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## Sampling techniques / William G. Cochran

Editor: New York : Wiley, [1963]Edición: 2nd edDescripción: 413 p. : il. ; 24 cmTema(s): Sampling (Statistics)Otra clasificación: *CODIGO*
Contenidos:
```I CHAPTER --
I 1 INTRODUCTION [1] --
1.1 Advantages of the Sampling Method [1] --
1.2 Some Uses of Sample Surveys [3] --
1.3 The Principal Steps in a Sample Survey [5] --
1.4 The Role of Sampling Theory [9] --
1.5 Probability Sampling [10] --
1.6 Use of the Normal Distribution [11] --
1.7 Bias and Its Effects --
1.8 The Mean Square Error [15] --
Exercises l6 --
References [17] --
2 SIMPLE RANDOM SAMPLING [18] --
2.1 Simple Random Sampling [18] --
2.2 Definitions and Notation [19] --
2.3 Properties of the Estimates [20] --
2.4 Variances of the Estimates [21] --
2.5 The Finite Population Correction [23] --
2.6 Estimation of the Standard Error from a Sample [24] --
2.7 Confidence Limits [26] --
2.8 An Alternative Method of Proof [27] --
2.9 Estimation of a Ratio [29] --
2.10 Estimates of Means Over Subpopulations [33] --
2.11 Estimates of Totals Over Subpopulations [34] --
2.12 Comparisons between Domain Means [37] --
2.13 Validity of the Normal Approximation --
2.14 Effect of Non-normality on the Estimated Variance [43] --
Exercises [44] --
References [47] --
3 SAMPLING FOR PROPORTIONS AND PERCENTAGES [49] --
3.1 Qualitative Characteristics [49] --
3.2 Variances of the Sample Estimates [49] --
3.3 The Effect of P on the Standard Errors [52] --
3.4 The Binomial Distribution [54] --
3.5 The Hypergeometric Distribution [55] --
3.6 Confidence Limits [56] --
3.7 Classification into More than Two Classes [59] --
3.8 Confidence Limits When There Are More than Two Classes [60] --
3.9 The Conditional Distribution of p [61] --
3.10 Proportions and Totals Over Subpopulations [62] --
3.11 Comparisons between Different Domains [63] --
3.12 Estimation of Proportions in Cluster Sampling [64] --
Exercises [68] --
References [70] --
THE ESTIMATION OF SAMPLE SIZE [71] --
4.1 A Hypothetical Example [71] --
4.2 Analysis of the Problem [72] --
4.3 The Specification of Precision [73] --
4.4 The Formula for n in Sampling for Proportions [74] --
4.5 The Formula for n with Continuous Data [75] --
4.6 Advance Estimates of Population Variances [77] --
4.7 Sample Size with More than One Item [79] --
4.8 Sample Size when Estimates Are Wanted for Subdivisions of the Population [81] --
4.9Sample Size in Decision Problems [82] --
Exercises [84] --
References [86] --
5 STRATIFIED RANDOM SAMPLING [87] --
5.1 Description [87] --
5.2 Notation [88] --
5.3 Properties of the Estimates [89] --
5.4 The Estimated Variance and Confidence Limits [93] --
5.5 Optimum Allocation [95] --
5.6 Relative Precision of Stratified Random and Simple Random Sampling [98] --
5.7 When Does Stratification Produce Large Gains in Precision [100] --
5.8 Allocation Requiring More than 100 Per Cent Sampling [103] --
5.9 Estimation of Sample Size with Continuous Data [103] --
5.10 Stratified Sampling for Proportions [106] --
5.11 Gains in Precision in Stratified Sampling for Proportions [107] --
5.12 Estimation of Sample Size with Proportions [109] --
Exercises [110] --
References [113] --
5A FURTHIR ASPECTS OE STRATIFIED SAMPLING [114] --
5A.1 Effects of Deviations from the Optimum Allocation [114] --
5A.2 Effects of Errors in the Stratum Sizes [116] --
5A.3 The Problem of Allocation with More than One Item [118] --
5A.4 Other Methods with More than One Item [120] --
5A.5 Two-Way Stratification with Small Samples [126] --
5A.6 The Construction of Strata [128] --
5A.7 Number of Strata [133] --
5A.8 Stratification After Selection of the Sample [135] --
5A.9 Quota Sampling [136] --
5A.10 Estimation from a Sample of the Gain Due to Stratification [137] --
5A.11 Estimation of Variance with One Unit per Stratum [141] --
