Mathematics
Sampling
Sampling is the process of selecting a subset of individuals or items from a larger population to make inferences or generalizations about the entire group. In mathematics, sampling is used to gather data for statistical analysis and to draw conclusions about a population based on the characteristics of the sample. It is a fundamental concept in probability and statistics.
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No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 1 Introduction to Sampling Sampling is that part of statistical practice concerned with the selection of a subset of individual observations within a population of individuals intended to yield some knowledge about the population of concern, especially for the purposes of making predictions based on statistical inference. Sampling is an important aspect of data collection. Researchers rarely survey the entire population for two reasons (Adèr, Mellenbergh, & Hand, 2008): the cost is too high, and the population is dynamic in that the individuals making up the population may change over time. The three main advantages of Sampling are that the cost is lower, data collection is faster, and since the data set is smaller it is possible to ensure homogeneity and to improve the accuracy and quality of the data. Each observation measures one or more properties (such as weight, location, color) of observable bodies distinguished as independent objects or individuals. In survey Sampling, survey weights can be applied to the data to adjust for the sample design. Results from probability theory and statistical theory are employed to guide practice. In business and medical research, Sampling is widely used for gathering information about a population. Process The Sampling process comprises several stages: • Defining the population of concern • Specifying a Sampling frame, a set of items or events possible to measure • Specifying a Sampling method for selecting items or events from the frame • Determining the sample size • Implementing the Sampling plan • Sampling and data collecting Population definition Successful statistical practice is based on focused problem definition. In Sampling, this includes defining the population from which our sample is drawn. A population can be
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 6 Sampling Sampling is that part of statistical practice concerned with the selection of a subset of individual observations within a population of individuals intended to yield some knowledge about the population of concern, especially for the purposes of making predictions based on statistical inference. Sampling is an important aspect of data collection. Researchers rarely survey the entire population for two reasons (Adèr, Mellenbergh, & Hand, 2008): the cost is too high, and the population is dynamic in that the individuals making up the population may change over time. The three main advantages of Sampling are that the cost is lower, data collection is faster, and since the data set is smaller it is possible to ensure homogeneity and to improve the accuracy and quality of the data. Each observation measures one or more properties (such as weight, location, color) of observable bodies distinguished as independent objects or individuals. In survey Sampling, survey weights can be applied to the data to adjust for the sample design. Results from probability theory and statistical theory are employed to guide practice. In business and medical research, Sampling is widely used for gathering information about a population. Process The Sampling process comprises several stages: • Defining the population of concern • Specifying a Sampling frame, a set of items or events possible to measure • Specifying a Sampling method for selecting items or events from the frame • Determining the sample size • Implementing the Sampling plan • Sampling and data collecting Population definition Successful statistical practice is based on focused problem definition. In Sampling, this includes defining the population from which our sample is drawn. A population can be
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 1 Sampling Sampling is that part of statistical practice concerned with the selection of a subset of individual observations within a population of individuals intended to yield some knowledge about the population of concern, especially for the purposes of making predictions based on statistical inference. Sampling is an important aspect of data collection. Researchers rarely survey the entire population for two reasons (Adèr, Mellenbergh, & Hand, 2008): the cost is too high, and the population is dynamic in that the individuals making up the population may change over time. The three main advantages of Sampling are that the cost is lower, data collection is faster, and since the data set is smaller it is possible to ensure homogeneity and to improve the accuracy and quality of the data. Each observation measures one or more properties (such as weight, location, color) of observable bodies distinguished as independent objects or individuals. In survey Sampling, survey weights can be applied to the data to adjust for the sample design. Results from probability theory and statistical theory are employed to guide practice. In business and medical research, Sampling is widely used for gathering information about a population. Process The Sampling process comprises several stages: • Defining the population of concern • Specifying a Sampling frame, a set of items or events possible to measure • Specifying a Sampling method for selecting items or events from the frame • Determining the sample size • Implementing the Sampling plan • Sampling and data collecting Population definition Successful statistical practice is based on focused problem definition. In Sampling, this includes defining the population from which our sample is drawn. A population can be
eBook - PDFStatistical Quality Control
Using MINITAB, R, JMP and Python
- Bhisham C. Gupta(Author)
- 2021(Publication Date)
- Wiley(Publisher)
4 Sampling Methods 4.1 Introduction The science of Sampling is as old as civilization. When trying a new cuisine, for example, we take only a small bite to decide whether the taste of the food is to our liking. However, modern advances in Sampling techniques have only taken place starting in the twentieth century. Now Sampling is a matter of routine, and the effects of the outcomes can be felt in our day-to-day lives. Most decisions about government policies, marketing, trade, and manufacturing are based on the outcomes of Sampling conducted in different fields. There are various types of Sampling. The particular type of Sampling used for a given situation depends on factors such as the composition of the population, objectives of the Sampling, or simply time and budgetary constraints. Since Sampling is an integral part of statistical quality control, we dedicate this chapter to the study of various types of Sampling and estimation problems. 4.2 Basic Concepts of Sampling The primary objective of Sampling is to use the information contained in a sample taken from some population to make inferences about a certain population parameter, such as the population mean, population total, population proportion, or population variance. To make such inferences in the form of estimates of parameters that otherwise are unknown, we collect data from the population of interest. The aggregate of these data constitutes a sample. Each data point in the sample provides us with some information about the population parameter. However, since collecting each data point costs time and money, it is important to keep a balance. Too small a sample may not provide enough information to obtain good estimates, and too large a sample may result in a waste of resources. Thus, it is very important that in any Sampling procedure, an appropriate Sampling scheme, normally known as the sample design, is put in place.
