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3.5 Simple Random Sampling and Other Sampling Methods

Population Parameter vs. Sample Statistic

❶In quota sampling the selection of the sample is non- random. Total errors can be classified into sampling errors and non-sampling errors.

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Probability vs. Non-Probability Samples

Probability samples are selected in such a way as to be representative of the population. They provide the most valid or credible results because they reflect the characteristics of the population from which they are selected e. There are two types of probability samples: The term random has a very precise meaning.

Each individual in the population of interest has an equal likelihood of selection. This is a very strict meaning -- you can't just collect responses on the street and have a random sample. The assumption of an equal chance of selection means that sources such as a telephone book or voter registration lists are not adequate for providing a random sample of a community. In both these cases there will be a number of residents whose names are not listed.

Telephone surveys get around this problem by random-digit dialing -- but that assumes that everyone in the population has a telephone.

The key to random selection is that there is no bias involved in the selection of the sample. Any variation between the sample characteristics and the population characteristics is only a matter of chance. A stratified sample is a mini-reproduction of the population. Before sampling, the population is divided into characteristics of importance for the research.

For example, by gender, social class, education level, religion, etc. Then the population is randomly sampled within each category or stratum.

How to Construct a probability representative sample. As they are not truly representative, non-probability samples are less desirable than probability samples. However, a researcher may not be able to obtain a random or stratified sample, or it may be too expensive. A researcher may not care about generalizing to a larger population.

The validity of non-probability samples can be increased by trying to approximate random selection, and by eliminating as many sources of bias as possible.

A researcher is interested in the attitudes of members of different religions towards the death penalty. In Iowa a random sample might miss Muslims because there are not many in that state. However, the sample will no longer be representative of the actual proportions in the population. This may limit generalizing to the state population. Although the population of interest often consists of physical objects, sometimes we need to sample over time, space, or some combination of these dimensions.

For instance, an investigation of supermarket staffing could examine checkout line length at various times, or a study on endangered penguins might aim to understand their usage of various hunting grounds over time. For the time dimension, the focus may be on periods or discrete occasions. In other cases, our 'population' may be even less tangible. For example, Joseph Jagger studied the behaviour of roulette wheels at a casino in Monte Carlo , and used this to identify a biased wheel.

In this case, the 'population' Jagger wanted to investigate was the overall behaviour of the wheel i. Similar considerations arise when taking repeated measurements of some physical characteristic such as the electrical conductivity of copper. This situation often arises when we seek knowledge about the cause system of which the observed population is an outcome. In such cases, sampling theory may treat the observed population as a sample from a larger 'superpopulation'.

For example, a researcher might study the success rate of a new 'quit smoking' program on a test group of patients, in order to predict the effects of the program if it were made available nationwide. Here the superpopulation is "everybody in the country, given access to this treatment" — a group which does not yet exist, since the program isn't yet available to all.

Note also that the population from which the sample is drawn may not be the same as the population about which we actually want information. Often there is large but not complete overlap between these two groups due to frame issues etc. Sometimes they may be entirely separate — for instance, we might study rats in order to get a better understanding of human health, or we might study records from people born in in order to make predictions about people born in Time spent in making the sampled population and population of concern precise is often well spent, because it raises many issues, ambiguities and questions that would otherwise have been overlooked at this stage.

In the most straightforward case, such as the sampling of a batch of material from production acceptance sampling by lots , it would be most desirable to identify and measure every single item in the population and to include any one of them in our sample.

However, in the more general case this is not usually possible or practical. There is no way to identify all rats in the set of all rats. Where voting is not compulsory, there is no way to identify which people will actually vote at a forthcoming election in advance of the election. These imprecise populations are not amenable to sampling in any of the ways below and to which we could apply statistical theory. As a remedy, we seek a sampling frame which has the property that we can identify every single element and include any in our sample.

For example, in an opinion poll , possible sampling frames include an electoral register and a telephone directory. A probability sample is a sample in which every unit in the population has a chance greater than zero of being selected in the sample, and this probability can be accurately determined. The combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their probability of selection.

We want to estimate the total income of adults living in a given street. We visit each household in that street, identify all adults living there, and randomly select one adult from each household. For example, we can allocate each person a random number, generated from a uniform distribution between 0 and 1, and select the person with the highest number in each household. We then interview the selected person and find their income.

People living on their own are certain to be selected, so we simply add their income to our estimate of the total. But a person living in a household of two adults has only a one-in-two chance of selection. To reflect this, when we come to such a household, we would count the selected person's income twice towards the total. The person who is selected from that household can be loosely viewed as also representing the person who isn't selected.

In the above example, not everybody has the same probability of selection; what makes it a probability sample is the fact that each person's probability is known. When every element in the population does have the same probability of selection, this is known as an 'equal probability of selection' EPS design. Such designs are also referred to as 'self-weighting' because all sampled units are given the same weight. These various ways of probability sampling have two things in common:.

It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection. Hence, because the selection of elements is nonrandom, nonprobability sampling does not allow the estimation of sampling errors.