5A.12 Short-Cuts in the Computation of Standard Errors [142] --
5A.13 Strata as Domains of Study [145] --
5A.14 Estimating Totals and Means Over Subpopulations [146] --
Exercises [149] --
References [152] --
6 RATIO ESTIMATES [154] --
6.1 Methods of Estimation [154] --
6.2 The Ratio Estimate [155] --
6.3 Approximate Variance of the Ratio Estimate [157] --
6.4 Accuracy of the Approximate Variance [159] --
6.5 Bias of the Ratio Estimate [160] --
6.6 Estimation of the Variance from a Sample [163] --
6.7 Confidence Limits [164] --
6.8 Comparison of the Ratio Estimate with the Mean per Unit [165] --
6.9 Conditions under which the Ratio Estimate is Optimum [166] --
6.10 Ratio Estimates in Stratified Random Sampling [167] --
6.11 The Combined Ratio Estimate [169] --
6.12 Comparison of the Combined and Separate Estimates [170] --
6.13 Short-Cut Computation of the Variance [173] --
6.14 Optimum Allocation with a Ratio Estimate [173] --
6.15 Unbiased Ratio-Type Estimates [176] --
6.16 Comparison of Two Ratios [181] --
6.17 Multivariate Ratio Estimates [184] --
Exercises [186] --
References [188] --
7 REGRESSION ESTIMATES [189] --
7.1 The Linear Regression Estimate [189] --
7.2 Regression Estimates with Preassigned b [190] --
7.3 Regression Estimates when b Is Computed from the Sample [193] --
7.4 Accuracy of the Large-Sample Formula for V(yir) [196] --
7.5 Further Notes on the Bias [198] --
7.6 Comparison with the Ratio Estimate and the Mean per Unit [199] --
7.7 Regression Estimates in Stratified Sampling [200] --
7.8 Regression Coefficients Estimated from the Sample [202] --
7.9 Comparison of the Two Types of Regression Estimate [203] --
Exercises [204] --
References [205] --
8 SYSTEMATIC SAMPLING [206] --
8.1 Description [206] --
8.2 Relation to Cluster Sampling [207] --
8.3 Variance of the Estimated Mean [208] --
8.4 Comparison of Systematic with Stratified Random Samplin [213] --
8.5 Populations in “Random” Order [214] --
8.6 Populations with Linear Trend [216] --
8.7 Populations with Periodic Variation [218] --
8.8 Autocorrelated Populations [219] --
8.9 Natural Populations [221] --
8.10 Estimation of the Variance from a Single Sample [224] --
8.11 Stratified Systematic Sampling [227] --
8.12 Systematic Sampling in Two Dimensions [228] --
8.13 Summary [230] --
Exercises [230] --
References [233] --
9 ONE-STAGE cluster sampling --
9.1 Reasons for Cluster Sampling [234] --
9.2 A Simple Rule [235] --
9.3 Comparisons of Precision Made from Survey Data [239] --
9.4 Variance in Terms of Intracluster Correlation [242] --
9.5 Variance Functions [244] --
9.6 A Cost Function [245] --
9.7 Cluster Sampling for Proportions [247] --
9.8 Cluster Units of Unequal Sizes [249] --
9.9 Sampling with Probability Proportional to Size [251] --
9.10 Theory for Selection with Arbitrary Probabilities [252] --
9.11 The Optimum Measure of Size [255] --
9.12 Relative Precisions of the Techniques [256] --
9.13 Extension to Stratified Sampling [259] --
9.14 Sampling with Unequal Probabilities without Replacement [260] --
9.15 Alternative Approaches [262] --
9.16 Some Comparisons for n — 2 [264] --
Exercises [266] --
References [269] --
10 SUBSAMPLING WITH UNITS OF EQUAL SIZE [270] --
10.1 Two-Stage Sampling [270] --
10.2 Two Useful Results [271] --
10.3 Variance of the Estimated Mean in Two-Stage Sampling [275] --
10.4 Estimation of the Variance [276] --
10.5 The Estimation of Proportions [278] --
10.6 Optimum Sampling and Subsampling Fractions [279] --
10.7 Estimation of mOpt from a Pilot Survey [283] --
10.8 Three-Stage Sampling [285] --
10.9 Stratified Sampling of the Units [288] --
10.10 Optimum Allocation with Stratified Sampling [288] --
Exercises [290] --
References [291] --
11 SUBSAMPLING yiTH UNITS OF UNEQUAL SIZE [292] --
11.1 Introduction [292] --
11.2 Sampling Methods when n = 1 [293] --
11.3 Sampling with Probability Proportional to Estimated Size [297] --
