Different Categories of Family Size on a Survey

Pick of information points in statistics.

A visual representation of the sampling procedure

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to guess characteristics of the whole population. Statisticians endeavor to collect samples that are representative of the population in question. Sampling has lower costs and faster data drove than measuring the entire population and can provide insights in cases where it is infeasible to sample an entire population.

Each ascertainment measures i or more than properties (such as weight, location, color) of independent objects or individuals. In survey sampling, weights can be applied to the information to conform for the sample design, especially in stratified sampling.^[1] Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population.^[two] Credence sampling is used to determine if a production lot of fabric meets the governing specifications.

Population definition [edit]

Successful statistical practice is based on focused trouble definition. In sampling, this includes defining the "population" from which our sample is drawn. A population can exist defined as including all people or items with the characteristic ane wishes to empathize. Because there is very rarely plenty fourth dimension or money to get together information from everyone or everything in a population, the goal becomes finding a representative sample (or subset) of that population.

Sometimes what defines a population is obvious. For example, a manufacturer needs to decide whether a batch of cloth from production is of loftier enough quality to be released to the client, or should be sentenced for fleck or rework due to poor quality. In this case, the batch is the population.

Although the population of interest frequently consists of physical objects, sometimes information technology is necessary to sample over fourth dimension, space, or some combination of these dimensions. For case, an investigation of supermarket staffing could examine checkout line length at various times, or a report on endangered penguins might aim to empathise their usage of various hunting grounds over time. For the time dimension, the focus may be on periods or discrete occasions.

In other cases, the examined '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 example, the 'population' Jagger wanted to investigate was the overall behaviour of the cycle (i.e. the probability distribution of its results over infinitely many trials), while his 'sample' was formed from observed results from that cycle. Similar considerations arise when taking repeated measurements of some physical characteristic such every bit the electrical conductivity of copper.

This situation ofttimes arises when seeking 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 written report the success charge per unit of a new 'quit smoking' program on a exam group of 100 patients, in order to predict the effects of the programme if it were made available nationwide. Here the superpopulation is "everybody in the country, given access to this treatment" – a group which does not nonetheless be, since the program isn't yet bachelor to all.

The population from which the sample is fatigued may not be the same every bit the population about which information is desired. Often there is large just not complete overlap between these two groups due to frame issues etc. (run across below). Sometimes they may be entirely split up – for instance, one might study rats in gild to get a better agreement of human health, or 1 might study records from people born in 2008 in order to make predictions about people born in 2009.

Time spent in making the sampled population and population of business organisation precise is oftentimes well spent, considering it raises many issues, ambiguities and questions that would otherwise take been overlooked at this stage.

Sampling frame [edit]

In the most straightforward case, such every bit the sampling of a batch of material from product (credence sampling by lots), it would be almost desirable to identify and measure every unmarried item in the population and to include any ane of them in our sample. Even so, in the more general case this is not usually possible or practical. There is no manner to identify all rats in the ready of all rats. Where voting is non compulsory, there is no way to identify which people will vote at a forthcoming election (in advance of the election). These imprecise populations are non amenable to sampling in whatsoever of the means beneath and to which we could employ statistical theory.

As a remedy, we seek a sampling frame which has the property that we tin can identify every unmarried element and include any in our sample.^[three] ^[iv] ^[5] ^[6] The well-nigh straightforward type of frame is a list of elements of the population (preferably the entire population) with appropriate contact information. For example, in an stance 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 cypher) of being selected in the sample, and this probability tin 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.

Example: We want to estimate the full income of adults living in a given street. We visit each household in that street, identify all adults living there, and randomly select 1 adult from each household. (For case, we tin allocate each person a random number, generated from a uniform distribution betwixt 0 and ane, and select the person with the highest number in each household). We and so interview the selected person and find their income.

People living on their own are certain to be selected, so nosotros simply add together their income to our estimate of the total. Just a person living in a household of two adults has only a i-in-two chance of selection. To reflect this, when nosotros come to such a household, nosotros would count the selected person'southward 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 chemical element in the population does accept the same probability of selection, this is known as an 'equal probability of selection' (EPS) pattern. Such designs are also referred to as 'self-weighting' because all sampled units are given the same weight.