- Ronald Asherson(Author)
- 2008(Publication Date)
- Elsevier Science(Publisher)
8 8 Sampling and the Sampling Distribution of a Statistic In the introduction (Chapter 1) we rather loosely explored an assortment of concepts such as statistical inference, population, random sample, statistic, and so on. In this chapter we shall firm up these notions by redefining them in a much more rigorous and technically correct fashion. This added degree of formality will then enable us to fully develop the concept of random Sampling and, in turn, the Sampling distribution of a statistic. 8.1 The Purpose of Random Sampling Statistical or inductive inference generally involves extracting a sample of a given size from an unknown population distribution in order to discern or infer something about the characteristics or behavior of that distribution. Given that conclusions or generalizations about a population are made from sample data and that (typically) only a small portion of the population is being examined, we essentially have incomplete information about the population. Hence an element of uncertainty enters into our analysis so that any conclusions or assertions about the characteristics of the population must be accompanied by a quantitative mea- sure of the risk or degree of uncertainty of the inference made. As was mentioned in Chapter 1, this process of inductively reaching conclusions in the face of uncer- tainty about the characteristics of a population (or some phenomenon), as well as quantitatively measuring the risk of the same, is called statistical inference. As we shall now see, the act of making such inferences is carried out using the technique of random Sampling. Inductive inference involves random Sampling so that the rules of probability theory can be applied in evaluating the magnitude of the risk inherent in this process. Hence uncertain inferences can be made, and the degree of uncertainty can be measured, if the Sampling experiment is performed in accordance with 293
eBook - PDF- Peter H. Rossi, James D Wright, Andy B. Anderson, Peter H. Rossi, James D Wright, Andy B. Anderson(Authors)
- 2013(Publication Date)
- Academic Press(Publisher)
Chapter 2 Sampling Theory Martin Frankel 2.1. I N T R O D U C T I O N Survey Sampling theory is a branch of statistics concerned with the meth-ods and techniques of selecting samples whose results may be projected to larger populations. The process of selecting samples and projecting from these samples to larger populations has gone on for centuries. Not until the develop-ment of probability Sampling, however, has the process become more a science than an art. When probability Sampling was first introduced into survey research, many practitioners felt that although the method was scientifically sound, it was too costly and restrictive. Many researchers predicted that after a short period of time it would be discarded in favor of traditional quota or purposive (nonprobability) methods. Much of this early skepticism was based on a misun-derstanding of the nature of probability Sampling methods. Many researchers mistakenly believed that the only type of probability Sampling was simple ran-dom (element) Sampling. In selecting a probability sample, it is necessary to adhere to one basic principle. Within this limitation, it is possible to select samples that are compat-ible with a wide variety of survey research designs. The basic principle that distinguishes probability Sampling from other types of Sampling is the condition that each element in the population is given a known nonzero probability of being selected into the sample. By adhering to this condition, the research assures that various techniques of statistical inference may be validly applied in the projection of sample results to larger populations. Nonadherence to this condition (i.e., the use of nonprobability Sampling) does not necessarily guaran-H A N D B O O K OF SURVEY RESEARCH Copyright © 1983 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-598226-7 22 Martin Frankel tee that the use of the techniques of statistical inference will produce invalid conclusions.
