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## Sampling techniques / William G. Cochran

Editor: New York : Wiley, Edición: 2nd edDescripción: 413 p. : il. ; 24 cmTema(s): Sampling (Statistics)Otra clasificación: *CODIGO*
Contenidos:
```I CHAPTER --
I 1 INTRODUCTION  --
1.1 Advantages of the Sampling Method  --
1.2 Some Uses of Sample Surveys  --
1.3 The Principal Steps in a Sample Survey  --
1.4 The Role of Sampling Theory  --
1.5 Probability Sampling  --
1.6 Use of the Normal Distribution  --
1.7 Bias and Its Effects --
1.8 The Mean Square Error  --
Exercises l6 --
References  --
2 SIMPLE RANDOM SAMPLING  --
2.1 Simple Random Sampling  --
2.2 Definitions and Notation  --
2.3 Properties of the Estimates  --
2.4 Variances of the Estimates  --
2.5 The Finite Population Correction  --
2.6 Estimation of the Standard Error from a Sample  --
2.7 Confidence Limits  --
2.8 An Alternative Method of Proof  --
2.9 Estimation of a Ratio  --
2.10 Estimates of Means Over Subpopulations  --
2.11 Estimates of Totals Over Subpopulations  --
2.12 Comparisons between Domain Means  --
2.13 Validity of the Normal Approximation --
2.14 Effect of Non-normality on the Estimated Variance  --
Exercises  --
References  --
3 SAMPLING FOR PROPORTIONS AND PERCENTAGES  --
3.1 Qualitative Characteristics  --
3.2 Variances of the Sample Estimates  --
3.3 The Effect of P on the Standard Errors  --
3.4 The Binomial Distribution  --
3.5 The Hypergeometric Distribution  --
3.6 Confidence Limits  --
3.7 Classification into More than Two Classes  --
3.8 Confidence Limits When There Are More than Two Classes  --
3.9 The Conditional Distribution of p  --
3.10 Proportions and Totals Over Subpopulations  --
3.11 Comparisons between Different Domains  --
3.12 Estimation of Proportions in Cluster Sampling  --
Exercises  --
References  --
THE ESTIMATION OF SAMPLE SIZE  --
4.1 A Hypothetical Example  --
4.2 Analysis of the Problem  --
4.3 The Specification of Precision  --
4.4 The Formula for n in Sampling for Proportions  --
4.5 The Formula for n with Continuous Data  --
4.6 Advance Estimates of Population Variances  --
4.7 Sample Size with More than One Item  --
4.8 Sample Size when Estimates Are Wanted for Subdivisions of the Population  --
4.9Sample Size in Decision Problems  --
Exercises  --
References  --
5 STRATIFIED RANDOM SAMPLING  --
5.1 Description  --
5.2 Notation  --
5.3 Properties of the Estimates  --
5.4 The Estimated Variance and Confidence Limits  --
5.5 Optimum Allocation  --
5.6 Relative Precision of Stratified Random and Simple Random Sampling  --
5.7 When Does Stratification Produce Large Gains in Precision  --
5.8 Allocation Requiring More than 100 Per Cent Sampling  --
5.9 Estimation of Sample Size with Continuous Data  --
5.10 Stratified Sampling for Proportions  --
5.11 Gains in Precision in Stratified Sampling for Proportions  --
5.12 Estimation of Sample Size with Proportions  --
Exercises  --
References  --
5A FURTHIR ASPECTS OE STRATIFIED SAMPLING  --
5A.1 Effects of Deviations from the Optimum Allocation  --
5A.2 Effects of Errors in the Stratum Sizes  --
5A.3 The Problem of Allocation with More than One Item  --
5A.4 Other Methods with More than One Item  --
5A.5 Two-Way Stratification with Small Samples  --
5A.6 The Construction of Strata  --
5A.7 Number of Strata  --
5A.8 Stratification After Selection of the Sample  --
5A.9 Quota Sampling  --
5A.10 Estimation from a Sample of the Gain Due to Stratification  --