These conditions give rise to exclusion bias , placing limits on how much information a sample can provide about the population. Information about the relationship between sample and population is limited, making it difficult to extrapolate from the sample to the population. We visit every household in a given street, and interview the first person to answer the door. In any household with more than one occupant, this is a nonprobability sample, because some people are more likely to answer the door e.

Nonprobability sampling methods include convenience sampling , quota sampling and purposive sampling. In addition, nonresponse effects may turn any probability design into a nonprobability design if the characteristics of nonresponse are not well understood, since nonresponse effectively modifies each element's probability of being sampled. Within any of the types of frames identified above, a variety of sampling methods can be employed, individually or in combination.

Factors commonly influencing the choice between these designs include:. In a simple random sample SRS of a given size, all such subsets of the frame are given an equal probability. Each element of the frame thus has an equal probability of selection: Furthermore, any given pair of elements has the same chance of selection as any other such pair and similarly for triples, and so on.

This minimizes bias and simplifies analysis of results. In particular, the variance between individual results within the sample is a good indicator of variance in the overall population, which makes it relatively easy to estimate the accuracy of results.

SRS can be vulnerable to sampling error because the randomness of the selection may result in a sample that doesn't reflect the makeup of the population. For instance, a simple random sample of ten people from a given country will on average produce five men and five women, but any given trial is likely to overrepresent one sex and underrepresent the other.

Systematic and stratified techniques attempt to overcome this problem by "using information about the population" to choose a more "representative" sample. SRS may also be cumbersome and tedious when sampling from an unusually large target population. In some cases, investigators are interested in "research questions specific" to subgroups of the population. For example, researchers might be interested in examining whether cognitive ability as a predictor of job performance is equally applicable across racial groups.

SRS cannot accommodate the needs of researchers in this situation because it does not provide subsamples of the population. Systematic sampling also known as interval sampling relies on arranging the study population according to some ordering scheme and then selecting elements at regular intervals through that ordered list. Systematic sampling involves a random start and then proceeds with the selection of every k th element from then onwards. It is important that the starting point is not automatically the first in the list, but is instead randomly chosen from within the first to the k th element in the list.

A simple example would be to select every 10th name from the telephone directory an 'every 10th' sample, also referred to as 'sampling with a skip of 10'. As long as the starting point is randomized , systematic sampling is a type of probability sampling. It is easy to implement and the stratification induced can make it efficient, if the variable by which the list is ordered is correlated with the variable of interest. For example, suppose we wish to sample people from a long street that starts in a poor area house No.

A simple random selection of addresses from this street could easily end up with too many from the high end and too few from the low end or vice versa , leading to an unrepresentative sample.

Note that if we always start at house 1 and end at , the sample is slightly biased towards the low end; by randomly selecting the start between 1 and 10, this bias is eliminated. However, systematic sampling is especially vulnerable to periodicities in the list. If periodicity is present and the period is a multiple or factor of the interval used, the sample is especially likely to be un representative of the overall population, making the scheme less accurate than simple random sampling.

For example, consider a street where the odd-numbered houses are all on the north expensive side of the road, and the even-numbered houses are all on the south cheap side. Under the sampling scheme given above, it is impossible to get a representative sample; either the houses sampled will all be from the odd-numbered, expensive side, or they will all be from the even-numbered, cheap side, unless the researcher has previous knowledge of this bias and avoids it by a using a skip which ensures jumping between the two sides any odd-numbered skip.

Another drawback of systematic sampling is that even in scenarios where it is more accurate than SRS, its theoretical properties make it difficult to quantify that accuracy. In the two examples of systematic sampling that are given above, much of the potential sampling error is due to variation between neighbouring houses — but because this method never selects two neighbouring houses, the sample will not give us any information on that variation.

As described above, systematic sampling is an EPS method, because all elements have the same probability of selection in the example given, one in ten. It is not 'simple random sampling' because different subsets of the same size have different selection probabilities — e. When the population embraces a number of distinct categories, the frame can be organized by these categories into separate "strata.

There are several potential benefits to stratified sampling. First, dividing the population into distinct, independent strata can enable researchers to draw inferences about specific subgroups that may be lost in a more generalized random sample.

Second, utilizing a stratified sampling method can lead to more efficient statistical estimates provided that strata are selected based upon relevance to the criterion in question, instead of availability of the samples. Even if a stratified sampling approach does not lead to increased statistical efficiency, such a tactic will not result in less efficiency than would simple random sampling, provided that each stratum is proportional to the group's size in the population.

Third, it is sometimes the case that data are more readily available for individual, pre-existing strata within a population than for the overall population; in such cases, using a stratified sampling approach may be more convenient than aggregating data across groups though this may potentially be at odds with the previously noted importance of utilizing criterion-relevant strata. Finally, since each stratum is treated as an independent population, different sampling approaches can be applied to different strata, potentially enabling researchers to use the approach best suited or most cost-effective for each identified subgroup within the population.

