Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben

1996 | Buch

Collection of Survey Data Kapitel lesen Erstes Kapitel lesen

Elements of Survey Sampling

verfasst von: Ravindra Singh, Naurang Singh Mangat

Verlag: Springer Netherlands

Buchreihe : Kluwer Texts in the Mathematical Sciences

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Über dieses Buch

Modern statistics consists of methods which help in drawing inferences about the population under consideration. These populations may actually exist, or could be generated by repeated· experimentation. The medium of drawing inferences about the population is the sample, which is a subset of measurements selected from the population. Each measurement in the sample is used for making inferences about the population. The populations and also the methods of sample selection differ from one field of science to the other. Social scientists use surveys tocollectthe sample information, whereas the physical scientists employ the method of experimentation for obtaining this information. This is because in social sciences the factors that cause variation in the measurements on the study variable for the population units can not be controlled, whereas in physical sciences these factors can be controlled, at least to some extent, through proper experimental design. Several excellent books on sampling theory are available in the market. These books discuss the theory of sample surveys in great depth and detail, and are suited to the postgraduate students majoring in statistics. Research workers in the field of sampling methodology can also make use of these books. However, not many suitable books are available, which can be used by the students and researchers in the fields of economics, social sciences, extension education, agriculture, medical sciences, business management, etc. These students and workers usually conduct sample surveys during their research projects.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Collection of Survey Data
Abstract
The need to gather information arises in almost every conceivable sphere of human activity. Many of the questions that are subject to common conversation and controversy require numerical data for their resolution. Data resulting from the physical, chemical, and biological experiments in the form of observations are used to test different theories and hypotheses. Various social and economic investigations are carried out through the use and analysis of relevant data. The data collected and analyzed in an objective manner and presented suitably serve as basis for taking policy decisions in different fields of daily life.
Ravindra Singh, Naurang Singh Mangat
Chapter 2. Elementary Concepts
Abstract
Knowledge of basic concepts is a prerequisite for an insight into the sample survey designs. Assuming some exposure to elementary probability theory on the part of the reader, we present in this chapter, a rapid review of some of these concepts. To begin with, preliminary statistical concepts including those of expectation, variance, and covariance, for random variables and linear functions of random variables will be defined. The idea of sampling distribution, being basic to the sampling theory, has been briefly explained. The concepts of measure of error, interval estimation, and sample size determination, which are related to sampling distribution, have also been discussed. The chapter concludes with a brief introduction to the sampling and nonsampling errors.
Ravindra Singh, Naurang Singh Mangat
Chapter 3. Simple Random Sampling
Abstract
In this book, we shall consider various sampling procedures (schemes) for selection of units in the sample. Since the objective of a survey is to make inferences about the population, a procedure that provides a precise estimator of the parameter of interest is desirable. Many sampling schemes have been developed to achieve this objective. To begin with, simple random sampling, the simplest and the most basic sample selection procedure, is discussed.
Ravindra Singh, Naurang Singh Mangat
Chapter 4. Sampling With Varying Probabilities
Abstract
In the preceding chapter, we have discussed simple random sampling in which each unit in the population gets equal chance of being included in the sample. However, when the units vary considerably in size, SRS does not seem to be an appropriate procedure, since it does not take into account the possible importance of the size of the unit. Under such circumstances, selection of units with unequal probabilities may provide more efficient estimators than equal probability sampling. In this scheme, the units are selected with probability proportional to a given measure of size. The size measure is the value of an auxiliary variable (say) x, which is closely associated with the study variable (say) y. This type of sampling is known as varying probability sampling or probability proportional to size (PPS) sampling. For instance, while estimating total number of unemployed youth in a district, the number of households in the village can be used as a size measure when villages are taken as sampling units. Similarly, for estimating total number of tube wells in a certain district, the number of tube wells in a village for a previous period, or net irrigated area for the village, may be taken as size variables.
Ravindra Singh, Naurang Singh Mangat
Chapter 5. Stratified Sampling
Abstract
The precision of an estimate of the population mean or total, besides sample size, also depends on the variability among the units of the population. Therefore, apart from increasing the sample size, another possible way to increase the precision of the estimate could be to divide the population units into certain number of groups, such that the variability within the groups is minimum whereas it is maximum between the groups. Smaller samples could then be selected from each of the groups so formed, such that the total number of sampled units over all the groups equal the required overall sample size. The groups thus formed are called strata,and the process of forming strata is known as stratification. In this connection, we have the following definitions:
Definition 5.1 The procedure of partitioning the population into groups, called strata, and then drawing a sample independently from each stratum, is known as stratified sampling.