5A.11 Estimation of Variance with One Unit per Stratum  --
5A.12 Short-Cuts in the Computation of Standard Errors  --
5A.13 Strata as Domains of Study  --
5A.14 Estimating Totals and Means Over Subpopulations  --
Exercises  --
References  --
6 RATIO ESTIMATES  --
6.1 Methods of Estimation  --
6.2 The Ratio Estimate  --
6.3 Approximate Variance of the Ratio Estimate  --
6.4 Accuracy of the Approximate Variance  --
6.5 Bias of the Ratio Estimate  --
6.6 Estimation of the Variance from a Sample  --
6.7 Confidence Limits  --
6.8 Comparison of the Ratio Estimate with the Mean per Unit  --
6.9 Conditions under which the Ratio Estimate is Optimum  --
6.10 Ratio Estimates in Stratified Random Sampling  --
6.11 The Combined Ratio Estimate  --
6.12 Comparison of the Combined and Separate Estimates  --
6.13 Short-Cut Computation of the Variance  --
6.14 Optimum Allocation with a Ratio Estimate  --
6.15 Unbiased Ratio-Type Estimates  --
6.16 Comparison of Two Ratios  --
6.17 Multivariate Ratio Estimates  --
Exercises  --
References  --
7 REGRESSION ESTIMATES  --
7.1 The Linear Regression Estimate  --
7.2 Regression Estimates with Preassigned b  --
7.3 Regression Estimates when b Is Computed from the Sample  --
7.4 Accuracy of the Large-Sample Formula for V(yir)  --
7.5 Further Notes on the Bias  --
7.6 Comparison with the Ratio Estimate and the Mean per Unit  --
7.7 Regression Estimates in Stratified Sampling  --
7.8 Regression Coefficients Estimated from the Sample  --
7.9 Comparison of the Two Types of Regression Estimate  --
Exercises  --
References  --
8 SYSTEMATIC SAMPLING  --
8.1 Description  --
8.2 Relation to Cluster Sampling  --
8.3 Variance of the Estimated Mean  --
8.4 Comparison of Systematic with Stratified Random Samplin  --
8.5 Populations in “Random” Order  --
8.6 Populations with Linear Trend  --
8.7 Populations with Periodic Variation  --
8.8 Autocorrelated Populations  --
8.9 Natural Populations  --
8.10 Estimation of the Variance from a Single Sample  --
8.11 Stratified Systematic Sampling  --
8.12 Systematic Sampling in Two Dimensions  --
8.13 Summary  --
Exercises  --
References  --
9 ONE-STAGE cluster sampling --
9.1 Reasons for Cluster Sampling  --
9.2 A Simple Rule  --
9.3 Comparisons of Precision Made from Survey Data  --
9.4 Variance in Terms of Intracluster Correlation  --
9.5 Variance Functions  --
9.6 A Cost Function  --
9.7 Cluster Sampling for Proportions  --
9.8 Cluster Units of Unequal Sizes  --
9.9 Sampling with Probability Proportional to Size  --
9.10 Theory for Selection with Arbitrary Probabilities  --
9.11 The Optimum Measure of Size  --
9.12 Relative Precisions of the Techniques  --
9.13 Extension to Stratified Sampling  --
9.14 Sampling with Unequal Probabilities without Replacement  --
9.15 Alternative Approaches  --
9.16 Some Comparisons for n — 2  --
Exercises  --
References  --
10 SUBSAMPLING WITH UNITS OF EQUAL SIZE  --
10.1 Two-Stage Sampling  --
10.2 Two Useful Results  --
10.3 Variance of the Estimated Mean in Two-Stage Sampling  --
10.4 Estimation of the Variance  --
10.5 The Estimation of Proportions  --
10.6 Optimum Sampling and Subsampling Fractions  --
10.7 Estimation of mOpt from a Pilot Survey  --
10.8 Three-Stage Sampling  --
10.9 Stratified Sampling of the Units  --
10.10 Optimum Allocation with Stratified Sampling  --
Exercises  --
References  --
11 SUBSAMPLING yiTH UNITS OF UNEQUAL SIZE  --
11.1 Introduction  --
11.2 Sampling Methods when n = 1  --
11.3 Sampling with Probability Proportional to Estimated Size  --