Probability sampling includes: Simple Random Sampling, Systematic Sampling, Stratified Sampling, Probability Proportional to Size Sampling, and Cluster or Multistage Sampling. These diverse means of probability sampling have two things in common:

Every chemical element has a known nonzero probability of being sampled and
involves random selection at some indicate.

Nonprobability sampling [edit]

Nonprobability sampling is any sampling method where some elements of the population have no hazard of choice (these are sometimes referred to every bit 'out of coverage'/'undercovered'), or where the probability of choice can't be accurately determined. It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection. Hence, because the choice of elements is nonrandom, nonprobability sampling does not allow the estimation of sampling errors. These weather condition give rise to exclusion bias, placing limits on how much information a sample tin can provide near the population. Information about the relationship between sample and population is limited, making it difficult to extrapolate from the sample to the population.

Example: We visit every household in a given street, and interview the commencement person to answer the door. In whatever household with more than i occupant, this is a nonprobability sample, because some people are more likely to answer the door (due east.g. an unemployed person who spends nigh of their time at home is more than likely to reply than an employed housemate who might be at work when the interviewer calls) and it'southward non practical to calculate these probabilities.

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 finer modifies each element's probability of being sampled.

Sampling methods [edit]

Within whatever of the types of frames identified above, a variety of sampling methods tin be employed, individually or in combination. Factors commonly influencing the selection between these designs include:

Nature and quality of the frame
Availability of auxiliary information about units on the frame
Accuracy requirements, and the need to measure accuracy
Whether detailed analysis of the sample is expected
Cost/operational concerns

Simple random sampling [edit]

A visual representation of selecting a simple random sample

In a simple random sample (SRS) of a given size, all subsets of a sampling frame have an equal probability of being selected. Each element of the frame thus has an equal probability of selection: the frame is not subdivided or partitioned. Furthermore, any given pair of elements has the same chance of selection as whatsoever other such pair (and similarly for triples, and so on). This minimizes bias and simplifies assay 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.

Simple random sampling tin can exist vulnerable to sampling error because the randomness of the selection may upshot in a sample that doesn't reflect the makeup of the population. For instance, a uncomplicated random sample of ten people from a given country volition on average produce v men and five women, but any given trial is probable to over represent one sex and underrepresent the other. Systematic and stratified techniques attempt to overcome this problem past "using information about the population" to choose a more than "representative" sample.

Too, uncomplicated random sampling can be cumbersome and deadening when sampling from a big 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 equally a predictor of job performance is equally applicative across racial groups. Simple random sampling cannot adjust the needs of researchers in this situation, considering it does non provide subsamples of the population, and other sampling strategies, such as stratified sampling, can be used instead.

Systematic sampling [edit]

A visual representation of selecting a random sample using the systematic sampling technique

Systematic sampling (also known as interval sampling) relies on arranging the study population according to some ordering scheme and and so selecting elements at regular intervals through that ordered listing. Systematic sampling involves a random start and then proceeds with the selection of every kth element from then onwards. In this case, k=(population size/sample size). It is important that the starting point is not automatically the first in the list, only is instead randomly chosen from within the first to the 1000th element in the list. A simple example would be to select every 10th name from the telephone directory (an 'every 10th' sample, as well referred to every bit 'sampling with a skip of 10').

Every bit long as the starting betoken is randomized, systematic sampling is a type of probability sampling. It is easy to implement and the stratification induced can get in efficient, if the variable by which the list is ordered is correlated with the variable of involvement. 'Every 10th' sampling is especially useful for efficient sampling from databases.

For example, suppose nosotros wish to sample people from a long street that starts in a poor area (house No. i) and ends in an expensive district (firm No. 1000). A unproblematic random selection of addresses from this street could easily end upward with too many from the high end and as well few from the low end (or vice versa), leading to an unrepresentative sample. Selecting (e.one thousand.) every 10th street number along the street ensures that the sample is spread evenly along the length of the street, representing all of these districts. (Notation that if we ever start at firm #1 and end at #991, the sample is slightly biased towards the depression terminate; by randomly selecting the start between #i and #10, this bias is eliminated.

