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3.5 Simple Random Sampling and Other Sampling Methods

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## The Purpose of Sampling

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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. 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.

This is called sampling. The group from which the data is drawn is a representative sample of the population the results of the study can be generalized to the population as a whole. The sample will be representative of the population if the researcher uses a random selection procedure to choose participants. The group of units or individuals who have a legitimate chance of being selected are sometimes referred to as the sampling frame. If a researcher studied developmental milestones of preschool children and target licensed preschools to collect the data, the sampling frame would be all preschool aged children in those preschools.

Students in those preschools could then be selected at random through a systematic method to participate in the study. This does, however, lead to a discussion of biases in research. For example, low-income children may be less likely to be enrolled in preschool and therefore, may be excluded from the study. Extra care has to be taken to control biases when determining sampling techniques. There are two main types of sampling: The difference between the two types is whether or not the sampling selection involves randomization.

Randomization occurs when all members of the sampling frame have an equal opportunity of being selected for the study. Following is a discussion of probability and non-probability sampling and the different types of each. Probability Sampling — Uses randomization and takes steps to ensure all members of a population have a chance of being selected. There are several variations on this type of sampling and following is a list of ways probability sampling may occur:.

Non-probability Sampling — Does not rely on the use of randomization techniques to select members. This is typically done in studies where randomization is not possible in order to obtain a representative sample. Bias is more of a concern with this type of sampling. The different types of non-probability sampling are as follows:. The following Slideshare presentation, Sampling in Quantitative and Qualitative Research — A practical how to, offers an overview of sampling methods for quantitative research and contrasts them with qualitative method for further understanding.

Examples of Data Collection Methods — Following is a link to a chart of data collection methods that examines types of data collection, advantages and challenges. Qualitative and Quantitative Data Collection Methods - The link below provides specific example of instruments and methods used to collect quantitative data. Sampling and Measurement - The link below defines sampling and discusses types of probability and nonprobability sampling.

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.

- Definition, Methods & Importance The sample of a study can have a profound impact on the outcome of a study. In this lesson, we'll look at the procedure for drawing a sample and why it is so important to draw a sample that represents the population.

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. Sampling is the process of selecting units (e.g., people, organizations) from a population of interest so that by studying the sample we may fairly generalize our results back to .

This was a presentation that was carried out in our research method class by our group. It will be useful for PHD and master students quantitative and qualitat. 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.