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Summary Business Research Methods
Te gebruiken bij
Auteur(s): Blumberg, B., Cooper, D.R., Schindler, P.S.
Druk/Jaar van uitgave: 4e druk / 2014
Remarks & Related
Summary of chapters 6, 7, 12, 13 and 14.
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Chapter 6. Sampling
The unit of analysis depicts the level at which the research is performed and which objects are researched.
The essential application of sampling is that it allows for drawing conclusions about the entire population, by studying some of the elements in a population.
A population element is the unit of study - the individual participant or object on which the measurement is taken. A population is the total collection of elements about which some conclusion is to be drawn.
A census is a count of all the elements in a population. The listing of all population elements from which the sample will be drawn is called the sample frame.
There are several compelling reasons for sampling:
Lower cost - the difference between the sample costs and census costs is substantial.
Greater accuracy of results – some argue that the quality of a study is often better with sampling than with a census.
However, when the population is small, accessible, and highly variable, accuracy is expected to be greater with a census than a sample (Thus, a census study is: feasible when the population is small and necessary when the elements are quite different from each other).
Greater speed of data collection – the time between the recognition of a need for information and the availability of that information is reduced.
Availability of population elements – Some situations simply require sampling. This is the case where e.g. the population is and infinite conditions are appropriate for a census study.
The advantages of sampling over census studies are less compelling when the population is small and the variability within the population high.
Feasible when the population is small
Necessary when the elements are quite different from each other
However, when the population is small and variable, any sample we draw may not be representative of the population from which it is drawn. The resulting values we calculate from the sample are incorrect as estimates of the population values.
The ultimate test of a sample design is how well it represents the characteristics of the population it claims to represent Thus, the sample must be valid.
Validity of a sample depends on two considerations: Accuracy and precision.
Accuracy: is the degree to which bias is absent from the sample. When the sample is drawn properly, the measure of behaviour, attitudes or knowledge of some sample elements will be less than the measure of those same variables drawn from the population. Also, the measure of the behaviour, attitudes, or knowledge of other sample elements will be more than the population values. Variations in these sample values offset each other, resulting in a sample value that is close to the population value.
Thus, an accurate (unbiased) sample is one in which the underestimators offset the overestimators.
Systematic variance has been defined as “the variation in measures due to some known or unknown influences that ‘cause’ the scores to lean in on direction more than another.” The systematic variance may be reduced by e.g. increasing the sample size.
Precision: precision of estimate is the second criterion of a good sample design. In order to interpret the findings of research, a measurement of how closely the sample represents the population is needed. The numerical descriptors that describe samples may be expected to differ from those that describe populations because of random fluctuations natural to the sampling process. This is called sampling error (or random sampling error) and reflects the influence of chance in drawing the sample members.
Sampling error is what is left after all known sources of systematic variance have been accounted for. Precision is measured by the standard error of estimate, a type of standard deviation measurement; the smaller the standard error of estimate, the higher is the precision of the sample. The ideal sample design produces a small standard error of estimate.
Two approaches of sample design are as follows: Different decisions researcher have to make can be found in exhibit 6.2 on page 179. Different types of sampling designs are described in table 6.3 on page 180.
Representation - The members of a sample are selected using probability or non-probability procedures.
Probability sampling is based on the concept of random selection – a controlled procedure which ensures that each population element is given a known non-zero change of selection. Non-probability sampling is arbitrary and subjective; when elements are chosen subjectively, there is usually some pattern or scheme used. Thus, each member of the population does not have a known chance of being included.
Element selection - Whether the elements are selected individually and directly from the population – viewed as a single pool – or additional controls are imposed, element selection may also classify samples. If each sample element is drawn individually from the population at large, it is an unrestricted sample. Restricted sampling covers all other forms of sampling.
Probability sampling - is based on the concept of random selection – a controlled procedure that assures that each population element is given a known nonzero chance of selection. Only probability samples provide estimates of precision and offer the opportunity to generalize the findings to the population of interest from the sample population. The unrestricted, simple random sample is the simplest form of probability sampling. Since all probability samples must provide a known non-zero chance of selection for each population element, the simple random sample is considered a special case in which each population element has a known and equal chance of selection. In this section, we use the simple random sample to build a foundation for understanding sampling procedures and choosing probability samples.
Steps in sampling design
STEPS IN SAMPLING DESIGN: There are several questions to be answered in securing a sample. Each requires unique information.
What is the target population? – Good operational definitions are critical in choosing the relevant population.
What are the parameters of interest? – Population parameters are summary descriptors (e.g., incidence proportion, mean, variance) of variables of interest in the population. Sample statistics are descriptors of those same relevant variables computed from sample data. Sample statistics are used as estimators of population parameters. The sample statistics are the basis of conclusions about the population. Depending on how measurement questions are phrased, each may collect a different level of data. Each different level of data also generates different sample statistics. The population proportion of incidence “is equal to the number of elements in the population belonging to the category of interest, divided by the total number of elements in the population.” Proportion measures are necessary for nominal data and are widely used for other measures as well. The most frequent proportion measure is the percentage.