Definition 5.2 If the sample drawn from each stratum is random one, the procedure is then termed as stratified random sampling.
Ravindra Singh, Naurang Singh Mangat
Chapter 6. Systematic Sampling
Abstract
In the preceding chapters, we have considered methods of sampling in which successive units are selected at random. In this chapter, an alternative sampling procedure is considered. The scheme, besides ensuring for each unit equal probability of inclusion in the sample, selects the whole sample with just one random number.
Ravindra Singh, Naurang Singh Mangat
Chapter 7. Ratio and Product Methods of Estimation
Abstract
In the preceding chapters, we have discussed some methods of using information on an auxiliary variable for improving the precision of the estimates of population mean/total. In chapter 4, the selection probabilities for the population units were determined from the measures of size provided by such supplementary information. Also, the use of information on the auxiliary variable for the purpose of stratification has been discussed in chapter 5. In this chapter, and also in the following chapter, we present some other estimators that make use of auxiliary information for achieving higher efficiency.
Ravindra Singh, Naurang Singh Mangat
Chapter 8. Regression Method of Estimation
Abstract
Analogous to the ratio and product estimators, the linear regression estimator is also designed to increase the efficiency of estimation by using information on the auxiliary variable x which is correlated with the study variable y. As stated before, the ratio method of estimation is at its best when the correlation between y and x is positive and high, and also the regression of y on x is linear through the origin. In practice, however, it is observed that even when the regression of y on x is linear, the regression line passes through a point away from the origin. The efficiency of the ratio estimator in such cases is very low, as it decreases with the increase in length of the intercept cut on y-axis by the regression line. Regression estimator is the appropriate estimator for such situations. Although this estimator requires little more calculations than the ratio estimator, it is always at least as efficient as the ratio estimator for estimating population mean or total. Similarly, the product estimator of population mean or total is never more efficient than the corresponding linear regression estimator.
Ravindra Singh, Naurang Singh Mangat
Chapter 9. Two-Phase Sampling
Abstract
The discussion in some of the previous chapters has revealed that the prior information on an auxiliary variable could be used to enhance the precision of an estimator. Ratio, product, and regression estimators require the knowledge of population mean \( \bar X \) (or equivalently of total X) for the auxiliary variable x. For stratifying the population on the basis of the auxiliary variable, knowledge of its frequency distribution is required.
Ravindra Singh, Naurang Singh Mangat
Chapter 10. Cluster Sampling
Abstract
Let us consider a situation where a study is to be carried out regarding the indebtedness of farmers of a particular region. For this purpose, a sample of farmers is to be selected. In case, the list of all the farmers (frame) in the region is not available, a simple random sample or a systematic sample of farmers, can not be selected. Even if the frame of all farmers in the region was available, a simple random sample of farmers will result in the sampled units (farmers) being scattered all over the region. This will require a good amount of travel to reach all the selected farmers for collecting information about the indebtedness and will, therefore, involve a formidable amount of travel expenditure.
Ravindra Singh, Naurang Singh Mangat
Chapter 11. Multistage Sampling
Abstract
In chapter 10, we have considered sampling procedures in which all the elements of the selected clusters are enumerated. It was seen that though cluster sampling is generally economical, but it is usually less efficient than sampling of same number of ultimate units directly from the population. This is because the former strategy restricts the spread of the sample over the population. It can, therefore, be logically expected that, for a given number of units in the sample, greater precision can be attained if (1) the units are distributed over a larger number of clusters, and (2) instead of completely enumerating all the units in each selected cluster, only a sample of units is observed. This logic gives rise to the following definition:
Definition 11.1 The procedure of sampling, which consists in first selecting the clusters and then randomly choosing a specified number of units from each selected cluster, is known as two-stage sampling.
Ravindra Singh, Naurang Singh Mangat
Chapter 12. Sampling from Mobile Populations
Abstract
The estimation of size is of immense importance in a variety of mobile biological populations. It helps to study population growth, ecological adaptation, natural selection, evolution, maintenance of many wildlife populations, and so on. Unlike other populations considered in previous chapters, the sampling units in the wildlife populations do not remain fixed at one place. They are rather highly mobile. Therefore, for mobile populations, it is essential to use alternative approach for sampling and estimation.
Ravindra Singh, Naurang Singh Mangat
Chapter 13. Nonresponse Errors
Abstract
In the preceding chapters, several survey designs have been discussed at length with respect to their applications. For each design, it was assumed that the true values of the variables of interest could be made available for the elements of the population under consideration. However, this is not usually the case in practice. The errors can occur at almost every stage of planning and execution of survey. These errors may be attributed to various causes right from the beginning stage, where the survey is planned and designed, to the final stage when the data are processed and analyzed. This gives rise to the following definition of nonsampling errors.
Ravindra Singh, Naurang Singh Mangat
Backmatter
Metadaten
Titel
Elements of Survey Sampling
verfasst von
Ravindra Singh
Naurang Singh Mangat
Copyright-Jahr
1996
Verlag
Springer Netherlands
Electronic ISBN
978-94-017-1404-4
Print ISBN
978-90-481-4703-8
DOI
https://doi.org/10.1007/978-94-017-1404-4