Sampling methodologies: with applications
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2000
|
| Series: | Texts in statistical science
[49] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 311 S. graph. Darst. |
| ISBN: | 158488214X |
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| adam_text | Contents
Preface xxiii
1 Introduction 1
1.1 Introduction 1
1.2 Censuses and surveys 3
1.3 Types of surveys 4
1.4 Sampling frame 5
1.5 Questionnaires, interviews, and sample sizes 5
Questionnaires 5
Interviewing methods 6
Sample sizes 6
1.6 Probability sampling 7
1.7 Nonprobability sampling 7
Purposive sampling 7
Quota sampling 8
Other types of surveys 8
1.8 Sampling in practice 8
Demographic and economic surveys 9
Educational surveys 9
Employment and expenditure surveys 9
Health and nutrition surveys 10
Agricultural surveys 11
Marketing surveys 12
Election surveys 13
Public polls and surveys 13
Campus surveys 14
Exercises 15
2 Simple Random Sampling:
Estimation of Means and Totals 19
2.1 Introduction 19
2.2 Population total, mean, and variance 19
Total and mean 19
Variance and standard deviation (S.D.) 20
Coefficient of variation (C.V.) 21
2.3 Sampling without replacement 21
2.4 Sample mean and variance 22
2.5 Properties of simple random sampling 23
2.6 Unbiasedness of the sample mean and variance 24
Sample mean 24
Sample variance 25
2.7 Standard error of the sample mean 25
2.8 Distribution of the sample mean 27
2.9 Confidence limits for the mean 28
2.10 Estimating the total 29
2.11 Coefficient of variation of the sample mean 30
2.12 Sample size determination 31
Precision 31
Error of estimation 32
Confidence width 32
Coefficient of variation 33
Relative error 33
2.13 Sample sizes for individual groups 34
Exercises 34
Appendix A2 36
Expected value, variance, and
standard deviation 36
Tschebycheff inequality 37
Unbiasedness of the sample variance 37
Variance of the sample mean 38
3 Simple Random Sampling: Related Topics 39
3.1 Introduction 39
3.2 Bias, variance, and mean square error
of an estimator 40
3.3 Precision, accuracy, and consistency 41
3.4 Covariance and correlation 42
Ungrouped data 42
Grouped data 43
3.5 Linear combination of two characteristics 45
Linear combination 45
The sum 47
The difference 47
Covariance and correlation of the sample means 48
3.6 Systematic sampling 48
Sample selection 48
Expectation and variance 49
Comparison with simple random sampling 50
Further properties 51
3.7 Nonresponse 52
3.8 Inference regarding the means 53
Population mean 53
Difference of two population means 54
Correlated samples 55
3.9 Sampling with replacement 56
Exercises 56
Appendix A3 60
Joint distribution 60
Expectation and variance 60
Covariance and correlation 61
Conditional and unconditional expectations
and variances 61
Variance of a linear combination 62
An expression for S 63
Cauchy Schwartz inequality 63
4 Proportions, Percentages, and Counts 65
4.1 Introduction 65
4.2 Two classes 65
4.3 Total number or count 68
4.4 Confidence limits 68
4.5 Sample sizes for specified requirements 69
4.6 Political and public polls 71
4.7 Estimation for more than two classes 73
Probabilities of the outcomes 73
Multinomial approximation 74
4.8 Combining estimates from surveys 74
4.9 Covariances of proportions 75
4.10 Difference between proportions 76
4.11 Sample sizes for more than two classes 76
4.12 Estimating population size 77
Exercises ^8
Appendix A4 . 81
Unbiasedness of the sample proportion
and variance 81
Binomial approximation 82
5 Stratification 83
5.1 Introduction 83
5.2 Notation 84
5.3 Estimation for a single stratum 86
5.4 Estimation of the population mean and total 88
5.5 Confidence limits 89
5.6 Proportions and totals 90
5.7 Population total and proportion 91
5.8 Proportional and equal division of the sample 92
Proportional allocation 92
Equal distribution 93
5.9 Neyman allocation 94
5.10 Gains from Neyman allocation 95
5.11 Summary on the precision of the allocations 97
5.12 Sample size allocation to estimate proportions 98
Proportional allocation 98
Neyman allocation 98
