Sampling methodologies : with applications

Preface 1 Introduction 1.1 Introduction 1.2 Censuses and surveys 1.3 Types of surveys 1.4 Sampling frame 1.5 Questionnaires, interviews, and sample sizes Questionnaires Interviewing methods Sample sizes 1.6 Probability sampling 1.7 Nonprobability sampling Purposive sampling Quota sampling Other types of surveys 1.8 Sampling in practice Demographic and economic surveys Educational surveys Employment and expenditure surveys Health and nutrition surveys Agricultural surveys Marketing surveys Election surveys Public polls and surveys Campus surveys Exercises 2 Simple Random Sampling: Estimation of Means and Totals 2.1 Introduction 2.2 Population total, mean, and variance Total and mean © 2000 by Chapman & Hall/CRC Variance and standard deviation (S.D.) Coefficient of variation (C.V.) 2.3 Sampling without replacement 2.4 Sample mean and variance 2.5 Properties of simple random sampling 2.6 Unbiasedness of the sample mean and variance Sample mean Sample variance 2.7 Standard error of the sample mean 2.8 Distribution of the sample mean 2.9 Confidence limits for the mean 2.10 Estimating the total 2.11 Coefficient of variation of the sample mean 2.12 Sample size determination Precision Error of estimation Confidence width Coefficient of variation Relative error 2.13 Sample sizes for individual groups Exercises Appendix A2 Expected value, variance, and standard deviation Tschebycheff inequality Unbiasedness of the sample variance Variance of the sample mean 3 Simple Random Sampling: Related Topics 3.1 Introduction 3.2 Bias, variance, and mean square error of an estimator 3.3 Precision, accuracy, and consistency 3.4 Covariance and correlation Ungrouped data Grouped data 3.5 Linear combination of two characteristics Linear combination The sum The difference Covariance and correlation of the sample means 3.6 Systematic sampling © 2000 by Chapman & Hall/CRC Sample selection Expectation and variance Comparison with simple random sampling Further properties 3.7 Nonresponse 3.8 Inference regarding the means Population mean Difference of two population means Correlated samples 3.9 Sampling with replacement Exercises Appendix A3 Joint distribution Expectation and variance Covariance and correlation Conditional and unconditional expectations and variances Variance of a linear combination An expression for Cauchy–Schwartz inequality 4 Proportions, Percentages, and Counts 4.1 Introduction 4.2 Two classes 4.3 Total number or count 4.4 Confidence limits 4.5 Sample sizes for specified requirement 4.6 Political and public polls 4.7 Estimation for more than two classes Probabilities of the outcomes Multinomial approximation 4.8 Combining estimates from surveys 4.9 Covariances of proportions 4.10 Difference between proportions 4.11 Sample sizes for more than two classes 4.12 Estimating population size Exercises Appendix A4 Unbiasedness of the sample proportion and variance Binomial approximation S2 © 2000 by Chapman & Hall/CRC 5 Stratification 5.1 Introduction 5.2 Notation 5.3 Estimation for a single stratum 5.4 Estimation of the population mean and total 5.5 Confidence limits 5.6 Proportions and totals 5.7 Population total and proportion 5.8 Proportional and equal division of the sample Proportional allocation Equal distribution 5.9 Neyman allocation 5.10 Gains from Neyman allocation 5.11 Summary on the precision of the allocations 5.12 Sample size allocation to estimate proportions Proportional allocation Neyman allocation 5.13 Sample sizes to estimate means and totals 5.14 Sample sizes to estimate proportions 5.15 Sample sizes for minimizing variance or cost 5.16 Further topics Poststratification Estimating differences of the stratum means Two-phase sampling for stratification Sample size determination for two or more characteristics Strata formation Exercises Appendix A5 An expression for the variance Variance of the estimator for the mean Neyman allocation Optimum allocation 6 Subpopulations 6.1 Introduction 6.2 Totals, means, and variances 6.3 Estimation of the means and their differences Means Difference between two groups 6.4 Totals of subpopulations Known sizes Estimated sizes © 2000 by Chapman & Hall/CRC 6.5 Sample sizes for estimating the means and totals 6.6 Proportions and counts 6.7 Subpopulations of a stratum 6.8 Totals and means of subpopulations in strata 6.9 Stratification: Proportions and counts of subpopulations Exercises 7 Cluster Sampling 7.1 Introduction 7.2 Clusters of equal sizes 7.3 Estimation of the means 7.4 Comparison with simple random sampling 7.5 Estimation of the standard error 7.6 Optimum cluster and sample sizes 7.7 Clusters of unequal size 7.8 Alternative estimation with unequal sizes 7.9 Proportions and percentages Average of the proportions Proportion of the totals or means 7.10 Stratification 7.11 Unequal probability selection A method of selecting