eBook - PDFResearch Methods For Business
A Skill Building Approach
- Uma Sekaran, Roger Bougie(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
For this purpose, the first 15 people who chose the special item might be interviewed, and their reactions obtained. In such cases, having instant information may be more gainful than obtaining the most representative facts. It should, however, be noted that the results of such convenient samples are not reliable and can never be generalized to the population. THE Sampling PROCESS Sampling is the process of selecting a sufficient number of the right elements from the population, so that a study of the sample and an understanding of its properties or characteristics make it possible for us to generalize such properties or characteristics to the population elements. The major steps in Sampling include: Low High F I G U R E 1 3 . 3 Normal distribution in a population 240 research methods for business 1. Define the population. 2. Determine the sample frame. 3. Determine the Sampling design. 4. Determine the appropriate sample size. 5. Execute the Sampling process. Defining the population Sampling begins with precisely defining the target population. The target population must be defined in terms of elements, geographical boundaries, and time. For instance, for a banker interested in saving habits of blue‐collar workers in the mining industry in the United States, the target population might be all blue‐collar workers in that industry throughout the country. For an advertising agency interested in reading habits of elderly people, the target population might be the German population aged 50 and over. These examples illustrate that the research objective and the scope of the study play a crucial role in defining the target population. Determining the sample frame The Sampling frame is a (physical) representation of all the elements in the population from which the sample is drawn. The payroll of an organization would serve as the Sampling frame if its members are to be studied.
- Jung-der Wang(Author)
- 2002(Publication Date)
- World Scientific(Publisher)
Besides, summary data obtained from a census study only have the advantage of smaller variance than Sampling, which is usually not cost-effective. Thus, in our daily life, one usually performs Sampling to explore the fact in a population to save time and all kinds of resources. Then, how can we conduct Sampling in a study? 9.2 The concept of probability Sampling Probability Sampling is a Sampling method, in which the selection of a Chapter 9 Sampling method and practical applications 2 13 subject or unit depends on a predetermined probability, or each unit of the sample space has a predetermined probability to be selected into the sample. Essentially, probability Sampling has two characteristics: 1) a collection of sample space {S,,S 2 , ... S n } exists in the source population, in which every sample Sj has a corresponding non-zero probability of n { to be selected; 2) the selection of Sj is random. In simple random Sampling, each subject or unit of the population has the same probability of being selected. To clarify this concept, let us examine several examples that did not conform to probability Sampling. Example 9.1 Aflatoxin contamination of soybeans In a study surveying average level of aflatoxin contamination on soybeans in Taiwan, investigators took samples from stores in 5 major Taiwanese cities. They drove along the highway, entered each city, randomly selected 3 stores selling soybeans, and contamination randomly selected samples from each store. Although they attempted to obtain a random sample, their Sampling procedure, in fact, was not dependent on any predetermined probability. By choosing stores more accessible from the highway, they introduced a bias into their sample. If this bias could be determined to be unrelated to the exposure, then the sample could still be considered quasi-random.
eBook - PDF- Carl McDaniel, Jr., Roger Gates(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
A census involves collecting the needed information from every member of the population of interest. A sample is simply a subset of a population. The steps in developing a Sampling plan are: define the population of interest, choose the data-collection method, identify the Sampling frame, select the Sampling method, determine sample size, develop and specify an operational plan for selecting Sampling elements, and execute the operational Sampling plan. The Sampling frame is a list of the elements of the population from which the sample will be drawn or a specified procedure for representing the list. In probability Sampling methods, samples are selected in such a way that every element of the population has a known, nonzero likelihood of selection. Nonprobability Sampling methods select specific elements from the population in a nonrandom manner. Probability samples have several advantages over nonprobability samples, including reasonable certainty that information will be obtained from a representative cross section of the population, a Sampling error that can be 262 CHAPTER 11 Basic Sampling Issues computed, and survey results that can be projected to the total population. However, probability samples are more expensive than nonprobability samples and usually take more time to design and execute. The accuracy of sample results is determined by both Sampling and nonSampling errors. Sampling error occurs because the sample selected is not perfectly representative of the population. There are two types of Sampling error: random Sampling error and administrative error. Random Sampling error is due to chance and cannot be avoided; it can only be reduced by increasing sample size. Probability samples include simple random samples, systematic samples, stratified samples, and cluster samples. Nonprobability samples include convenience samples, judgment samples, quota samples, and snowball samples. At the present time, Internet samples tend to be conveni- ence samples.