5.13 Sample sizes to estimate means and totals 99
5.14 Sample sizes to estimate proportions 100
5.15 Sample sizes for minimizing variance or cost 101
5.16 Further topics 103
Poststratification 103
Estimating differences of the stratum means 104
Two phase sampling for stratification 104
Sample size determination for two
or more characteristics 104
Strata formation 105
Exercises 105
Appendix A5 108
An expression for the variance 108
Variance of the estimator for the mean 109
Neyman allocation 109
Optimum allocation 109
6 Subpopulations 110
6.1 Introduction 110
6.2 Totals, means, and variances 111
6.3 Estimation of the means and their differences 111
Means 111
Difference between two groups 114
6.4 Totals of subpopulations 115
Known sizes 115
Estimated sizes 115
6.5 Sample sizes for estimating the means
and totals 116
6.6 Proportions and counts H?
6.7 Subpopulations of a stratum 118
6.8 Totals and means of subpopulations in strata 121
6.9 Stratification: Proportions and counts
of subpopulations 122
Exercises 123
7 Cluster Sampling 125
7.1 Introduction 125
7.2 Clusters of equal sizes i26
7.3 Estimation of the means l28
7.4 Comparison with simple random sampling 130
7.5 Estimation of the standard error 131
7.6 Optimum cluster and sample sizes 131
7.7 Clusters of unequal size 132
7.8 Alternative estimation with unequal sizes 133
7.9 Proportions and percentages 135
Average of the proportions 13t
Proportion of the totals or means 136
7.10 Stratification jf?
7.11 Unequal probability selection |^»
A method of selecting the cluster units ld»
Probabilities of selecting the units 139
7.12 Horvitz Thompson estimator 140
Variance of the estimator 141
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 ^47
Appendix A7 2 147
Alternative expression tor 5 ^g
Estimator for S2
Bias of the ratio estimator for the mean 148
Variance of the ratio estimator
Expectation and variance of the
Horvitz—Thompson estimator 149
Expectation and variance of the
PPSS estimator 150
Variance of pps estimator and the
variance estimator 150
8 Sampling in Two Stages 153
8.1 Introduction 153
8.2 Equal size first stage units 153
8.3 Estimating the mean 154
Estimator for the mean and its variance 154
Estimation of the variance 155
8.4 Sample size determination 156
8.5 Unequal size primary units 157
Estimators for the population total
and mean 157
Estimation of the variance 158
8.6 Ratio adjustment for the sizes 159
8.7 Proportions and totals 160
Equal size PSUs 160
Unequal size PSUs 161
An alternative estimator 162
8.8 Unequal probability selection 163
Horvitz Thompson estimator 163
Selection with unequal probabilities
and replacement 164
Exercises 164
Appendix A8 166
Expected value and variance of the estimator
for the mean 166
Expectation and variance of the estimator
for the total 168
Estimation of the variance—unequal
cluster sizes 169
Variance of the ratio estimator for the total 170
Expectation and variance of VHt 171
Estimator for V(Vht) 171
Variance of Vpps and its estimator 172
9 Ratios and Ratio Estimators 175
9.1 Introduction 175
9.2 Bias and variance of the sample ratio 176
9.3 Confidence limits for the ratio of means 177
9.4 Ratio estimators for the mean and total 177
9.5 Confidence limits for the mean and total 179
9.6 Differences between ratios, means, or totals 179
A common supplementary variable 179
Different supplementary variables 180
9.7 Regression through the origin and the BLUEs 181
Least squares 182
Superpopulation model for evaluations
and estimation 184
9.8 Ratio estimation vs. stratification 185
9.9 Ratio estimation with stratification 186
Single stratum 187
The separate ratio estimator 187
The combined ratio estimator 189
Statistical test for the equality
of the slopes 189
9.10 Bias reduction 190
9.11 Two phase or double sampling ratio estimators 191
9.12 Ratio estimator with unequal
probability selection 192
9.13 Multivariate ratio estimator 192
Exercises 192
Appendix A9 195
Bias of the ratio of two sample means 195
MSE of the ratio of two sample means 196
Variance of the combined ratio estimator 197
10 Regression Estimation 199