11.4 Summary of Methods for n = 1 [299] --
11.5 Sampling Methods when n >1 [300] --
11.6 Units Selected with Equal Probabilities. “Ratio to Size” Estimate [300] --
11.7 Units Selected with Equal Probabilities. Unbiased Estimate [304] --
11.8 Units Selected with Probability Proportional to a Measure of Size. Unbiased Estimate [305] --
11.9 Units Selected with Probability Proportional to Size. Un-biased Estimate [308] --
11.10 Units Selected with Probability Proportional to a Measure of Size. Estimate: Ratio to Size [308] --
11.11 Comparison of the Methods [309] --
11.12 Ratios to Another Variable [311] --
11.13 Variance of the Ratio with Equal Probabilities of Selection [311] --
11 14 Variance of the Ratio withppes Selection [312] --
11.15 Choice of Sampling and Subsampling Fractions. Equal Probabilities [313] --
11.16 Sampling and Subsampling Fractions for ppes Sampling [314] --
11.17 Stratified Sampling. Unbiased Estimates [318] --
11.18 Stratified Sampling. Ratio Estimates [320] --
11.19 Selection with Unequal Probabilities without Replacement [321] --
Exercises [324] --
References [326] --
12 DOUBLE SAMPLING [327] --
12.1 Description of the Technique [327] --
12.2 Double Sampling for Stratification [328] --
12.3 Optimum Allocation [330] --
12.4 Estimated Variance in Double Sampling for Stratification [332] --
12.5 Regression Estimates [334] --
12.6 Double Sampling with Regression versus Single Sampling [336] --
12.7 Estimated Variance in Double Sample for Regression [339] --
12.8 Ratio Estimates [339] --
12.9 Repeated Sampling of the Same Population [341] --
12.10 Sampling on Two Occasions [342] --
12.11 Sampling on More than Two Occasions [345] --
12.12 Simplifications and Further Developments [347] --
Exercises [352] --
References [353] --
13 SOURCES OF ERROR IN SURVEYS [355] --
13.1 Introduction [355] --
13.2 Effects of Nonresponse --
13.3 Types of Nonresponse [359] --
13.4 Call-Backs [361] --
13.5 A Mathematical Model of the Effects of Call-Backs [363] --
13.6 Optimum Sampling Fraction among the Nonrespondents [367] --
13.7 Adjustments for Bias without Call-Backs [371] --
13.8 A Mathematical Model for Errors of Measurement [374] --
13.9 Effects of Constant Bias [376] --
13.10 Effects of Errors that Are Uncorrelated within the Sample [377] --
13.11 Effects of Intrasample Correlation between Errors [380] --
13.12 Summary of the Effects of Errors of Measurement [381] --
13.13 The Study of Errors of Measurement [381] --
13.14 Interpenetrating Subsamples [383] --
13.15 Extension to More Complex Plans [385] --
13.16 Controlled Experiments Imbedded in Surveys [387] --
13.17 Summary [389] --
Exercises [390] --
References [392] --
Author Index [401] --
Subject Index [405] --```
List(s) this item appears in: Últimas adquisiciones
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I CHAPTER --
I 1 INTRODUCTION [1] --
1.1 Advantages of the Sampling Method [1] --
1.2 Some Uses of Sample Surveys [3] --
1.3 The Principal Steps in a Sample Survey [5] --
1.4 The Role of Sampling Theory [9] --
1.5 Probability Sampling [10] --
1.6 Use of the Normal Distribution [11] --
1.7 Bias and Its Effects --
1.8 The Mean Square Error [15] --
Exercises l6 --
References [17] --
2 SIMPLE RANDOM SAMPLING [18] --
2.1 Simple Random Sampling [18] --
2.2 Definitions and Notation [19] --
2.3 Properties of the Estimates [20] --
2.4 Variances of the Estimates [21] --
2.5 The Finite Population Correction [23] --
2.6 Estimation of the Standard Error from a Sample [24] --
2.7 Confidence Limits [26] --
2.8 An Alternative Method of Proof [27] --
2.9 Estimation of a Ratio [29] --
2.10 Estimates of Means Over Subpopulations [33] --
2.11 Estimates of Totals Over Subpopulations [34] --
2.12 Comparisons between Domain Means [37] --
2.13 Validity of the Normal Approximation --
2.14 Effect of Non-normality on the Estimated Variance [43] --
Exercises [44] --
References [47] --