11.4 Summary of Methods for n = 1  --
11.5 Sampling Methods when n >1  --
11.6 Units Selected with Equal Probabilities. “Ratio to Size” Estimate  --
11.7 Units Selected with Equal Probabilities. Unbiased Estimate  --
11.8 Units Selected with Probability Proportional to a Measure of Size. Unbiased Estimate  --
11.9 Units Selected with Probability Proportional to Size. Un-biased Estimate  --
11.10 Units Selected with Probability Proportional to a Measure of Size. Estimate: Ratio to Size  --
11.11 Comparison of the Methods  --
11.12 Ratios to Another Variable  --
11.13 Variance of the Ratio with Equal Probabilities of Selection  --
11 14 Variance of the Ratio withppes Selection  --
11.15 Choice of Sampling and Subsampling Fractions. Equal Probabilities  --
11.16 Sampling and Subsampling Fractions for ppes Sampling  --
11.17 Stratified Sampling. Unbiased Estimates  --
11.18 Stratified Sampling. Ratio Estimates  --
11.19 Selection with Unequal Probabilities without Replacement  --
Exercises  --
References  --
12 DOUBLE SAMPLING  --
12.1 Description of the Technique  --
12.2 Double Sampling for Stratification  --
12.3 Optimum Allocation  --
12.4 Estimated Variance in Double Sampling for Stratification  --
12.5 Regression Estimates  --
12.6 Double Sampling with Regression versus Single Sampling  --
12.7 Estimated Variance in Double Sample for Regression  --
12.8 Ratio Estimates  --
12.9 Repeated Sampling of the Same Population  --
12.10 Sampling on Two Occasions  --
12.11 Sampling on More than Two Occasions  --
12.12 Simplifications and Further Developments  --
Exercises  --
References  --
13 SOURCES OF ERROR IN SURVEYS  --
13.1 Introduction  --
13.2 Effects of Nonresponse --
13.3 Types of Nonresponse  --
13.4 Call-Backs  --
13.5 A Mathematical Model of the Effects of Call-Backs  --
13.6 Optimum Sampling Fraction among the Nonrespondents  --
13.7 Adjustments for Bias without Call-Backs  --
13.8 A Mathematical Model for Errors of Measurement  --
13.9 Effects of Constant Bias  --
13.10 Effects of Errors that Are Uncorrelated within the Sample  --
13.11 Effects of Intrasample Correlation between Errors  --
13.12 Summary of the Effects of Errors of Measurement  --
13.13 The Study of Errors of Measurement  --
13.14 Interpenetrating Subsamples  --
13.15 Extension to More Complex Plans  --
13.16 Controlled Experiments Imbedded in Surveys  --
13.17 Summary  --
Exercises  --
References  --
Author Index  --
Subject Index  --```
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I CHAPTER --
I 1 INTRODUCTION  --
1.1 Advantages of the Sampling Method  --
1.2 Some Uses of Sample Surveys  --
1.3 The Principal Steps in a Sample Survey  --
1.4 The Role of Sampling Theory  --
1.5 Probability Sampling  --
1.6 Use of the Normal Distribution  --
1.7 Bias and Its Effects --
1.8 The Mean Square Error  --
Exercises l6 --
References  --
2 SIMPLE RANDOM SAMPLING  --
2.1 Simple Random Sampling  --
2.2 Definitions and Notation  --
2.3 Properties of the Estimates  --
2.4 Variances of the Estimates  --
2.5 The Finite Population Correction  --
2.6 Estimation of the Standard Error from a Sample  --
2.7 Confidence Limits  --
2.8 An Alternative Method of Proof  --
2.9 Estimation of a Ratio  --
2.10 Estimates of Means Over Subpopulations  --
2.11 Estimates of Totals Over Subpopulations  --
2.12 Comparisons between Domain Means  --
2.13 Validity of the Normal Approximation --
2.14 Effect of Non-normality on the Estimated Variance  --
Exercises  --
References  --
