distribution of p

(2)

3.10 Proportions and Totals Over Subpopulations

(1)

3.11 Comparisons Between Different Domains

(1)

3.12 Estimation of Proportions in Cluster Sampling

(4)

Exercises

(4)

CHAPTER 4 THE ESTIMATION OF SAMPLE SIZE

(17)

4.1 A Hypothetical Example

(1)

4.2 Analysis of the Problem

(1)

4.3 The Specification of Precision

(1)

4.4 The Formula for n in Sampling for Proportions

(1)

4.5 Rare Items--Inverse Sampling

(1)

4.6 The Formula for n with Continuous Data

(1)

4.7 Advance Estimates of Population Variances

(3)

4.8 Sample Size with More than One Item

(1)

4.9 Sample Size when Estimates Are Wanted for Subdivisions of the Population

(1)

4.10 Sample Size in Decision Problems

(2)

4.11 The Design Effect (Deff)

(1)

Exercises

(3)

CHAPTER 5 STRATIFIED RANDOM SAMPLING

(26)

5.1 Description

(1)

5.2 Notation

(1)

5.3 Properties of the Estimates

(4)

5.4 The Estimated Variance and Confidence Limits

(1)

5.5 Optimum Allocation

(3)

5.6 Relative Precision of Stratified Random and Simple Random Sampling

(2)

5.7 When Does Stratification Produce Large Gains in Precision?

101

(3)

5.8 Allocation Requiring More than 100 Per Cent Sampling

104

(1)

5.9 Estimation of Sample Size with Continuous Data

105

(2)

5.10 Stratified Sampling for Proportions

107

(2)

5.11 Gains in Precision in Stratified Sampling for Proportions

109

(1)

5.12 Estimation of Sample Size with Proportions

110

(1)

Exercises

111

(4)

CHAPTER 5A FURTHER ASPECTS OF STRATIFIED SAMPLING

115

(35)

5A.1 Effects of Deviations from the Optimum Allocation

115

(2)

5A.2 Effects of Errors in the Stratum Sizes

117

(2)

5A.3 The Problem of Allocation with More than One Item

119

(2)

5A.4 Other Methods of Allocation with More than One Item

121

(3)

5A.5 Two-Way Stratification with Small Samples

124

(2)

5A.6 Controlled Selection

126

(1)

5A.7 The Construction of Strata

127

(5)

5A.8 Number of Strata

132

(2)

5A.9 Stratification After Selection of the Sample (Poststratification)

134

(1)

5A.10 Quota Sampling

135

(1)

5A.11 Estimation from a Sample of the Gain Due to Stratification

136

(2)

5A.12 Estimation of Variance with One Unit per Stratum

138

(2)

5A.13 Strata as Domains of Study

140

(2)

5A.14 Estimating Totals Means Over Subpopulations

142

(2)

5A.15 Sampling from Two Frames

144

(2)

Exercises

146

(4)

CHAPTER 6 RATIO ESTIMATORS

150

(39)

6.1 Methods of Estimation

150

(1)

6.2 The Ratio Estimate

150

(3)

6.3 Approximate Variance of the Ratio Estimate

153

(2)

6.4 Estimation of the Variance from a Sample

155

(1)

6.5 Confidence Limits

156

(1)

6.6 Comparison of the Ratio Estimate with Mean per Unit

157

(1)

6.7 Conditions Under Which the Ratio Estimate Is a Best Linear Unbiased Estimator

158

(2)

6.8 Bias of the Ratio Estimate

160

(2)

6.9 Accuracy of the Formulas for the Variance and Estimated Variance

162

(2)

6.10 Ratio Estimates in Stratified Random Sampling

164

(1)

6.11 The Combined Ratio Estimate

165

(2)

6.12 Comparison of the Combined and Separate Estimates

167

(2)

6.13 Short-Cut Computation of the Estimated Variance

169

(3)

6.14 Optimum Allocation with a Ratio Estimate

172

(2)

6.15 Unbiased Ratio-type Estimates

174

(3)

6.16 Comparison of the Methods

177

(1)

6.17 Improved Estimation of Variance

178

(2)

6.18 Comparison of Two Ratios

180

(3)