3 SAMPLING FOR PROPORTIONS AND PERCENTAGES [49] --
3.1 Qualitative Characteristics [49] --
3.2 Variances of the Sample Estimates [49] --
3.3 The Effect of P on the Standard Errors [52] --
3.4 The Binomial Distribution [54] --
3.5 The Hypergeometric Distribution [55] --
3.6 Confidence Limits [56] --
3.7 Classification into More than Two Classes [59] --
3.8 Confidence Limits When There Are More than Two Classes [60] --
3.9 The Conditional Distribution of p [61] --
3.10 Proportions and Totals Over Subpopulations [62] --
3.11 Comparisons between Different Domains [63] --
3.12 Estimation of Proportions in Cluster Sampling [64] --
Exercises [68] --
References [70] --
THE ESTIMATION OF SAMPLE SIZE [71] --
4.1 A Hypothetical Example [71] --
4.2 Analysis of the Problem [72] --
4.3 The Specification of Precision [73] --
4.4 The Formula for n in Sampling for Proportions [74] --
4.5 The Formula for n with Continuous Data [75] --
4.6 Advance Estimates of Population Variances [77] --
4.7 Sample Size with More than One Item [79] --
4.8 Sample Size when Estimates Are Wanted for Subdivisions of the Population [81] --
4.9Sample Size in Decision Problems [82] --
Exercises [84] --
References [86] --
5 STRATIFIED RANDOM SAMPLING [87] --
5.1 Description [87] --
5.2 Notation [88] --
5.3 Properties of the Estimates [89] --
5.4 The Estimated Variance and Confidence Limits [93] --
5.5 Optimum Allocation [95] --
5.6 Relative Precision of Stratified Random and Simple Random Sampling [98] --
5.7 When Does Stratification Produce Large Gains in Precision [100] --
5.8 Allocation Requiring More than 100 Per Cent Sampling [103] --
5.9 Estimation of Sample Size with Continuous Data [103] --
5.10 Stratified Sampling for Proportions [106] --
5.11 Gains in Precision in Stratified Sampling for Proportions [107] --
5.12 Estimation of Sample Size with Proportions [109] --
Exercises [110] --
References [113] --
5A FURTHIR ASPECTS OE STRATIFIED SAMPLING [114] --
5A.1 Effects of Deviations from the Optimum Allocation [114] --
5A.2 Effects of Errors in the Stratum Sizes [116] --
5A.3 The Problem of Allocation with More than One Item [118] --
5A.4 Other Methods with More than One Item [120] --
5A.5 Two-Way Stratification with Small Samples [126] --
5A.6 The Construction of Strata [128] --
5A.7 Number of Strata [133] --
5A.8 Stratification After Selection of the Sample [135] --
5A.9 Quota Sampling [136] --
5A.10 Estimation from a Sample of the Gain Due to Stratification [137] --
5A.11 Estimation of Variance with One Unit per Stratum [141] --
5A.12 Short-Cuts in the Computation of Standard Errors [142] --
5A.13 Strata as Domains of Study [145] --
5A.14 Estimating Totals and Means Over Subpopulations [146] --
Exercises [149] --
References [152] --
6 RATIO ESTIMATES [154] --
6.1 Methods of Estimation [154] --
6.2 The Ratio Estimate [155] --
6.3 Approximate Variance of the Ratio Estimate [157] --
6.4 Accuracy of the Approximate Variance [159] --
6.5 Bias of the Ratio Estimate [160] --
6.6 Estimation of the Variance from a Sample [163] --
6.7 Confidence Limits [164] --
6.8 Comparison of the Ratio Estimate with the Mean per Unit [165] --
6.9 Conditions under which the Ratio Estimate is Optimum [166] --
6.10 Ratio Estimates in Stratified Random Sampling [167] --
6.11 The Combined Ratio Estimate [169] --
6.12 Comparison of the Combined and Separate Estimates [170] --
6.13 Short-Cut Computation of the Variance [173] --
6.14 Optimum Allocation with a Ratio Estimate [173] --
6.15 Unbiased Ratio-Type Estimates [176] --
6.16 Comparison of Two Ratios [181] --
6.17 Multivariate Ratio Estimates [184] --
Exercises [186] --
References [188] --
7 REGRESSION ESTIMATES [189] --
7.1 The Linear Regression Estimate [189] --
7.2 Regression Estimates with Preassigned b [190] --
7.3 Regression Estimates when b Is Computed from the Sample [193] --
7.4 Accuracy of the Large-Sample Formula for V(yir) [196] --