Withal, systematic sampling is especially vulnerable to periodicities in the list. If periodicity is present and the flow is a multiple or factor of the interval used, the sample is especially likely to be unrepresentative of the overall population, making the scheme less accurate than unproblematic random sampling.

For instance, consider a street where the odd-numbered houses are all on the north (expensive) side of the route, and the fifty-fifty-numbered houses are all on the south (cheap) side. Under the sampling scheme given to a higher place, it is incommunicable to become a representative sample; either the houses sampled will all exist from the odd-numbered, expensive side, or they will all be from the even-numbered, cheap side, unless the researcher has previous noesis of this bias and avoids it past 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 information technology is more accurate than SRS, its theoretical properties brand it hard to quantify that accuracy. (In the 2 examples of systematic sampling that are given above, much of the potential sampling error is due to variation between neighbouring houses – only considering this method never selects two neighbouring houses, the sample will non give usa any data on that variation.)

As described above, systematic sampling is an EPS method, because all elements have the same probability of option (in the example given, one in 10). It is non 'uncomplicated random sampling' because different subsets of the same size have different choice probabilities – eastward.chiliad. the set up {4,14,24,...,994} has a ane-in-x probability of selection, but the gear up {iv,13,24,34,...} has zippo probability of selection.

Systematic sampling tin can likewise be adapted to a non-EPS arroyo; for an case, see discussion of PPS samples below.

Stratified sampling [edit]

A visual representation of selecting a random sample using the stratified sampling technique

When the population embraces a number of singled-out categories, the frame can be organized by these categories into separate "strata." Each stratum is and then sampled every bit an contained sub-population, out of which private elements can exist randomly selected.^[three] The ratio of the size of this random selection (or sample) to the size of the population is called a sampling fraction. There are several potential benefits to stratified sampling.

Get-go, dividing the population into singled-out, independent strata tin enable researchers to depict inferences virtually 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 benchmark in question, instead of availability of the samples). Even if a stratified sampling arroyo does not pb to increased statistical efficiency, such a tactic will non result in less efficiency than would uncomplicated random sampling, provided that each stratum is proportional to the group's size in the population.

Tertiary, it is sometimes the case that data are more readily available for individual, pre-existing strata inside a population than for the overall population; in such cases, using a stratified sampling arroyo 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 contained population, different sampling approaches can exist applied to unlike strata, potentially enabling researchers to use the approach best suited (or nearly cost-constructive) for each identified subgroup within the population.

In that location are, however, some potential drawbacks to using stratified sampling. Commencement, identifying strata and implementing such an approach tin can increase the toll and complexity of sample pick, likewise as leading to increased complexity of population estimates. Second, when examining multiple criteria, stratifying variables may be related to some, but non to others, farther complicating the design, and potentially reducing the utility of the strata. Finally, in some cases (such every bit designs with a big number of strata, or those with a specified minimum sample size per grouping), 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 unproblematic random sampling).

A stratified sampling approach is most effective when iii atmospheric condition are met

Variability within strata are minimized
Variability betwixt strata are maximized
The variables upon which the population is stratified are strongly correlated with the desired dependent variable.

Advantages over other sampling methods

Focuses on important subpopulations and ignores irrelevant ones.
Allows use of dissimilar sampling techniques for dissimilar subpopulations.
Improves the accuracy/efficiency of estimation.
Permits greater balancing of statistical ability of tests of differences betwixt strata by sampling equal numbers from strata varying widely in size.

Disadvantages

Requires selection of relevant stratification variables which can be difficult.
Is non useful when there are no homogeneous subgroups.
Tin can be expensive to implement.