What is the sampling frame? – The sampling frame is closely related to the population. It is the list of elements from which the sample is actually drawn. Ideally, it is a complete and correct list of population members only. A too inclusive frame is a frame that includes many elements other than the ones in which the researcher is interested.
What is the appropriate sampling method? – A researcher must follow an appropriate method and make sure that interviewers (or others) cannot modify the selections made and only the selected elements from the original sampling are included.
What size sample is needed? - Some principles that influence sample size include:
The narrower or smaller the error range, the larger the sample must be.
The greater the dispersion or variance within the population, the larger the sample must be to provide estimation precision.
The higher the confidence level in the estimate, the larger the sample must be.
The greater the desired precision of the estimate, the larger the sample must be.
The greater the number of subgroups of interest within a sample, the greater the sample size must be, as each subgroup must meet minimum sample size requirements.
How much will it cost? – also the costs for each and every experiment have to be taken into consideration, since money is often the factor which limits most of the research.
Probability sampling :
Simple random sampling -
Since all probability samples must provide a known nonzero probability of selection for each population element, the simple random sample is considered a special case in which each population element has a known and equal chance of selection. However, Simple random sampling is often impractical, i.e. it requires a population list (sampling frame) that is often not available; and it fails to use all the information about a population, thus resulting in a design that may be wasteful. It may also be expensive to implement. Therefore alternative probability sampling approaches such as, systematic sampling, stratified sampling, cluster sampling and double sampling, will be considered.
In this approach, every kth element in the population is sampled, beginning with a random start of an element in the range of 1 to k. The kth element, or skip interval, is determined by dividing the sample size into the population size to obtain the skip pattern applied to the sampling frame.
K = skip interval = total population size / size of the desired sample
The major advantage of systematic sampling is its simplicity and flexibility. A concern with systematic sampling is the possible periodicity in the population that parallels the sampling ratio. Another difficulty may arise when there is a monotonic trend in the population elements. That is, the population list varies from the smallest to the largest element or vice versa.
Most populations can be segregated into several mutually exclusive subpopulations, or strata. A stratified random sampling is the process by which the sample is constrained to include elements from each of the segments. After a population is divided into the appropriate strata, a simple random sample can be taken within each stratum. The results from the study can then be weighted (based on the proportion of the strata to the population) and combined into appropriate population estimates.
A stratified random sample is often chosen in order to:
Increase a sample’s statistical efficiency;
Provide adequate data for analysing the various subpopulations or strata;
Enable different research methods and procedures to be used in different strata.
Stratification is usually more efficient statistically than simple random sampling and at worst is equal to it. With the ideal stratification, each stratum is homogeneous internally and heterogeneous with other strata. Also, the more strata used, the closer a researcher comes to maximizing interstrata differences (differences between strata) and minimizing intrastratum variances (differences within a given stratum). The size of the strata can be computed with the following pieces of information:
how large the total sample should be
how the total sample should be allocated among strata.
Proportionate stratified sampling
In proportionate stratified sampling, each stratum is properly represented so that the sample size drawn from the stratum is proportionate to the stratum’s share of the total population. This approach has higher statistical efficiency than a simple random sample and is much easier to carry out than other stratifying methods.
It also provides a self-weighting sample; the population mean or proportion can be estimated simply by calculating the mean or proportion of all sample cases, eliminating the weighting of responses. On the other hand, proportionate stratified samples often gain little in statistical efficiency if the strata measures and their variances are similar for the major variables under study. Any stratification that departs from the proportionate relationship is disproportionate.
This is where the population is divided into groups of elements with some groups randomly selected for study. Two conditions foster the use of cluster sampling:
The need for more economic efficiency than can be provided by simple random sampling;
The frequent unavailability of a practical sampling frame for individual elements
Statistical efficiency for cluster samples is usually lower than for simple random samples, mainly because clusters often don’t meet the need for heterogeneity and, instead, are homogeneous.
An area sampling is the most important form of cluster sampling. It is possible to use when a research involves populations that can be identified with some geographic area. This method overcomes the problems of both high sampling cost and the unavailability of a practical sampling frame for individual elements. In designing cluster samples, including area samples, the following questions should be answered:
How homogeneous are the resulting clusters? – When clusters are homogeneous, this contributes to low statistical efficiency. Sometimes one can improve this efficiency by constructing clusters to increase intracluster variance.
Shall equal-size or unequal-size clusters be sought for? – A cluster sample may be composed of clusters of equal or unequal size.
The theory of clustering is that the means of sample clusters are unbiased estimates of the population mean. This is more often true when clusters are naturally equal, such as households in city blocks. While one can deal with clusters of unequal size, it may be desirable to reduce or counteract the effects of unequal size.
How large a cluster should be taken? – Comparing the efficiency of differing cluster sizes requires that the different costs for each size are discovered and that the different variances of the cluster means are estimated.
Shall a single-stage or multistage cluster be used? – Concerning single-stage or multistage cluster design, for most large-scale area sampling, the tendency is to use multistage designs. Several situations justify drawing a sample within a cluster, in preference to the direct creation of smaller clusters and taking a census of that cluster using one-stage cluster sampling.