6.19 Ratio of Two Ratios

183

(1)

6.20 Multivariate Ratio Estimates

184

(2)

6.21 Product Estimators

186

(1)

Exercises

186

(3)

CHAPTER 7 REGRESSION ESTIMATORS

189

(16)

7.1 The Linear Regression Estimate

189

(1)

7.2 Regression Estimates with Preassigned b

190

(3)

7.3 Regression Estimates when b Is Computed from the Sample

193

(2)

7.4 Sample Estimate of Variance

195

(1)

7.5 Large-Sample Comparison with the Ratio Estimate and the Mean per Unit

195

(2)

7.6 Accuracy of the Large-Sample Formulas for V(y(tr)) and v(y(tr))

197

(1)

7.7 Bias of the Linear Regression Estimate

198

(1)

7.8 The Linear Regression Estimator Under a Linear Regression Model

199

(1)

7.9 Regression Estimates in Stratified Sampling

200

(1)

7.10 Regression Coefficients Estimated from the Sample

201

(2)

7.11 Comparison of the Two Types of Regression Estimate

203

(1)

Exercises

203

(2)

CHAPTER 8 SYSTEMATIC SAMPLING

205

(28)

8.1 Description

205

(2)

8.2 Relation to Cluster Sampling

207

(1)

8.3 Variance of the Estimated Mean

207

(5)

8.4 Comparison of Systematic with Stratified Random Sampling

212

(1)

8.5 Populations in "Random" Order

212

(2)

8.6 Populations with Linear Trend

214

(2)

8.7 Methods for Populations with Linear Trends

216

(1)

8.8 Populations with Periodic Variation

217

(2)

8.9 Autocorrelated Populations

219

(2)

8.10 Natural Populations

221

(2)

8.11 Estimation of the Variance from a Single Sample

223

(3)

8.12 Stratified Systematic Sampling

226

(1)

8.13 Systematic Sampling in Two Dimensions

227

(2)

8.14 Summary

229

(2)

Exercises

231

(2)

CHAPTER 9 SINGLE-STAGE CLUSTER SAMPLING: CLUSTERS OF EQUAL SIZES

233

(16)

9.1 Reasons for Cluster Sampling

233

(1)

9.2 A Simple Rule

234

(4)

9.3 Comparisons of Precision Made from Survey Data

238

(2)

9.4 Variance in Terms of Intracluster Correlation

240

(3)

9.5 Variance Functions

243

(1)

9.6 A Cost Function

244

(2)

9.7 Cluster Sampling for Proportions

246

(1)

Exercises

247

(2)

CHAPTER 9A SINGLE-STAGE CLUSTER SAMPLING: CLUSTERS OF UNEQUAL SIZES

249

(25)

9A.1 Cluster Units of Unequal Sizes

249

(1)

9A.2 Sampling with Probability Proportional to Size

250

(2)

9A.3 Selection with Unequal Probabilities with Replacement

252

(3)

9A.4 The Optimum Measure of Size

255

(1)

9A.5 Relative Accuracies of Three Techniques

255

(3)

9A.6 Sampling with Unequal Probabilities Without Replacement

258

(1)

9A.7 The Horvitz-Thompson Estimator

259

(2)

9A.8 Brewer's Method

261

(2)

9A.9 Murthy's Method

263

(2)

9A.10 Methods Related to Systematic Sampling

265

(1)

9A.11 The Rao, Hartley, Cochran Method

266

(1)

9A.12 Numerical Comparisons

267

(3)

9A.13 Stratified and Ratio Estimates

270

(2)

Exercises

272

(2)

CHAPTER 10 SUBSAMPLING WITH UNITS OF EQUAL SIZE

274

(18)

10.1 Two-Stage Sampling

274

(1)

10.2 Finding Means and Variances in Two-Stage Sampling

275

(1)

10.3 Variance of the Estimated Mean in Two-Stage Sampling

276

(2)

10.4 Sample Estimation of the Variance

278

(1)

10.5 The Estimation of Proportions

279

(1)

10.6 Optimum Sampling and Subsampling Fractions

280

(3)