3 SAMPLING FOR PROPORTIONS AND PERCENTAGES  --
3.1 Qualitative Characteristics  --
3.2 Variances of the Sample Estimates  --
3.3 The Effect of P on the Standard Errors  --
3.4 The Binomial Distribution  --
3.5 The Hypergeometric Distribution  --
3.6 Confidence Limits  --
3.7 Classification into More than Two Classes  --
3.8 Confidence Limits When There Are More than Two Classes  --
3.9 The Conditional Distribution of p  --
3.10 Proportions and Totals Over Subpopulations  --
3.11 Comparisons between Different Domains  --
3.12 Estimation of Proportions in Cluster Sampling  --
Exercises  --
References  --
THE ESTIMATION OF SAMPLE SIZE  --
4.1 A Hypothetical Example  --
4.2 Analysis of the Problem  --
4.3 The Specification of Precision  --
4.4 The Formula for n in Sampling for Proportions  --
4.5 The Formula for n with Continuous Data  --
4.6 Advance Estimates of Population Variances  --
4.7 Sample Size with More than One Item  --
4.8 Sample Size when Estimates Are Wanted for Subdivisions of the Population  --
4.9Sample Size in Decision Problems  --
Exercises  --
References  --
5 STRATIFIED RANDOM SAMPLING  --
5.1 Description  --
5.2 Notation  --
5.3 Properties of the Estimates  --
5.4 The Estimated Variance and Confidence Limits  --
5.5 Optimum Allocation  --
5.6 Relative Precision of Stratified Random and Simple Random Sampling  --
5.7 When Does Stratification Produce Large Gains in Precision  --
5.8 Allocation Requiring More than 100 Per Cent Sampling  --
5.9 Estimation of Sample Size with Continuous Data  --
5.10 Stratified Sampling for Proportions  --
5.11 Gains in Precision in Stratified Sampling for Proportions  --
5.12 Estimation of Sample Size with Proportions  --
Exercises  --
References  --
5A FURTHIR ASPECTS OE STRATIFIED SAMPLING  --
5A.1 Effects of Deviations from the Optimum Allocation  --
5A.2 Effects of Errors in the Stratum Sizes  --
5A.3 The Problem of Allocation with More than One Item  --
5A.4 Other Methods with More than One Item  --
5A.5 Two-Way Stratification with Small Samples  --
5A.6 The Construction of Strata  --
5A.7 Number of Strata  --
5A.8 Stratification After Selection of the Sample  --
5A.9 Quota Sampling  --
5A.10 Estimation from a Sample of the Gain Due to Stratification  --
5A.11 Estimation of Variance with One Unit per Stratum  --
5A.12 Short-Cuts in the Computation of Standard Errors  --
5A.13 Strata as Domains of Study  --
5A.14 Estimating Totals and Means Over Subpopulations  --
Exercises  --
References  --
6 RATIO ESTIMATES  --
6.1 Methods of Estimation  --
6.2 The Ratio Estimate  --
6.3 Approximate Variance of the Ratio Estimate  --
6.4 Accuracy of the Approximate Variance  --
6.5 Bias of the Ratio Estimate  --
6.6 Estimation of the Variance from a Sample  --
6.7 Confidence Limits  --
6.8 Comparison of the Ratio Estimate with the Mean per Unit  --
6.9 Conditions under which the Ratio Estimate is Optimum  --
6.10 Ratio Estimates in Stratified Random Sampling  --
6.11 The Combined Ratio Estimate  --
6.12 Comparison of the Combined and Separate Estimates  --
6.13 Short-Cut Computation of the Variance  --
6.14 Optimum Allocation with a Ratio Estimate  --
6.15 Unbiased Ratio-Type Estimates  --
6.16 Comparison of Two Ratios  --
6.17 Multivariate Ratio Estimates  --
Exercises  --
References  --
7 REGRESSION ESTIMATES  --
7.1 The Linear Regression Estimate  --
7.2 Regression Estimates with Preassigned b  --
7.3 Regression Estimates when b Is Computed from the Sample  --
7.4 Accuracy of the Large-Sample Formula for V(yir)  --