10.1 Introduction 199
10.2 The regression estimator 199
10.3 Estimation from the sample 200
10.4 Classical linear regression 201
10.5 Difference between regression estimators 203
Common supplementary variable 203
Different supplementary variables 203
10.6 Regression estimation vs. stratification 204
10.7 Stratification and regression estimator 205
Separate estimator 205
Combined regression estimator 206
Preliminary analysis and tests
of hypotheses 207
10.8 Multiple regression estimator 208
10.9 Double sampling regression estimator 210
10.10 Generalized regression and calibration estimators 211
Exercises 211
11 Nonresponse and Remedies 215
11.1 Introduction 215
11.2 Effects of survey topics and interviewing methods 216
Subject matter 216
Types of interviewing 216
Types of respondents 217
11.3 Response rates 217
11.4 Bias and MSE 218
11.5 Estimating proportions 218
11.6 Subsampling the nonrespondents 219
The procedure of Hansen and Hurwitz 219
Estimator and its variance 220
Optimum sample sizes 220
Variance estimation 222
Ratio and regression estimators 222
11.7 Estimating the missing observations 224
Least squares estimation 224
Alternative predictions 227
11.8 Ratio and regression estimation 227
Ratio estimation 227
Regression estimation 228
11.9 Poststratification and weighting 229
Estimators for the mean and total 229
Subpopulations 231
11.10 Response probabilities and weighting 233
11.11 Imputation 235
Mean imputation 235
Random duplication 236
Variance estimation 237
Confidence limits 237
Multiple imputation 238
Hot and cold deck imputation 238
11.12 Related topics 239
Efforts to increase response rates 239
Imputation, estimation, and analysis 239
Models for prediction, poststratification,
and weighting 239
Qualitative and categorical observations 240
11.13 Bayesian procedures 240
11.14 Census undercount 240
Exercises 241
Appendix All 242
Variance of the Hansen—Hurwitz estimator 242
Variance estimator for the Hansen—Hurwitz
estimator 242
12 Further Topics 245
12.1 Introduction 245
12.2 Linearization 245
12.3 The jackknife 246
Bias reduction 246
Variance estimation 247
12.4 The bootstrap 249
Infinite population 249
Finite population 250
Bootstrap for estimating the variance
of the sample ratio 251
12.5 Balanced repeated replication (BRR) 251
12.6 Small area estimation 253
Sample estimates 253
Synthetic and composite estimators 254
Best linear unbiased predictor (BLUP) 254
Applications, extensions, and evaluations 255
12.7 Complex surveys 257
Exercises 257
Appendix A12 258
The Bayesian approach 258
Appendix Tables 261
Solutions to Exercises 269
References 285
Index 301
List of tables
2.1 SAT verbal and math scores 20
2.2 All possible samples of size two; means and variances
of the math scores 24
2.3 Distribution of the sample mean 27
2.4 Frequency distribution 27
3.1 Joint distribution of age and education in 1995
in the 50 states and DC 44
3.2 Arrangement of 40 population units into four
systematic samples 45
3.3 Systematic samples of the savings ( )
of 40 employees 50
4.1 Presidential election—Percentages of voters for
the three candidates 71
4.2 Public surveys—Percentages of responses for
different items 72
4.3 Classification of voters participation in the primaries
on Super Tuesday, March, 2000 (percentages) 72
5.1 Rice production (in million metric tons) 84
5.2 Strata and samples 86
5.3 Variances for simple random sampling and
proportional and Neyman allocations; relative
precision of Neyman allocation 96
6.1 Means (top) and standard deviations (bottom) for
a sample of 40 hospitals H4
6.2 Household composition 117
6.3 Usage of athletic facilities 120
7.1 Employment in 54 counties of New York State,
divided into nine clusters of size six each; number of
establishments (1000s) and number of persons
employed (1000s) 126
7.2 Means and variances of the nine clusters of Table 7.1 127
7.3 Unequal size clusters: totals and variances 133
7.4 Composition of the 54 counties 135
7.5 Probabilities of selection 141
8.1 A sample of three clusters of equal sizes (M = 6) and
samples of three counties from the selected clusters 156