10.7 Estimation of m(opt) from a Pilot Survey

283

(2)

10.8 Three-Stage Sampling

285

(3)

10.9 Stratified Sampling of the Units

288

(1)

10.10 Optimum Allocation with Stratified Sampling

289

(1)

Exercises

290

(2)

CHAPTER 11 SUBSAMPLING WITH UNITS OF UNEQUAL SIZES

292

(35)

11.1 Introduction

292

(1)

11.2 Sampling Methods when n = 1

293

(4)

11.3 Sampling with Probability Proportional to Estimated Size

297

(2)

11.4 Summary of Methods for n = 1

299

(1)

11.5 Sampling Methods When n is greater than 1

300

(1)

11.6 Two Useful Results

300

(3)

11.7 Units Selected with Equal Probabilities: Unbiased Estimator

303

(1)

11.8 Units Selected with Equal Probabilities: Ratio to Size Estimate

303

(3)

11.9 Units Selected with Unequal Probabilities with Replacement: Unbiased Estimator

306

(2)

11.10 Units Selected Without Replacement

308

(2)

11.11 Comparison of the Methods

310

(1)

11.12 Ratios to Another Variable

311

(2)

11.13 Choice of Sampling and Subsampling Fractions. Equal Probabilities

313

(1)

11.14 Optimum Selection Probabilities and Sampling and Subsampling Rates

314

(2)

11.15 Stratified Sampling. Unbiased Estimators

316

(1)

11.16 Stratified Sampling. Ratio Estimates

317

(1)

11.17 Nonlinear Estimators in Complex Surveys

318

(1)

11.18 Taylor Series Expansion

319

(1)

11.19 Balanced Repeated Replications

320

(1)

11.20 The Jackknife Method

321

(1)

11.21 Comparison of the Three Approaches

322

(2)

Exercises

324

(3)

CHAPTER 12 DOUBLE SAMPLING

327

(32)

12.1 Description of the Technique

327

(1)

12.2 Double Sampling for Stratification

327

(4)

12.3 Optimum Allocation

331

(2)

12.4 Estimated Variance in Double Sampling for Stratification

333

(2)

12.5 Double Sampling for Analytical Comparisons

335

(3)

12.6 Regression Estimators

338

(3)

12.7 Optimum Allocation and Comparison with Single Sampling

341

(2)

12.8 Estimated Variance in Double Sampling for Regression

343

(1)

12.9 Ratio Estimators

343

(1)

12.10 Repeated Sampling of the Same Population

344

(2)

12.11 Sampling on Two Occasions

346

(2)

12.12 Sampling on More than Two Occasions

348

(3)

12.13 Simplifications and Further Developments

351

(4)

Exercises

355

(4)

CHAPTER 13 SOURCES OF ERROR IN SURVEYS

359

(41)

13.1 Introduction

359

(1)

13.2 Effects of Nonresponse

359

(5)

13.3 Types of Nonresponse

364

(1)

13.4 Call-backs

365

(2)

13.5 A Mathematical Model of the Effects of Call-backs

367

(3)

13.6 Optimum Sampling Fraction Among the Nonrespondents

370

(4)

13.7 Adjustments for Bias Without Call-backs

374

(3)

13.8 A Mathematical Model for Errors of Measurement

377

(2)

13.9 Effects of Constant Bias

379

(1)

13.10 Effects of Errors that Are Uncorrelated Within the Sample

380

(3)

13.11 Effects of Intrasample Correlation Between Errors of Measurement

383

(1)

13.12 Summary of the Effects of Errors of Measurement

384

(1)

13.13 The Study of Errors of Measurement

384

(2)

13.14 Repeated Measurement of Subsamples

386

(2)

13.15 Interpenetrating Subsamples

388

(3)

13.16 Combination of Interpenetration and Repeated Measurement

391

(1)

13.17 Sensitive Questions: Randomized Responses

392

(1)

13.18 The Unrelated Second Question

393

(2)

13.19 Summary

395

(1)

Exercises

396

(4)

References

400

(12)

Answers to Exercises

412

(7)

Author Index

419

(3)

Subject Index

422

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Sampling Techniques

Summary

Author Biography

Table of Contents

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