7.5 Further Notes on the Bias [198] --
7.6 Comparison with the Ratio Estimate and the Mean per Unit [199] --
7.7 Regression Estimates in Stratified Sampling [200] --
7.8 Regression Coefficients Estimated from the Sample [202] --
7.9 Comparison of the Two Types of Regression Estimate [203] --
Exercises [204] --
References [205] --
8 SYSTEMATIC SAMPLING [206] --
8.1 Description [206] --
8.2 Relation to Cluster Sampling [207] --
8.3 Variance of the Estimated Mean [208] --
8.4 Comparison of Systematic with Stratified Random Samplin [213] --
8.5 Populations in “Random” Order [214] --
8.6 Populations with Linear Trend [216] --
8.7 Populations with Periodic Variation [218] --
8.8 Autocorrelated Populations [219] --
8.9 Natural Populations [221] --
8.10 Estimation of the Variance from a Single Sample [224] --
8.11 Stratified Systematic Sampling [227] --
8.12 Systematic Sampling in Two Dimensions [228] --
8.13 Summary [230] --
Exercises [230] --
References [233] --
9 ONE-STAGE cluster sampling --
9.1 Reasons for Cluster Sampling [234] --
9.2 A Simple Rule [235] --
9.3 Comparisons of Precision Made from Survey Data [239] --
9.4 Variance in Terms of Intracluster Correlation [242] --
9.5 Variance Functions [244] --
9.6 A Cost Function [245] --
9.7 Cluster Sampling for Proportions [247] --
9.8 Cluster Units of Unequal Sizes [249] --
9.9 Sampling with Probability Proportional to Size [251] --
9.10 Theory for Selection with Arbitrary Probabilities [252] --
9.11 The Optimum Measure of Size [255] --
9.12 Relative Precisions of the Techniques [256] --
9.13 Extension to Stratified Sampling [259] --
9.14 Sampling with Unequal Probabilities without Replacement [260] --
9.15 Alternative Approaches [262] --
9.16 Some Comparisons for n — 2 [264] --
Exercises [266] --
References [269] --
10 SUBSAMPLING WITH UNITS OF EQUAL SIZE [270] --
10.1 Two-Stage Sampling [270] --
10.2 Two Useful Results [271] --
10.3 Variance of the Estimated Mean in Two-Stage Sampling [275] --
10.4 Estimation of the Variance [276] --
10.5 The Estimation of Proportions [278] --
10.6 Optimum Sampling and Subsampling Fractions [279] --
10.7 Estimation of mOpt from a Pilot Survey [283] --
10.8 Three-Stage Sampling [285] --
10.9 Stratified Sampling of the Units [288] --
10.10 Optimum Allocation with Stratified Sampling [288] --
Exercises [290] --
References [291] --
11 SUBSAMPLING yiTH UNITS OF UNEQUAL SIZE [292] --
11.1 Introduction [292] --
11.2 Sampling Methods when n = 1 [293] --
11.3 Sampling with Probability Proportional to Estimated Size [297] --
11.4 Summary of Methods for n = 1 [299] --
11.5 Sampling Methods when n >1 [300] --
11.6 Units Selected with Equal Probabilities. “Ratio to Size” Estimate [300] --
11.7 Units Selected with Equal Probabilities. Unbiased Estimate [304] --
11.8 Units Selected with Probability Proportional to a Measure of Size. Unbiased Estimate [305] --
11.9 Units Selected with Probability Proportional to Size. Un-biased Estimate [308] --
11.10 Units Selected with Probability Proportional to a Measure of Size. Estimate: Ratio to Size [308] --
11.11 Comparison of the Methods [309] --
11.12 Ratios to Another Variable [311] --
11.13 Variance of the Ratio with Equal Probabilities of Selection [311] --
11 14 Variance of the Ratio withppes Selection [312] --
11.15 Choice of Sampling and Subsampling Fractions. Equal Probabilities [313] --
11.16 Sampling and Subsampling Fractions for ppes Sampling [314] --
11.17 Stratified Sampling. Unbiased Estimates [318] --
11.18 Stratified Sampling. Ratio Estimates [320] --
11.19 Selection with Unequal Probabilities without Replacement [321] --
Exercises [324] --
References [326] --
12 DOUBLE SAMPLING [327] --
12.1 Description of the Technique [327] --
12.2 Double Sampling for Stratification [328] --
12.3 Optimum Allocation [330] --
12.4 Estimated Variance in Double Sampling for Stratification [332] --
12.5 Regression Estimates [334] --