7.5 Further Notes on the Bias  --
7.6 Comparison with the Ratio Estimate and the Mean per Unit  --
7.7 Regression Estimates in Stratified Sampling  --
7.8 Regression Coefficients Estimated from the Sample  --
7.9 Comparison of the Two Types of Regression Estimate  --
Exercises  --
References  --
8 SYSTEMATIC SAMPLING  --
8.1 Description  --
8.2 Relation to Cluster Sampling  --
8.3 Variance of the Estimated Mean  --
8.4 Comparison of Systematic with Stratified Random Samplin  --
8.5 Populations in “Random” Order  --
8.6 Populations with Linear Trend  --
8.7 Populations with Periodic Variation  --
8.8 Autocorrelated Populations  --
8.9 Natural Populations  --
8.10 Estimation of the Variance from a Single Sample  --
8.11 Stratified Systematic Sampling  --
8.12 Systematic Sampling in Two Dimensions  --
8.13 Summary  --
Exercises  --
References  --
9 ONE-STAGE cluster sampling --
9.1 Reasons for Cluster Sampling  --
9.2 A Simple Rule  --
9.3 Comparisons of Precision Made from Survey Data  --
9.4 Variance in Terms of Intracluster Correlation  --
9.5 Variance Functions  --
9.6 A Cost Function  --
9.7 Cluster Sampling for Proportions  --
9.8 Cluster Units of Unequal Sizes  --
9.9 Sampling with Probability Proportional to Size  --
9.10 Theory for Selection with Arbitrary Probabilities  --
9.11 The Optimum Measure of Size  --
9.12 Relative Precisions of the Techniques  --
9.13 Extension to Stratified Sampling  --
9.14 Sampling with Unequal Probabilities without Replacement  --
9.15 Alternative Approaches  --
9.16 Some Comparisons for n — 2  --
Exercises  --
References  --
10 SUBSAMPLING WITH UNITS OF EQUAL SIZE  --
10.1 Two-Stage Sampling  --
10.2 Two Useful Results  --
10.3 Variance of the Estimated Mean in Two-Stage Sampling  --
10.4 Estimation of the Variance  --
10.5 The Estimation of Proportions  --
10.6 Optimum Sampling and Subsampling Fractions  --
10.7 Estimation of mOpt from a Pilot Survey  --
10.8 Three-Stage Sampling  --
10.9 Stratified Sampling of the Units  --
10.10 Optimum Allocation with Stratified Sampling  --
Exercises  --
References  --
11 SUBSAMPLING yiTH UNITS OF UNEQUAL SIZE  --
11.1 Introduction  --
11.2 Sampling Methods when n = 1  --
11.3 Sampling with Probability Proportional to Estimated Size  --
11.4 Summary of Methods for n = 1  --
11.5 Sampling Methods when n >1  --
11.6 Units Selected with Equal Probabilities. “Ratio to Size” Estimate  --
11.7 Units Selected with Equal Probabilities. Unbiased Estimate  --
11.8 Units Selected with Probability Proportional to a Measure of Size. Unbiased Estimate  --
11.9 Units Selected with Probability Proportional to Size. Un-biased Estimate  --
11.10 Units Selected with Probability Proportional to a Measure of Size. Estimate: Ratio to Size  --
11.11 Comparison of the Methods  --
11.12 Ratios to Another Variable  --
11.13 Variance of the Ratio with Equal Probabilities of Selection  --
11 14 Variance of the Ratio withppes Selection  --
11.15 Choice of Sampling and Subsampling Fractions. Equal Probabilities  --
11.16 Sampling and Subsampling Fractions for ppes Sampling  --
11.17 Stratified Sampling. Unbiased Estimates  --
11.18 Stratified Sampling. Ratio Estimates  --
11.19 Selection with Unequal Probabilities without Replacement  --
Exercises  --
References  --
12 DOUBLE SAMPLING  --
12.1 Description of the Technique  --
12.2 Double Sampling for Stratification  --
12.3 Optimum Allocation  --
12.4 Estimated Variance in Double Sampling for Stratification  --
12.5 Regression Estimates  --
