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# Sampling (statistics)

❶Describe how sample size is determined.

## 2. Non-probability Sampling Methods

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. For example, an interviewer may be told to sample females and males between the age of 45 and It is this second step which makes the technique one of non-probability sampling.

In quota sampling the selection of the sample is non- random. For example, interviewers might be tempted to interview those who look most helpful. The problem is that these samples may be biased because not everyone gets a chance of selection. This random element is its greatest weakness and quota versus probability has been a matter of controversy for several years. In imbalanced datasets, where the sampling ratio does not follow the population statistics, one can resample the dataset in a conservative manner called minimax sampling.

The minimax sampling has its origin in Anderson minimax ratio whose value is proved to be 0. This ratio can be proved to be minimax ratio only under the assumption of LDA classifier with Gaussian distributions. The notion of minimax sampling is recently developed for a general class of classification rules, called class-wise smart classifiers. In this case, the sampling ratio of classes is selected so that the worst case classifier error over all the possible population statistics for class prior probabilities, would be the.

Accidental sampling sometimes known as grab , convenience or opportunity sampling is a type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand.

That is, a population is selected because it is readily available and convenient. It may be through meeting the person or including a person in the sample when one meets them or chosen by finding them through technological means such as the internet or through phone. The researcher using such a sample cannot scientifically make generalizations about the total population from this sample because it would not be representative enough. This type of sampling is most useful for pilot testing.

Several important considerations for researchers using convenience samples include:. In social science research, snowball sampling is a similar technique, where existing study subjects are used to recruit more subjects into the sample. Some variants of snowball sampling, such as respondent driven sampling, allow calculation of selection probabilities and are probability sampling methods under certain conditions. The voluntary sampling method is a type of non-probability sampling.

A voluntary sample is made up of people who self-select into the survey. Often, these subjects have a strong interest in the main topic of the survey. Volunteers may be invited through advertisements on Social Media Sites [9]. This method is suitable for a research which can be done through filling a questionnaire.

The target population for advertisements can be selected by characteristics like demography, age, gender, income, occupation, education level or interests using advertising tools provided by the social media sites. The advertisement may include a message about the research and will link to a web survey.

After voluntary following the link and submitting the web based questionnaire, the respondent will be included in the sample population.

This method can reach a global population and limited by the advertisement budget. This method may permit volunteers outside the reference population to volunteer and get included in the sample. It is difficult to make generalizations about the total population from this sample because it would not be representative enough. Line-intercept sampling is a method of sampling elements in a region whereby an element is sampled if a chosen line segment, called a "transect", intersects the element.

Panel sampling is the method of first selecting a group of participants through a random sampling method and then asking that group for potentially the same information several times over a period of time.

Therefore, each participant is interviewed at two or more time points; each period of data collection is called a "wave". The method was developed by sociologist Paul Lazarsfeld in as a means of studying political campaigns. Panel sampling can also be used to inform researchers about within-person health changes due to age or to help explain changes in continuous dependent variables such as spousal interaction.

Snowball sampling involves finding a small group of initial respondents and using them to recruit more respondents. It is particularly useful in cases where the population is hidden or difficult to enumerate.

Theoretical sampling [12] occurs when samples are selected on the basis of the results of the data collected so far with a goal of developing a deeper understanding of the area or develop theories. Sampling schemes may be without replacement 'WOR'—no element can be selected more than once in the same sample or with replacement 'WR'—an element may appear multiple times in the one sample. For example, if we catch fish, measure them, and immediately return them to the water before continuing with the sample, this is a WR design, because we might end up catching and measuring the same fish more than once.

However, if we do not return the fish to the water, this becomes a WOR design. If we tag and release the fish we caught, we can see whether we have caught a particular fish before. Sampling enables the selection of right data points from within the larger data set to estimate the characteristics of the whole population.

For example, there are about million tweets produced every day. It is not necessary to look at all of them to determine the topics that are discussed during the day, nor is it necessary to look at all the tweets to determine the sentiment on each of the topics.

A theoretical formulation for sampling Twitter data has been developed. In manufacturing different types of sensory data such as acoustics, vibration, pressure, current, voltage and controller data are available at short time intervals.

To predict down-time it may not be necessary to look at all the data but a sample may be sufficient. Survey results are typically subject to some error. Total errors can be classified into sampling errors and non-sampling errors.