12.6 Double Sampling with Regression versus Single Sampling [336] --
12.7 Estimated Variance in Double Sample for Regression [339] --
12.8 Ratio Estimates [339] --
12.9 Repeated Sampling of the Same Population [341] --
12.10 Sampling on Two Occasions [342] --
12.11 Sampling on More than Two Occasions [345] --
12.12 Simplifications and Further Developments [347] --
Exercises [352] --
References [353] --
13 SOURCES OF ERROR IN SURVEYS [355] --
13.1 Introduction [355] --
13.2 Effects of Nonresponse --
13.3 Types of Nonresponse [359] --
13.4 Call-Backs [361] --
13.5 A Mathematical Model of the Effects of Call-Backs [363] --
13.6 Optimum Sampling Fraction among the Nonrespondents [367] --
13.7 Adjustments for Bias without Call-Backs [371] --
13.8 A Mathematical Model for Errors of Measurement [374] --
13.9 Effects of Constant Bias [376] --
13.10 Effects of Errors that Are Uncorrelated within the Sample [377] --
13.11 Effects of Intrasample Correlation between Errors [380] --
13.12 Summary of the Effects of Errors of Measurement [381] --
13.13 The Study of Errors of Measurement [381] --
13.14 Interpenetrating Subsamples [383] --
13.15 Extension to More Complex Plans [385] --
13.16 Controlled Experiments Imbedded in Surveys [387] --
13.17 Summary [389] --
Exercises [390] --
References [392] --
Author Index [401] --
Subject Index [405] --

Includes bibliography.

I CHAPTER --
I 1 INTRODUCTION [1] --
1.1 Advantages of the Sampling Method [1] --
1.2 Some Uses of Sample Surveys [3] --
1.3 The Principal Steps in a Sample Survey [5] --
1.4 The Role of Sampling Theory [9] --
1.5 Probability Sampling [10] --
1.6 Use of the Normal Distribution [11] --
1.7 Bias and Its Effects --
1.8 The Mean Square Error [15] --
Exercises l6 --
References [17] --
2 SIMPLE RANDOM SAMPLING [18] --
2.1 Simple Random Sampling [18] --
2.2 Definitions and Notation [19] --
2.3 Properties of the Estimates [20] --
2.4 Variances of the Estimates [21] --
2.5 The Finite Population Correction [23] --
2.6 Estimation of the Standard Error from a Sample [24] --
2.7 Confidence Limits [26] --
2.8 An Alternative Method of Proof [27] --
2.9 Estimation of a Ratio [29] --
2.10 Estimates of Means Over Subpopulations [33] --
2.11 Estimates of Totals Over Subpopulations [34] --
2.12 Comparisons between Domain Means [37] --
2.13 Validity of the Normal Approximation --
2.14 Effect of Non-normality on the Estimated Variance [43] --
Exercises [44] --
References [47] --
3 SAMPLING FOR PROPORTIONS AND PERCENTAGES [49] --
3.1 Qualitative Characteristics [49] --
3.2 Variances of the Sample Estimates [49] --
3.3 The Effect of P on the Standard Errors [52] --
3.4 The Binomial Distribution [54] --
3.5 The Hypergeometric Distribution [55] --
3.6 Confidence Limits [56] --
3.7 Classification into More than Two Classes [59] --
3.8 Confidence Limits When There Are More than Two Classes [60] --
3.9 The Conditional Distribution of p [61] --
3.10 Proportions and Totals Over Subpopulations [62] --
3.11 Comparisons between Different Domains [63] --
3.12 Estimation of Proportions in Cluster Sampling [64] --
Exercises [68] --
References [70] --
THE ESTIMATION OF SAMPLE SIZE [71] --
4.1 A Hypothetical Example [71] --
4.2 Analysis of the Problem [72] --
4.3 The Specification of Precision [73] --
4.4 The Formula for n in Sampling for Proportions [74] --
4.5 The Formula for n with Continuous Data [75] --
4.6 Advance Estimates of Population Variances [77] --
4.7 Sample Size with More than One Item [79] --
4.8 Sample Size when Estimates Are Wanted for Subdivisions of the Population [81] --
4.9Sample Size in Decision Problems [82] --
Exercises [84] --
References [86] --
5 STRATIFIED RANDOM SAMPLING [87] --
5.1 Description [87] --
5.2 Notation [88] --
5.3 Properties of the Estimates [89] --
5.4 The Estimated Variance and Confidence Limits [93] --
5.5 Optimum Allocation [95] --
