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# Sampling (statistics)

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❶For 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. Learn when systematic sampling is better than simple random sampling, such as in the absence of data patterns and when there

## BREAKING DOWN 'Sampling'

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. Similar to stratified but does not involve random selection. Quotas for subgroups proportions are established.

Purposive - aka judgmental or expert ' s choice sampling. Researcher uses personal judgement to select subjects that are considered to be representative of the population. Typical subjects experiencing problem being studied. Subjects refer the researcher to others who might be recruited as subjects. Time Frame for Studying the Sample. General rule - as large as possible to increase the representativeness of the sample.

Relatively small samples in qualitative, exploratory, case studies, experimental and quasi-experimental studies. Descriptive studies need large samples; e. As the number of variables studied increases, the sample size also needs to increase in order to detect significant relationships or differences. A minimum of 30 subjects is needed for use of the central limit theorem statistics based on the mean. Statistical tests used require minimum sample or subgroup size.

Background Information for Understanding Power Analysis: Type I and Type II errors. Based on the statistical analysis of data, the researcher wrongly rejects a true null hypothesis; and therefore, accepts a false alternative hypothesis.

Probability of committing a type I error is controlled by the researcher with the level of significance, alpha. Alpha a is the probability that a Type I error will occur. Based on the statistical analysis of data, the researcher wrongly accepts a false null hypothesis; and therefore, rejects a true alternate hypothesis.

Probability of committing a Type II error is reduced by a power analysis. Probability of a Type II error is called beta b. Power, or 1- b is the probability of rejecting the null hypothesis and obtaining a statistically significant result. In the real world, the actual situations is that the null hypothesis is: Based on statistical analysis, the researcher concludes that: Null hypothesis is accepted. Population Effect Size - Gamma g. Gamma g measures how wrong the null hypothesis is; it measures how strong the effect of the IV is on the DV; and it is used in performing a power analysis.

Gamma g is calculated based on population data from prior research studies, or determined several different ways depending on the nature of the data and the statistical tests to be performed. The textbook discusses 4 ways to estimate gamma population effect size based upon: Testing bivariate correlation relationship between 2 variables Pearson's r. Testing the difference in proportions between 2 groups chi-square. If there is no relevant research on topic to estimate the population effect size gamma , then use guidelines for gamma g or its equivalent.

Testing the difference in proportions between 2 groups chi-square - no conventions for unknown populations. Determining Sample Size through Power Analysis. Mathematical formulas and computer programs can also be used for calculation of sample size. Sampling Error and Sampling Bias. Also called systematic bias or systematic variance.

The difference between sample data and population data that can be attributed to faulty sampling of the population. 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:.

## Main Topics

- 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.

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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.

Types of Sampling Methods and Techniques in Research The main goal of any marketing or statistical research is to provide quality results that are a reliable basis for decision-making. That is why the different types of sampling methods and techniques have a crucial role in research methodology and statistics. RESEARCH METHOD - SAMPLING 1. Sampling Techniques & Samples Types 2. Outlines Sample definition Purpose of sampling Stages in the selection of a sample Types of sampling in quantitative researches Types of sampling in qualitative researches Ethical Considerations in Data Collection.