12.6 Double Sampling with Regression versus Single Sampling  --
12.7 Estimated Variance in Double Sample for Regression  --
12.8 Ratio Estimates  --
12.9 Repeated Sampling of the Same Population  --
12.10 Sampling on Two Occasions  --
12.11 Sampling on More than Two Occasions  --
12.12 Simplifications and Further Developments  --
Exercises  --
References  --
13 SOURCES OF ERROR IN SURVEYS  --
13.1 Introduction  --
13.2 Effects of Nonresponse --
13.3 Types of Nonresponse  --
13.4 Call-Backs  --
13.5 A Mathematical Model of the Effects of Call-Backs  --
13.6 Optimum Sampling Fraction among the Nonrespondents  --
13.7 Adjustments for Bias without Call-Backs  --
13.8 A Mathematical Model for Errors of Measurement  --
13.9 Effects of Constant Bias  --
13.10 Effects of Errors that Are Uncorrelated within the Sample  --
13.11 Effects of Intrasample Correlation between Errors  --
13.12 Summary of the Effects of Errors of Measurement  --
13.13 The Study of Errors of Measurement  --
13.14 Interpenetrating Subsamples  --
13.15 Extension to More Complex Plans  --
13.16 Controlled Experiments Imbedded in Surveys  --
13.17 Summary  --
Exercises  --
References  --
Author Index  --
Subject Index  --

Includes bibliography.

I CHAPTER --
I 1 INTRODUCTION  --
1.1 Advantages of the Sampling Method  --
1.2 Some Uses of Sample Surveys  --
1.3 The Principal Steps in a Sample Survey  --
1.4 The Role of Sampling Theory  --
1.5 Probability Sampling  --
1.6 Use of the Normal Distribution  --
1.7 Bias and Its Effects --
1.8 The Mean Square Error  --
Exercises l6 --
References  --
2 SIMPLE RANDOM SAMPLING  --
2.1 Simple Random Sampling  --
2.2 Definitions and Notation  --
2.3 Properties of the Estimates  --
2.4 Variances of the Estimates  --
2.5 The Finite Population Correction  --
2.6 Estimation of the Standard Error from a Sample  --
2.7 Confidence Limits  --
2.8 An Alternative Method of Proof  --
2.9 Estimation of a Ratio  --
2.10 Estimates of Means Over Subpopulations  --
2.11 Estimates of Totals Over Subpopulations  --
2.12 Comparisons between Domain Means  --
2.13 Validity of the Normal Approximation --
2.14 Effect of Non-normality on the Estimated Variance  --
Exercises  --
References  --
3 SAMPLING FOR PROPORTIONS AND PERCENTAGES  --
3.1 Qualitative Characteristics  --
3.2 Variances of the Sample Estimates  --
3.3 The Effect of P on the Standard Errors  --
3.4 The Binomial Distribution  --
3.5 The Hypergeometric Distribution  --
3.6 Confidence Limits  --
3.7 Classification into More than Two Classes  --
3.8 Confidence Limits When There Are More than Two Classes  --
3.9 The Conditional Distribution of p  --
3.10 Proportions and Totals Over Subpopulations  --
3.11 Comparisons between Different Domains  --
3.12 Estimation of Proportions in Cluster Sampling  --
Exercises  --
References  --
THE ESTIMATION OF SAMPLE SIZE  --
4.1 A Hypothetical Example  --
4.2 Analysis of the Problem  --
4.3 The Specification of Precision  --
4.4 The Formula for n in Sampling for Proportions  --
4.5 The Formula for n with Continuous Data  --
4.6 Advance Estimates of Population Variances  --
4.7 Sample Size with More than One Item  --
4.8 Sample Size when Estimates Are Wanted for Subdivisions of the Population  --
4.9Sample Size in Decision Problems  --
Exercises  --
References  --
5 STRATIFIED RANDOM SAMPLING  --
5.1 Description  --
5.2 Notation  --
5.3 Properties of the Estimates  --
5.4 The Estimated Variance and Confidence Limits  --
5.5 Optimum Allocation  --