the cluster units Probabilities of selecting the units 7.12 Horvitz–Thompson estimator Variance of the estimator Variance estimators Estimators for the mean per unit and the population mean 7.13 Alternative approaches Probabilities proportional to the sum of sizes Randomization approach Selection with probabilities proportional to size and replacement Exercises Appendix A7 Alternative expression for Estimator for Bias of the ratio estimator for the mean Variance of the ratio estimato S2 S2 © 2000 by Chapman & Hall/CRC Expectation and variance of the Horvitz–Thompson estimator Expectation and variance of the PPSS estimator Variance of pps estimator and the variance estimator 8 Sampling in Two Stages 8.1 Introduction 8.2 Equal size first-stage units 8.3 Estimating the mean Estimator for the mean and its variance Estimation of the variance 8.4 Sample size determination 8.5 Unequal size primary units Estimators for the population total and mean Estimation of the variance 8.6 Ratio adjustment for the sizes 8.7 Proportions and totals Equal size PSUs Unequal size PSUs An alternative estimator 8.8 Unequal probability selectio Horvitz-Thompson estimator Selection with unequal probabilities and replacement Exercises Appendix A8 Expected value and variance of the estimator for the mean Expectation and variance of the estimator for the total Estimation of the variance—unequal cluster sizes Variance of the ratio estimator for the total Expectation and variance of Estimator for Variance of and its estimator 9 Ratios and Ratio Estimators 9.1 Introduction Yˆ HT V(Yˆ HT) Yˆ pps © 2000 by Chapman & Hall/CRC 9.2 Bias and variance of the sample ratio 9.3 Confidence limits for the ratio of means 9.4 Ratio estimators for the mean and total 9.5 Confidence limits for the mean and total 9.6 Differences between ratios, means, or totals A common supplementary variable Different supplementary variables 9.7 Regression through the origin and the BLUEs Least squares Superpopulation model for evaluations and estimation 9.8 Ratio estimation vs. stratification 9.9 Ratio estimation with stratification Single stratum The separate ratio estimator The combined ratio estimator Statistical test for the equality of the slopes 9.10 Bias reduction 9.11 Two-phase or double sampling ratio estimators 9.12 Ratio estimator with unequal probability selection 9.13 Multivariate ratio estimator Exercises Appendix A9 Bias of the ratio of two sample means MSE of the ratio of two sample means Variance of the combined ratio estimator 10 Regression Estimation 10.1 Introduction 10.2 The regression estimator 10.3 Estimation from the sample 10.4 Classical linear regression 10.5 Difference between regression estimators Common supplementary variable Different supplementary variables 10.6 Regression estimation vs. stratification 10.7 Stratification and regression estimator Separate estimator Combined regression estimator Preliminary analysis and tests of hypotheses © 2000 by Chapman & Hall/CRC 10.8 Multiple regression estimator 10.9 Double sampling regression estimator 10.10 Generalized regression and calibration estimators Exercises 11 Nonresponse and Remedies 11.1 Introduction 11.2 Effects of survey topics and interviewing methods Subject matter Types of interviewing Types of respondents 11.3 Response rates 11.4 Bias and MSE 11.5 Estimating proportions 11.6 Subsampling the nonrespondents The procedure of Hansen and Hurwitz Estimator and its variance Optimum sample sizes Variance estimation Ratio and regression estimators 11.7 Estimating the missing observations Least squares estimation Alternative predictions 11.8 Ratio and regression estimation Ratio estimation Regression estimation 11.9 Poststratification and weighting Estimators for the mean and total Subpopulations 11.10 Response probabilities and weighting 11.11 Imputation Mean imputation Random duplication Variance estimation Confidence limits Multiple imputation Hot- and cold-deck imputation 11.12 Related topics Efforts to increase response rates Imputation, estimation, and analysis Models for prediction, poststratification, and weighting Qualitative and categorical observations © 2000 by Chapman & Hall/CRC 11.13 Bayesian procedures 11.14 Census undercount Exercises Appendix A11 Variance of the Hansen–Hurwitz estimator Variance estimator for the Hansen–Hurwitz estimator 12 Further Topics 12.1 Introduction 12.2 Linearization 12.3 The jackknife Bias reduction Variance estimation 12.4 The bootstrap Infinite population Finite population Bootstrap for estimating the variance of the sample ratio 12.5 Balanced repeated replication (BRR) 12.6 Small-area estimation Sample estimates Synthetic and composite estimators Best linear unbiased predictor (BLUP) Applications, extensions, and evaluations 12.7 Complex surveys Exercises Appendix A12 The Bayesian approach Appendix Tables Solutions to Exercises References