8.2 Sample of clusters of unequal size and sample
of counties 159
9.1 Heights, weights, and blood pressures 178
9.2 Wheat production 186
11.1 Survey of families 225
11.2 Two types of stratification 230
11.3 Part time employment of students 232
12.1 Jackknife calculations for college enrollment 248
Tl 1920 random numbers 262
T2 SAT scores of 30 candidates 264
T3 Persons over age 25 in the U.S. (1000s), 1995 264
T4 Ten states with the largest college enrollments (1000s) 265
T5 Ten states with the smallest college enrollments (1000s) 265
T6 Blood pressures of 20 persons (mm Hg) 266
T7 Physicians in the U.S. in 1995 and hospital expenditure for a
sample of ten states 266
T8 Wheat production in 25 countries (million metric tons) 267
T9 Energy production and consumption in 1996 in 25 countries 268
List of figures
2.1 Approximate distribution of the sample mean
for the math scores 28
3.1 Joint distribution of the number of persons over
25 years of age and the percentage of college
graduates in the 50 states and DC 44
5.1 Precision of Neyman allocation relative to simple
random sampling (top) and proportional
allocation (bottom) 97
6.1 Usage of the athletic facility by the male
and female groups 121
9.1 Regression through the origin of weight on height 183
10.1 Regression of 1997 wheat production on
1995 production 204
10.2 Regression of the wheat productions for the
two strata 206
11.1 Regressions of income on husband s age
and wife s age 226
|
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| series2 | Texts in statistical science |
| spelling | Rao, Poduri S. Verfasser aut Sampling methodologies with applications Poduri S. R. S. Rao Boca Raton [u.a.] Chapman & Hall/CRC 2000 311 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science [49] Methodologie gtt Sciences sociales - Méthodes statistiques Steekproeven gtt Toepassingen gtt Échantillonnage (Statistique) Methode Sozialwissenschaften Sampling (Statistics) Social sciences Statistical methods Stichprobe (DE-588)4057502-0 gnd rswk-swf Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Stichprobe (DE-588)4057502-0 s Statistik (DE-588)4056995-0 s Sozialwissenschaften (DE-588)4055916-6 s DE-604 Texts in statistical science [49] (DE-604)BV022819715 49 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009646132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rao, Poduri S. Sampling methodologies with applications Texts in statistical science Methodologie gtt Sciences sociales - Méthodes statistiques Steekproeven gtt Toepassingen gtt Échantillonnage (Statistique) Methode Sozialwissenschaften Sampling (Statistics) Social sciences Statistical methods Stichprobe (DE-588)4057502-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4057502-0 (DE-588)4055916-6 (DE-588)4056995-0 |
| title | Sampling methodologies with applications |
| title_auth | Sampling methodologies with applications |
| title_exact_search | Sampling methodologies with applications |
| title_full | Sampling methodologies with applications Poduri S. R. S. Rao |
| title_fullStr | Sampling methodologies with applications Poduri S. R. S. Rao |
| title_full_unstemmed | Sampling methodologies with applications Poduri S. R. S. Rao |
| title_short | Sampling methodologies |
| title_sort | sampling methodologies with applications |
| title_sub | with applications |
| topic | Methodologie gtt Sciences sociales - Méthodes statistiques Steekproeven gtt Toepassingen gtt Échantillonnage (Statistique) Methode Sozialwissenschaften Sampling (Statistics) Social sciences Statistical methods Stichprobe (DE-588)4057502-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Methodologie Sciences sociales - Méthodes statistiques Steekproeven Toepassingen Échantillonnage (Statistique) Methode Sozialwissenschaften Sampling (Statistics) Social sciences Statistical methods Stichprobe Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009646132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022819715 |
| work_keys_str_mv | AT raopoduris samplingmethodologieswithapplications |