5.6 Relative Precision of Stratified Random and Simple Random Sampling  --
5.7 When Does Stratification Produce Large Gains in Precision  --
5.8 Allocation Requiring More than 100 Per Cent Sampling  --
5.9 Estimation of Sample Size with Continuous Data  --
5.10 Stratified Sampling for Proportions  --
5.11 Gains in Precision in Stratified Sampling for Proportions  --
5.12 Estimation of Sample Size with Proportions  --
Exercises  --
References  --
5A FURTHIR ASPECTS OE STRATIFIED SAMPLING  --
5A.1 Effects of Deviations from the Optimum Allocation  --
5A.2 Effects of Errors in the Stratum Sizes  --
5A.3 The Problem of Allocation with More than One Item  --
5A.4 Other Methods with More than One Item  --
5A.5 Two-Way Stratification with Small Samples  --
5A.6 The Construction of Strata  --
5A.7 Number of Strata  --
5A.8 Stratification After Selection of the Sample  --
5A.9 Quota Sampling  --
5A.10 Estimation from a Sample of the Gain Due to Stratification  --
5A.11 Estimation of Variance with One Unit per Stratum  --
5A.12 Short-Cuts in the Computation of Standard Errors  --
5A.13 Strata as Domains of Study  --
5A.14 Estimating Totals and Means Over Subpopulations  --
Exercises  --
References  --
6 RATIO ESTIMATES  --
6.1 Methods of Estimation  --
6.2 The Ratio Estimate  --
6.3 Approximate Variance of the Ratio Estimate  --
6.4 Accuracy of the Approximate Variance  --
6.5 Bias of the Ratio Estimate  --
6.6 Estimation of the Variance from a Sample  --
6.7 Confidence Limits  --
6.8 Comparison of the Ratio Estimate with the Mean per Unit  --
6.9 Conditions under which the Ratio Estimate is Optimum  --
6.10 Ratio Estimates in Stratified Random Sampling  --
6.11 The Combined Ratio Estimate  --
6.12 Comparison of the Combined and Separate Estimates  --
6.13 Short-Cut Computation of the Variance  --
6.14 Optimum Allocation with a Ratio Estimate  --
6.15 Unbiased Ratio-Type Estimates  --
6.16 Comparison of Two Ratios  --
6.17 Multivariate Ratio Estimates  --
Exercises  --
References  --
7 REGRESSION ESTIMATES  --
7.1 The Linear Regression Estimate  --
7.2 Regression Estimates with Preassigned b  --
7.3 Regression Estimates when b Is Computed from the Sample  --
7.4 Accuracy of the Large-Sample Formula for V(yir)  --
7.5 Further Notes on the Bias  --
7.6 Comparison with the Ratio Estimate and the Mean per Unit  --
7.7 Regression Estimates in Stratified Sampling  --
7.8 Regression Coefficients Estimated from the Sample  --
7.9 Comparison of the Two Types of Regression Estimate  --
Exercises  --
References  --
8 SYSTEMATIC SAMPLING  --
8.1 Description  --
8.2 Relation to Cluster Sampling  --
8.3 Variance of the Estimated Mean  --
8.4 Comparison of Systematic with Stratified Random Samplin  --
8.5 Populations in “Random” Order  --
8.6 Populations with Linear Trend  --
8.7 Populations with Periodic Variation  --
8.8 Autocorrelated Populations  --
8.9 Natural Populations  --
8.10 Estimation of the Variance from a Single Sample  --
8.11 Stratified Systematic Sampling  --
8.12 Systematic Sampling in Two Dimensions  --
8.13 Summary  --
Exercises  --
References  --
9 ONE-STAGE cluster sampling --
9.1 Reasons for Cluster Sampling  --
9.2 A Simple Rule  --
9.3 Comparisons of Precision Made from Survey Data  --
9.4 Variance in Terms of Intracluster Correlation  --
9.5 Variance Functions  --
9.6 A Cost Function  --
9.7 Cluster Sampling for Proportions  --
9.8 Cluster Units of Unequal Sizes  --
9.9 Sampling with Probability Proportional to Size  --