5.6 Relative Precision of Stratified Random and Simple Random Sampling [98] --
5.7 When Does Stratification Produce Large Gains in Precision [100] --
5.8 Allocation Requiring More than 100 Per Cent Sampling [103] --
5.9 Estimation of Sample Size with Continuous Data [103] --
5.10 Stratified Sampling for Proportions [106] --
5.11 Gains in Precision in Stratified Sampling for Proportions [107] --
5.12 Estimation of Sample Size with Proportions [109] --
Exercises [110] --
References [113] --
5A FURTHIR ASPECTS OE STRATIFIED SAMPLING [114] --
5A.1 Effects of Deviations from the Optimum Allocation [114] --
5A.2 Effects of Errors in the Stratum Sizes [116] --
5A.3 The Problem of Allocation with More than One Item [118] --
5A.4 Other Methods with More than One Item [120] --
5A.5 Two-Way Stratification with Small Samples [126] --
5A.6 The Construction of Strata [128] --
5A.7 Number of Strata [133] --
5A.8 Stratification After Selection of the Sample [135] --
5A.9 Quota Sampling [136] --
5A.10 Estimation from a Sample of the Gain Due to Stratification [137] --
5A.11 Estimation of Variance with One Unit per Stratum [141] --
5A.12 Short-Cuts in the Computation of Standard Errors [142] --
5A.13 Strata as Domains of Study [145] --
5A.14 Estimating Totals and Means Over Subpopulations [146] --
Exercises [149] --
References [152] --
6 RATIO ESTIMATES [154] --
6.1 Methods of Estimation [154] --
6.2 The Ratio Estimate [155] --
6.3 Approximate Variance of the Ratio Estimate [157] --
6.4 Accuracy of the Approximate Variance [159] --
6.5 Bias of the Ratio Estimate [160] --
6.6 Estimation of the Variance from a Sample [163] --
6.7 Confidence Limits [164] --
6.8 Comparison of the Ratio Estimate with the Mean per Unit [165] --
6.9 Conditions under which the Ratio Estimate is Optimum [166] --
6.10 Ratio Estimates in Stratified Random Sampling [167] --
6.11 The Combined Ratio Estimate [169] --
6.12 Comparison of the Combined and Separate Estimates [170] --
6.13 Short-Cut Computation of the Variance [173] --
6.14 Optimum Allocation with a Ratio Estimate [173] --
6.15 Unbiased Ratio-Type Estimates [176] --
6.16 Comparison of Two Ratios [181] --
6.17 Multivariate Ratio Estimates [184] --
Exercises [186] --
References [188] --
7 REGRESSION ESTIMATES [189] --
7.1 The Linear Regression Estimate [189] --
7.2 Regression Estimates with Preassigned b [190] --
7.3 Regression Estimates when b Is Computed from the Sample [193] --
7.4 Accuracy of the Large-Sample Formula for V(yir) [196] --
7.5 Further Notes on the Bias [198] --
7.6 Comparison with the Ratio Estimate and the Mean per Unit [199] --
7.7 Regression Estimates in Stratified Sampling [200] --
7.8 Regression Coefficients Estimated from the Sample [202] --
7.9 Comparison of the Two Types of Regression Estimate [203] --
Exercises [204] --
References [205] --
8 SYSTEMATIC SAMPLING [206] --
8.1 Description [206] --
8.2 Relation to Cluster Sampling [207] --
8.3 Variance of the Estimated Mean [208] --
8.4 Comparison of Systematic with Stratified Random Samplin [213] --
8.5 Populations in “Random” Order [214] --
8.6 Populations with Linear Trend [216] --
8.7 Populations with Periodic Variation [218] --
8.8 Autocorrelated Populations [219] --
8.9 Natural Populations [221] --
8.10 Estimation of the Variance from a Single Sample [224] --
8.11 Stratified Systematic Sampling [227] --
8.12 Systematic Sampling in Two Dimensions [228] --
8.13 Summary [230] --
Exercises [230] --
References [233] --
9 ONE-STAGE cluster sampling --
9.1 Reasons for Cluster Sampling [234] --
9.2 A Simple Rule [235] --
9.3 Comparisons of Precision Made from Survey Data [239] --
9.4 Variance in Terms of Intracluster Correlation [242] --
9.5 Variance Functions [244] --
9.6 A Cost Function [245] --
9.7 Cluster Sampling for Proportions [247] --
9.8 Cluster Units of Unequal Sizes [249] --
9.9 Sampling with Probability Proportional to Size [251] --