How large a sample is needed? – It depends mainly on the specific cluster design.
It may be more convenient or economical to collect some information by sample and then use this information as the basis for selecting a subsample for further study. This procedure is called double sampling, sequential sampling, or multiphase sampling. It is usually found with stratified and/or cluster designs.
Non probability sampling
With a subjective approach like non-probability sampling, the probability of selecting population elements is unknown. There are a variety of ways to choose persons or cases to include in the sample. A greater opportunity for bias to enter the sample selection procedure and to distort the findings of the study exists. Any range within which to expect the population parameter cannot be estimated. There are some practical reasons for using the less precise methods.
1) Convenience – Non-probability samples that are unrestricted are called convenience samples. They are the least reliable design but normally the cheapest and easiest to conduct. Researches or field workers have the freedom to choose whomever they find.
2) Purposive sampling - A non-probability sample that conforms to certain criteria is called purposive sampling. There are two major types – judgment sampling and quota sampling:
Judgment sampling occurs when a researcher selects sample members to conform to some criterion. When used in the early stages of an exploratory study, a judgment sample is appropriate. When one wishes to select a biased group for screening purposes, this sampling method is also a good choice.
Quota sampling is the second type of purposive sampling. It is used to improve representativeness. The logic behind quota sampling is that certain relevant characteristics describe the dimensions of the population. If a sample has the same distribution on these characteristics, then it is likely to be representative of the population regarding other variables on which the researcher has no control. In most quota samples, researchers specify more than one control dimension. Each should meet two tests: (1) It should have a distribution in the population that can be estimated, and (2) be pertinent to the topic studied.
3) Snowball - In the initial stage of snowball sampling, individuals are discovered and may or may not be selected through probability methods. This group is then used to refer the researcher to others who possess similar characteristics and who, in turn, identify others.
Eventually sampling on the internet has significantly increased in the past decades and almost every firm uses the Internet to conduct research.
The unit of analysis describes the level at which the research is performed and which objects are reached. A population element is the subject on which the measurement is being taken. A population is the total collection of elements about which we wish to make some inferences. A census is a count of all the elements in a population.
There are a couple of reasons for sampling:
Greater accuracy of results
Greater speed of data collection
Availability of population elements
There are two conditions for a census study, namely that it should be feasible when the population is small and that it is necessary when the elements are quite different from each other. In order for a sample to be appropriate, it has to be accurate and precise. With regards to accuracy, there should be no systematic variance within a sample. It is the ‘’variation in measures due to some known or unknown influences that ‘’cause’’ the scores to lean in one direction more than another.
Probability sampling is a controlled procedure that ensures that each population element is given a non-zero change of selection. Non-probability sampling is arbitrary and subjective. A simple random sample is the easiest form of probability sampling. It is known as a special case in which every population element has a known and equal chance of selection.
Population parameters are summary descriptors of variables of interest in the population. Sample statistics are descriptors of the relevant variables computed from sample data. The population proportion of incidence is ‘’equal to the number of elements in the population belonging to the category of interest, divided by the total number of elements in the population’’. In addition to figuring out what the parameters of interest are, it is also important for researchers to find out about the relevant population, sampling frame, sample size and costs.
The standard error of the mean is a measure of the standard deviation of the distribution of sample means.
Systematic sampling is an approach in with every nth element in the population is sampled, starting with a random start of an element in the range of one to n. The nth element is determined by dividing the sample size into the population size to obtain the skip pattern applied to the sampling frame.
Stratified random sampling is the process by which the sample is constrained to include elements from each of the segments. Proportionate stratified sampling is a way of sampling in which every single stratum is neatly represented in such a way that the sample drawn from it is proportionate to the stratum’s share of the total population. Disproportionate stratified sampling is a way of sampling in which any stratification that departs from the proportionate relationship is disproportionate.
Cluster sampling is a way of sampling in which the population can also be divided into groups of elements with some groups randomly selected for study. Area sampling is a way of sampling that does not have problems of high sampling cost and the unavailability of a practical sampling frame for individual elements. Simple-cluster sampling is a way of sampling in which only single-stage samples with equally-sized clusters are treated.
Double sampling, sequential sampling or multi-phase sampling are ways of sampling in which some information is collected by sample and then used as the bases for selecting a sub-sample for further study, because this is more convenient.
Convenience samples are samples that are non-probability and unrestricted. Purposive sampling is also a type of non-probability sampling, but one that conforms to certain criteria. There are two types:
Judgement sampling: occurs when a researcher selects sample members to conform to some criterion.
Quota sampling: Improves representativeness. In this type there are usually more than one control dimensions, and each one of them should have a distribution in the population that can be estimated, and should be pertinent to the topic that is being studied.
Snowball sampling is a way of sampling in which individuals are discovered in the initial stage, and may/may not be selected through probability methods. This type of sampling can be very useful if the aim is to sample subjects that are very difficult to identify, as they are nowhere registered as a population.
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