eBook - PDFStatistics Using Stata
An Integrative Approach
- Sharon Lawner Weinberg, Sarah Knapp Abramowitz(Authors)
- 2016(Publication Date)
- Cambridge University Press(Publisher)
259 CHAPTER NINE The Role of Sampling in Inferential Statistics As noted at the beginning of Chapter 7, a distinction exists between descriptive and infer- ential statistics. Whereas descriptive statistics are used to describe the data at hand, infer- ential statistics are used to draw inferences from results based on the data at hand to a larger population from which the data at hand have been selected. The data at hand form what is called a sample. In this chapter we discuss some fundamental components of inferential statistics, including Sampling, Sampling distributions, and characteristics of estimators. SAMPLES AND POPULATIONS Why, you may ask, should we study a sample at all if what we are really interested in is the population? Why not just study the population itself and be done with it? The answer to this question is that in actual research situations, it is often not possible, in terms of both time and resources, to obtain the desired data from the entire population. For example, suppose we wanted to know, in a particular election year, how people were going to vote in the upcoming presidential election. The population, in this case, consists of all the people eligible to vote in the general election. Clearly, it would be enor- mously expensive and time-consuming to gather and tabulate data from each person in the population. Instead, we would select a sample that is somehow representative of the entire population, poll the sample on how they will vote, and then draw conclusions about the population from the sample. Though we are studying the sample, our real interest in inferential statistics is the population, and the conclusions we will draw are always about it. We can describe measures taken on populations of things in the same ways that we can describe measures taken on samples of things.
eBook - PDFStatistics Using R
An Integrative Approach
- Sharon Lawner Weinberg, Daphna Harel, Sarah Knapp Abramowitz(Authors)
- 2020(Publication Date)
- Cambridge University Press(Publisher)
CHAPTER NINE THE ROLE OF Sampling IN INFERENTIAL STATISTICS As noted at the beginning of Chapter 7, a distinction exists between descriptive and inferential statistics. Whereas descriptive statistics are used to describe the data at hand, inferential statistics are used to draw inferences from results based on the data at hand to a larger population from which the data at hand have been selected. The data at hand form what is called a sample. In this chapter we discuss some fundamental components of inferential statistics, including Sampling, Sampling distributions, and characteristics of estimators. SAMPLES AND POPULATIONS Why, you may ask, should we study a sample at all if what we are really interested in is the population? Why not just study the population itself and be done with it? The answer to this question is that in actual research situations, it is often not possible, in terms of both time and resources, to obtain the desired data from the entire population. For example, suppose we wanted to know, in a particular election year, how people were going to vote in the upcoming presidential election. The population, in this case, consists of all the people eligible to vote in the general election. Clearly, it would be enormously expensive and time-consuming to gather and tabulate data from each person in the population. Instead, we would select a sample that is somehow representative of the entire population, poll the sample on how they will vote, and then draw conclusions about the population from the sample. Though we are studying the sample, our real interest in inferential statistics is the population, and the conclusions we will draw are always about it. We can describe measures taken on populations of things in the same ways that we can describe measures taken on samples of things.
eBook - PDF- Barry Babin(Author)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
In particular, if accuracy rep-resents the generalizability of results to a broad population, haphazard Sampling is problematic. Generalizability may not always be a concern though. multistage area Sampling Sampling that involves using a combination of two or more probability Sampling techniques. Population Element Possible Clusters in the United States U.S. adult population States Counties Metropolitan Statistical Areas Census Tracts Blocks Households College seniors Colleges Manufacturing firms Counties Metropolitan Statistical Areas Localities Plants Airline travelers Airports Planes Sports fans Football Stadiums Basketball Arenas Baseball Parks EXHIBIT 12.6 Examples of Clusters Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 352 PART FOUR Sampling and Statistical Theory For example, when the sample is part of an exploratory research project, accuracy may not be the highest priority. For other, more conclusive projects, the sample result must precisely represent a population’s characteristics, and the researcher must be willing to spend the time and money needed to achieve that accuracy. When researchers use a convenience sample, they may sometimes even think backward and only describe what population the results might extend to based on the sample that can be obtained. Any results are qualified based on the deviation of that population from a relevant target population (see Exhbit 12.4). Typically, a market research report will qualify results based on Sampling characteristics.
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