Poststratification

Stratification is sometimes introduced after the sampling phase in a process called "poststratification".^[3] This approach is typically implemented due to a lack of prior cognition of an advisable stratifying variable or when the experimenter lacks the necessary information to create a stratifying variable during the sampling stage. Although the method is susceptible to the pitfalls of post hoc approaches, it can provide several benefits in the right situation. Implementation ordinarily follows a simple random sample. In addition to allowing for stratification on an ancillary variable, poststratification tin be used to implement weighting, which can better the precision of a sample'southward estimates.^[three]

Oversampling

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 and then that the rare target class will be more represented in the sample. The model is so congenital 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 exist adjusted to right for the oversampling.

Probability-proportional-to-size sampling [edit]

In some cases the sample designer has access to an "auxiliary variable" or "size measure", believed to be correlated to the variable of involvement, for each element in the population. These data tin be used to meliorate accuracy in sample design. 1 option is to use the auxiliary variable equally a basis for stratification, as discussed in a higher place.

Another option is probability proportional to size ('PPS') sampling, in which the selection probability for each element is fix to be proportional to its size measure out, up to a maximum of 1. In a simple PPS pattern, these selection probabilities can and 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 take a chance variation in selections.

Systematic sampling theory can exist used to create a probability proportionate to size sample. This is done past treating each count within the size variable as a single sampling unit. Samples are then identified by selecting at fifty-fifty intervals among these counts within the size variable. This method is sometimes called PPS-sequential or monetary unit of measurement sampling in the example of audits or forensic sampling.

Instance: Suppose we have six schools with populations of 150, 180, 200, 220, 260, and 490 students respectively (total 1500 students), and we want to utilize educatee population equally the basis for a PPS sample of size three. To do this, we could classify the starting time school numbers one to 150, the second schoolhouse 151 to 330 (= 150 + 180), the third schoolhouse 331 to 530, and and then on to the concluding school (1011 to 1500). We and so generate a random offset betwixt 1 and 500 (equal to 1500/3) and count through the schoolhouse populations by multiples of 500. If our random start was 137, we would select the schools which have been allocated numbers 137, 637, and 1137, i.e. the first, fourth, and sixth schools.

The PPS arroyo tin improve accurateness for a given sample size by concentrating sample on large elements that take the greatest touch on population estimates. PPS sampling is unremarkably used for surveys of businesses, where chemical element size varies profoundly and auxiliary information is often available – for instance, a survey attempting to measure the number of guest-nights spent in hotels might utilize each hotel'southward number of rooms as an auxiliary variable. In some cases, an older measurement of the variable of interest can be used every bit an auxiliary variable when attempting to produce more than electric current estimates.^[viii]

Cluster sampling [edit]

A visual representation of selecting a random sample using the cluster sampling technique

Sometimes it is more cost-effective to select respondents in groups ('clusters'). Sampling is often clustered by geography, or past time periods. (Nearly all samples are in some sense 'clustered' in time – although this is rarely taken into account in the assay.) For example, if surveying households within a metropolis, we might choose to select 100 metropolis blocks and and so interview every household within the selected blocks.

Clustering can reduce travel and administrative costs. In the example to a higher place, an interviewer can make a single trip to visit several households in ane cake, rather than having to drive to a different cake for each household.

Information technology besides means that one does not demand a sampling frame list all elements in the target population. Instead, clusters can be chosen from a cluster-level frame, with an chemical element-level frame created simply for the selected clusters. In the example higher up, the sample merely requires a block-level city map for initial selections, and and then a household-level map of the 100 selected blocks, rather than a household-level map of the whole metropolis.

Cluster sampling (likewise known as clustered sampling) mostly increases the variability of sample estimates above that of elementary random sampling, depending on how the clusters differ between one another equally compared to the inside-cluster variation. For this reason, cluster sampling requires a larger sample than SRS to reach the aforementioned level of accurateness – merely cost savings from clustering might even so make this a cheaper option.

Cluster sampling is usually implemented as multistage sampling. This is a complex form of cluster sampling in which two or more than levels of units are embedded one in the other. The starting time stage consists of amalgam the clusters that will be used to sample from. In the 2d phase, a sample of master 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 example) selected at the last stride 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 synthetic (earlier other sampling methods could be applied). Past eliminating the piece of work involved in describing clusters that are not selected, multistage sampling can reduce the large costs associated with traditional cluster sampling.^[8] However, each sample may not be a full representative of the whole population.