There are, however, some potential drawbacks to using stratified sampling. First, identifying strata and implementing such an approach can increase the cost and complexity of sample selection, as well as leading to increased complexity of population estimates. Second, when examining multiple criteria, stratifying variables may be related to some, but not to others, further complicating the design, and potentially reducing the utility of the strata. Finally, in some cases such as designs with a large number of strata, or those with a specified minimum sample size per group , stratified sampling can potentially require a larger sample than would other methods although in most cases, the required sample size would be no larger than would be required for simple random sampling.

Stratification is sometimes introduced after the sampling phase in a process called "poststratification". Although the method is susceptible to the pitfalls of post hoc approaches, it can provide several benefits in the right situation. Implementation usually follows a simple random sample. In addition to allowing for stratification on an ancillary variable, poststratification can be used to implement weighting, which can improve the precision of a sample's estimates.

Choice-based sampling is one of the stratified sampling strategies. In choice-based sampling, [7] the data are stratified on the target and a sample is taken from each stratum so that the rare target class will be more represented in the sample. The model is then built on this biased sample. The effects of the input variables on the target are often estimated with more precision with the choice-based sample even when a smaller overall sample size is taken, compared to a random sample.

The results usually must be adjusted to correct for the oversampling. In some cases the sample designer has access to an "auxiliary variable" or "size measure", believed to be correlated to the variable of interest, for each element in the population. These data can be used to improve accuracy in sample design.

One option is to use the auxiliary variable as a basis for stratification, as discussed above. Another option is probability proportional to size 'PPS' sampling, in which the selection probability for each element is set to be proportional to its size measure, up to a maximum of 1. In a simple PPS design, these selection probabilities can then be used as the basis for Poisson sampling.

However, this has the drawback of variable sample size, and different portions of the population may still be over- or under-represented due to chance variation in selections. Systematic sampling theory can be used to create a probability proportionate to size sample. This is done by treating each count within the size variable as a single sampling unit.

Samples are then identified by selecting at even intervals among these counts within the size variable. This method is sometimes called PPS-sequential or monetary unit sampling in the case of audits or forensic sampling.

The PPS approach can improve accuracy for a given sample size by concentrating sample on large elements that have the greatest impact on population estimates. PPS sampling is commonly used for surveys of businesses, where element size varies greatly and auxiliary information is often available—for instance, a survey attempting to measure the number of guest-nights spent in hotels might use each hotel's number of rooms as an auxiliary variable.

In some cases, an older measurement of the variable of interest can be used as an auxiliary variable when attempting to produce more current estimates. Sometimes it is more cost-effective to select respondents in groups 'clusters'. Sampling is often clustered by geography, or by time periods. Nearly all samples are in some sense 'clustered' in time — although this is rarely taken into account in the analysis.

For instance, if surveying households within a city, we might choose to select city blocks and then interview every household within the selected blocks. Clustering can reduce travel and administrative costs. In the example above, an interviewer can make a single trip to visit several households in one block, rather than having to drive to a different block for each household. It also means that one does not need a sampling frame listing all elements in the target population.

Instead, clusters can be chosen from a cluster-level frame, with an element-level frame created only for the selected clusters. In the example above, the sample only requires a block-level city map for initial selections, and then a household-level map of the selected blocks, rather than a household-level map of the whole city.

Cluster sampling also known as clustered sampling generally increases the variability of sample estimates above that of simple random sampling, depending on how the clusters differ between one another as compared to the within-cluster variation. For this reason, cluster sampling requires a larger sample than SRS to achieve the same level of accuracy — but cost savings from clustering might still make this a cheaper option.

Cluster sampling is commonly implemented as multistage sampling. This is a complex form of cluster sampling in which two or more levels of units are embedded one in the other. The first stage consists of constructing the clusters that will be used to sample from. In the second stage, a sample of primary units is randomly selected from each cluster rather than using all units contained in all selected clusters.

In following stages, in each of those selected clusters, additional samples of units are selected, and so on. All ultimate units individuals, for instance selected at the last step of this procedure are then surveyed.

This technique, thus, is essentially the process of taking random subsamples of preceding random samples. Multistage sampling can substantially reduce sampling costs, where the complete population list would need to be constructed before other sampling methods could be applied. By eliminating the work involved in describing clusters that are not selected, multistage sampling can reduce the large costs associated with traditional cluster sampling.

In quota sampling , the population is first segmented into mutually exclusive sub-groups, just as in stratified sampling. Then judgement is used to select the subjects or units from each segment based on a specified proportion.


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There are many methods of sampling when doing research. This guide can help you choose which method to use. Simple random sampling is the ideal, but researchers seldom have the luxury of time or money to access the whole population, so many compromises often have to be made.

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Sampling Methods. Sampling and types of sampling methods commonly used in quantitative research are discussed in the following module. Learning Objectives.

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How to do sampling for qual and quant research designs. Sampling Let's begin by covering some of the key terms in sampling like "population" and "sampling frame." Then, because some types of sampling rely upon quantitative models, we'll talk about some of the statistical terms used in sampling.

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In probability sampling it is possible to both determine which sampling units belong to which sample and the probability that each sample will be selected. The following sampling methods are examples of probability sampling: Of the five methods listed above, students have the most trouble. Covers survey sampling methods. Describes probability and non-probability samples, from convenience samples to multistage random samples. Includes free video.