9.10 Theory for Selection with Arbitrary Probabilities  --
9.11 The Optimum Measure of Size  --
9.12 Relative Precisions of the Techniques  --
9.13 Extension to Stratified Sampling  --
9.14 Sampling with Unequal Probabilities without Replacement  --
9.15 Alternative Approaches  --
9.16 Some Comparisons for n — 2  --
Exercises  --
References  --
10 SUBSAMPLING WITH UNITS OF EQUAL SIZE  --
10.1 Two-Stage Sampling  --
10.2 Two Useful Results  --
10.3 Variance of the Estimated Mean in Two-Stage Sampling  --
10.4 Estimation of the Variance  --
10.5 The Estimation of Proportions  --
10.6 Optimum Sampling and Subsampling Fractions  --
10.7 Estimation of mOpt from a Pilot Survey  --
10.8 Three-Stage Sampling  --
10.9 Stratified Sampling of the Units  --
10.10 Optimum Allocation with Stratified Sampling  --
Exercises  --
References  --
11 SUBSAMPLING yiTH UNITS OF UNEQUAL SIZE  --
11.1 Introduction  --
11.2 Sampling Methods when n = 1  --
11.3 Sampling with Probability Proportional to Estimated Size  --
11.4 Summary of Methods for n = 1  --
11.5 Sampling Methods when n >1  --
11.6 Units Selected with Equal Probabilities. “Ratio to Size” Estimate  --
11.7 Units Selected with Equal Probabilities. Unbiased Estimate  --
11.8 Units Selected with Probability Proportional to a Measure of Size. Unbiased Estimate  --
11.9 Units Selected with Probability Proportional to Size. Un-biased Estimate  --
11.10 Units Selected with Probability Proportional to a Measure of Size. Estimate: Ratio to Size  --
11.11 Comparison of the Methods  --
11.12 Ratios to Another Variable  --
11.13 Variance of the Ratio with Equal Probabilities of Selection  --
11 14 Variance of the Ratio withppes Selection  --
11.15 Choice of Sampling and Subsampling Fractions. Equal Probabilities  --
11.16 Sampling and Subsampling Fractions for ppes Sampling  --
11.17 Stratified Sampling. Unbiased Estimates  --
11.18 Stratified Sampling. Ratio Estimates  --
11.19 Selection with Unequal Probabilities without Replacement  --
Exercises  --
References  --
12 DOUBLE SAMPLING  --
12.1 Description of the Technique  --
12.2 Double Sampling for Stratification  --
12.3 Optimum Allocation  --
12.4 Estimated Variance in Double Sampling for Stratification  --
12.5 Regression Estimates  --
12.6 Double Sampling with Regression versus Single Sampling  --
12.7 Estimated Variance in Double Sample for Regression  --
12.8 Ratio Estimates  --
12.9 Repeated Sampling of the Same Population  --
12.10 Sampling on Two Occasions  --
12.11 Sampling on More than Two Occasions  --
12.12 Simplifications and Further Developments  --
Exercises  --
References  --
13 SOURCES OF ERROR IN SURVEYS  --
13.1 Introduction  --
13.2 Effects of Nonresponse --
13.3 Types of Nonresponse  --
13.4 Call-Backs  --
13.5 A Mathematical Model of the Effects of Call-Backs  --
13.6 Optimum Sampling Fraction among the Nonrespondents  --
13.7 Adjustments for Bias without Call-Backs  --
13.8 A Mathematical Model for Errors of Measurement  --
13.9 Effects of Constant Bias  --
13.10 Effects of Errors that Are Uncorrelated within the Sample  --
13.11 Effects of Intrasample Correlation between Errors  --
13.12 Summary of the Effects of Errors of Measurement  --
13.13 The Study of Errors of Measurement  --
13.14 Interpenetrating Subsamples  --
13.15 Extension to More Complex Plans  --
13.16 Controlled Experiments Imbedded in Surveys  --
13.17 Summary  --
Exercises  --
References  --
Author Index  --
Subject Index  --

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