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# Sampling (statistics)

❶The textbook by Groves et alia provides an overview of survey methodology, including recent literature on questionnaire development informed by cognitive psychology:.

## What is 'Sampling'

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. A list of all institutionalized elderly with Alzheimer ' s in St. Louis area who are members of the St. Probability Sampling Methods Also called random sampling.

Using a table of random numbers in book. Population is divided into subgroups, called strata, according to some variable or variables in importance to the study Variables often used include: Subgroup sample sizes equal the proportions of the subgroup in the population Example: A high school population has.

Subgroup sample sizes are not equal to the proportion of the subgroup in the population Example. A random sampling process that involves stages of sampling The population is first listed by clusters or categories Procedure.

Randomly select 1 or more clusters and take all of their elements single stage cluster sampling ; e. Midwest region of the US Or, in a second stage randomly select clusters from the first stage of clusters; eg 3 states within the Midwest region In a third stage, randomly select elements from the second stage of clusters; e.

A random sampling process in which every kth e. Probably will have to return to the beginning of the list to complete the selection of the sample. Non-probability sampling methods Characteristics. Selection of sample to reflect certain characteristics of the population Similar to stratified but does not involve random selection Quotas for subgroups proportions are established E.

Also known as network sampling Subjects refer the researcher to others who might be recruited as subjects. Sample Size General rule - as large as possible to increase the representativeness of the sample Increased size decreases sampling error Relatively small samples in qualitative, exploratory, case studies, experimental and quasi-experimental studies Descriptive studies need large samples; e.

Background Information for Understanding Power Analysis:. 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. 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:. 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: 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 Consequence of selecting subjects whose characteristics scores are different in some way from the population they are suppose to represent This usually occurs when randomization is not used.

The assignment of subjects to treatment conditions in a random manner. It has no bearing on how the subjects participating in an experiment are initially selected.

Definition - a complete set of elements persons or objects that possess some common characteristic defined by the sampling criteria established by the researcher. The entire group of people or objects to which the researcher wishes to generalize the study findings. Meet set of criteria of interest to researcher. All institutionalized elderly with Alzheimer ' s. May be limited to region, state, city, county, or institution. Louis county nursing homes.

All low birth weight infants admitted to the neonatal ICUs in St. All school-age children with asthma treated in pediatric asthma clinics in university-affiliated medical centers in the Midwest. Could be extremely large if population is national or international in nature. Frame is needed so that everyone in the population is identified so they will have an equal opportunity for selection as a subject element.

Louis county nursing homes affiliated with BJC. A list of all low birth weight infants admitted to the neonatal ICUs in St. Systematic sampling uses a random starting point and a periodic interval to select items for a sample. The sampling interval is calculated as the population size divided by the sample size. The CPA tests the sample of 60 checks and finds no errors; the accountant concludes that the internal control over cash is working properly. Before presenting products to the market, companies generally identify the needs and wants of their target audience.

Gathering the opinions of the sample helps to identify the needs of the whole. A sampling distribution is a probability distribution of a statistic The central limit theorem states that when one aggregates samples A T distribution is a type of probability function that is appropriate Learn more about the convenience of the subscription beauty box industry, and discover why the Birchbox company in particular has become so popular.

## Main Topics

Once you know your population, sampling frame, sampling method, and sample size, you can use all that information to choose your sample. Importance As you can see, choosing a sample is a complicated process.

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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 the population from which they were chosen.