9.10 Theory for Selection with Arbitrary Probabilities [252] --
9.11 The Optimum Measure of Size [255] --
9.12 Relative Precisions of the Techniques [256] --
9.13 Extension to Stratified Sampling [259] --
9.14 Sampling with Unequal Probabilities without Replacement [260] --
9.15 Alternative Approaches [262] --
9.16 Some Comparisons for n — 2 [264] --
Exercises [266] --
References [269] --
10 SUBSAMPLING WITH UNITS OF EQUAL SIZE [270] --
10.1 Two-Stage Sampling [270] --
10.2 Two Useful Results [271] --
10.3 Variance of the Estimated Mean in Two-Stage Sampling [275] --
10.4 Estimation of the Variance [276] --
10.5 The Estimation of Proportions [278] --
10.6 Optimum Sampling and Subsampling Fractions [279] --
10.7 Estimation of mOpt from a Pilot Survey [283] --
10.8 Three-Stage Sampling [285] --
10.9 Stratified Sampling of the Units [288] --
10.10 Optimum Allocation with Stratified Sampling [288] --
Exercises [290] --
References [291] --
11 SUBSAMPLING yiTH UNITS OF UNEQUAL SIZE [292] --
11.1 Introduction [292] --
11.2 Sampling Methods when n = 1 [293] --
11.3 Sampling with Probability Proportional to Estimated Size [297] --
11.4 Summary of Methods for n = 1 [299] --
11.5 Sampling Methods when n >1 [300] --
11.6 Units Selected with Equal Probabilities. “Ratio to Size” Estimate [300] --
11.7 Units Selected with Equal Probabilities. Unbiased Estimate [304] --
11.8 Units Selected with Probability Proportional to a Measure of Size. Unbiased Estimate [305] --
11.9 Units Selected with Probability Proportional to Size. Un-biased Estimate [308] --
11.10 Units Selected with Probability Proportional to a Measure of Size. Estimate: Ratio to Size [308] --
11.11 Comparison of the Methods [309] --
11.12 Ratios to Another Variable [311] --
11.13 Variance of the Ratio with Equal Probabilities of Selection [311] --
11 14 Variance of the Ratio withppes Selection [312] --
11.15 Choice of Sampling and Subsampling Fractions. Equal Probabilities [313] --
11.16 Sampling and Subsampling Fractions for ppes Sampling [314] --
11.17 Stratified Sampling. Unbiased Estimates [318] --
11.18 Stratified Sampling. Ratio Estimates [320] --
11.19 Selection with Unequal Probabilities without Replacement [321] --
Exercises [324] --
References [326] --
12 DOUBLE SAMPLING [327] --
12.1 Description of the Technique [327] --
12.2 Double Sampling for Stratification [328] --
12.3 Optimum Allocation [330] --
12.4 Estimated Variance in Double Sampling for Stratification [332] --
12.5 Regression Estimates [334] --
12.6 Double Sampling with Regression versus Single Sampling [336] --
12.7 Estimated Variance in Double Sample for Regression [339] --
12.8 Ratio Estimates [339] --
12.9 Repeated Sampling of the Same Population [341] --
12.10 Sampling on Two Occasions [342] --
12.11 Sampling on More than Two Occasions [345] --
12.12 Simplifications and Further Developments [347] --
Exercises [352] --
References [353] --
13 SOURCES OF ERROR IN SURVEYS [355] --
13.1 Introduction [355] --
13.2 Effects of Nonresponse --
13.3 Types of Nonresponse [359] --
13.4 Call-Backs [361] --
13.5 A Mathematical Model of the Effects of Call-Backs [363] --
13.6 Optimum Sampling Fraction among the Nonrespondents [367] --
13.7 Adjustments for Bias without Call-Backs [371] --
13.8 A Mathematical Model for Errors of Measurement [374] --
13.9 Effects of Constant Bias [376] --
13.10 Effects of Errors that Are Uncorrelated within the Sample [377] --
13.11 Effects of Intrasample Correlation between Errors [380] --
13.12 Summary of the Effects of Errors of Measurement [381] --
13.13 The Study of Errors of Measurement [381] --
13.14 Interpenetrating Subsamples [383] --
13.15 Extension to More Complex Plans [385] --
13.16 Controlled Experiments Imbedded in Surveys [387] --
13.17 Summary [389] --
Exercises [390] --
References [392] --
Author Index [401] --
Subject Index [405] --

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