The term "error" here includes systematic biases as well as random errors. Non-sampling errors are other errors which can impact the final survey estimates, caused by problems in data collection, processing, or sample design. After sampling, a review should be held of the exact process followed in sampling, rather than that intended, in order to study any effects that any divergences might have on subsequent analysis.

A particular problem is that of non-response. Two major types of non-response exist: In this case, there is a risk of differences, between respondents and nonrespondents, leading to biased estimates of population parameters.

This is often addressed by improving survey design, offering incentives, and conducting follow-up studies which make a repeated attempt to contact the unresponsive and to characterize their similarities and differences with the rest of the frame. Nonresponse is particularly a problem in internet sampling. Reasons for this problem include improperly designed surveys, [16] over-surveying or survey fatigue , [11] [19] and the fact that potential participants hold multiple e-mail addresses, which they don't use anymore or don't check regularly.

In many situations the sample fraction may be varied by stratum and data will have to be weighted to correctly represent the population.

Thus for example, a simple random sample of individuals in the United Kingdom might include some in remote Scottish islands who would be inordinately expensive to sample. A cheaper method would be to use a stratified sample with urban and rural strata. The rural sample could be under-represented in the sample, but weighted up appropriately in the analysis to compensate.

More generally, data should usually be weighted if the sample design does not give each individual an equal chance of being selected. For instance, when households have equal selection probabilities but one person is interviewed from within each household, this gives people from large households a smaller chance of being interviewed.

This can be accounted for using survey weights. Similarly, households with more than one telephone line have a greater chance of being selected in a random digit dialing sample, and weights can adjust for this. Random sampling by using lots is an old idea, mentioned several times in the Bible. In Pierre Simon Laplace estimated the population of France by using a sample, along with ratio estimator.

He also computed probabilistic estimates of the error. His estimates used Bayes' theorem with a uniform prior probability and assumed that his sample was random.

When you are finished reading this article you may want to go to the Gallup Poll Web site, https: It is important to be mindful of margin or error as discussed in this article. We all need to remember that public opinion on a given topic cannot be appropriately measured with one question that is only asked on one poll.

Such results only provide a snapshot at that moment under certain conditions. The concept of repeating procedures over different conditions and times leads to more valuable and durable results. Within this section of the Gallup article, there is also an error: In 5 of those surveys, the confidence interval would not contain the population percent. Eberly College of Science. Printer-friendly version Sampling Methods can be classified into one of two categories: Sample has a known probability of being selected Non-probability Sampling: Sample does not have known probability of being selected as in convenience or voluntary response surveys Probability Sampling 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.

Simple Random Sampling SRS Stratified Sampling Cluster Sampling Systematic Sampling Multistage Sampling in which some of the methods above are combined in stages Of the five methods listed above, students have the most trouble distinguishing between stratified sampling and cluster sampling. With stratified sampling one should: With cluster sampling one should divide the population into groups clusters.

Stratified sampling would be preferred over cluster sampling, particularly if the questions of interest are affected by time zone. For example the percentage of people watching a live sporting event on television might be highly affected by the time zone they are in. Cluster sampling really works best when there are a reasonable number of clusters relative to the entire population.

In this case, selecting 2 clusters from 4 possible clusters really does not provide much advantage over simple random sampling. Either stratified sampling or cluster sampling could be used. It would depend on what questions are being asked. For instance, consider the question "Do you agree or disagree that you receive adequate attention from the team of doctors at the Sports Medicine Clinic when injured?

In contrast, if the question of interest is "Do you agree or disagree that weather affects your performance during an athletic event? Consequently, stratified sampling would be preferred. Cluster sampling would probably be better than stratified sampling if each individual elementary school appropriately represents the entire population as in aschool district where students from throughout the district can attend any school.

Stratified sampling could be used if the elementary schools had very different locations and served only their local neighborhood i. Again, the questions of interest would affect which sampling method should be used. Non-probability Sampling The following sampling methods that are listed in your text are types of non-probability sampling that should be avoided: Welcome to STAT !

Benefits, Risks, and Measurements Lesson 3: Lesson 3 - Have Fun With It! Getting the Big Picture and Summaries Lesson 5: Relationships Between Measurement Variables Lesson 7: Relationships Between Categorical Variables Lesson 8:

## Main Topics

Sampling Methods. Sampling and types of sampling methods commonly used in quantitative research are discussed in the following module. Learning Objectives: Define sampling and randomization. Explain probability and non-probability sampling and describes the different types of each.

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