Quota sampling [edit]

In quota sampling, the population is showtime segmented into mutually sectional sub-groups, just every bit in stratified sampling. So 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 200 females and 300 males between the historic period of 45 and 60.

Information technology is this second step which makes the technique 1 of non-probability sampling. In quota sampling the selection of the sample is not-random. For instance, interviewers might exist tempted to interview those who look about helpful. The problem is that these samples may be biased because not everyone gets a hazard of selection. This random element is its greatest weakness and quota versus probability has been a matter of controversy for several years.

Minimax sampling [edit]

In imbalanced datasets, where the sampling ratio does not follow the population statistics, one tin can resample the dataset in a bourgeois style called minimax sampling. The minimax sampling has its origin in Anderson minimax ratio whose value is proved to exist 0.5: in a binary classification, the class-sample sizes should exist chosen equally. 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, chosen class-wise smart classifiers. In this case, the sampling ratio of classes is selected so that the worst instance classifier fault over all the possible population statistics for grade prior probabilities, would be the all-time.^[9]

Accidental sampling [edit]

Accidental sampling (sometimes known as grab, convenience or opportunity sampling) is a type of nonprobability sampling which involves the sample being fatigued from that part of the population which is close to paw. That is, a population is selected because it is readily available and user-friendly. It may exist through meeting the person or including a person in the sample when one meets them or chosen past finding them through technological means such every bit the internet or through phone. The researcher using such a sample cannot scientifically brand generalizations almost the full population from this sample because information technology would not exist representative enough. For example, if the interviewer were to acquit such a survey at a shopping center early in the morning on a given day, the people that he/she could interview would be limited to those given there at that given time, which would not represent the views of other members of society in such an area, if the survey were to be conducted at dissimilar times of twenty-four hours and several times per calendar week. This blazon of sampling is nigh useful for pilot testing. Several important considerations for researchers using convenience samples include:

Are there controls within the research design or experiment which can serve to lessen the touch of a non-random convenience sample, thereby ensuring the results will be more representative of the population?
Is there skilful reason to believe that a particular convenience sample would or should answer or behave differently than a random sample from the same population?
Is the question being asked by the inquiry i that can adequately be answered using a convenience sample?

In social science inquiry, snowball sampling is a similar technique, where existing study subjects are used to recruit more than subjects into the sample. Some variants of snowball sampling, such every bit respondent driven sampling, permit adding of choice probabilities and are probability sampling methods under certain conditions.

Voluntary Sampling [edit]

The voluntary sampling method is a type of not-probability sampling. Volunteers choose to consummate a survey.

Volunteers may be invited through advertisements in social media.^[10] The target population for advertisements tin can be selected by characteristics like location, age, sex, income, occupation, instruction or interests using tools provided past the social medium. The advert may include a bulletin near the enquiry and link to a survey. After post-obit the link and completing the survey the volunteer submits the information to be included in the sample population. This method can reach a global population but is express past the campaign budget. Volunteers outside the invited population may also be included in the sample.

Information technology is hard to make generalizations from this sample because it may not represent the full population. Often, volunteers accept a strong interest in the main topic of the survey.

Line-intercept sampling [edit]

Line-intercept sampling is a method of sampling elements in a region whereby an element is sampled if a chosen line segment, chosen a "transect", intersects the element.

Panel sampling [edit]

Panel sampling is the method of get-go selecting a group of participants through a random sampling method and so asking that grouping for (potentially the same) data several times over a period of time. Therefore, each participant is interviewed at ii or more time points; each period of data drove is called a "wave". The method was adult by sociologist Paul Lazarsfeld in 1938 as a ways of studying political campaigns.^[11] This longitudinal sampling-method allows estimates of changes in the population, for instance with regard to chronic illness to task stress to weekly food expenditures. Console sampling can as well be used to inform researchers nearly within-person wellness changes due to age or to aid explain changes in continuous dependent variables such as spousal interaction.^[12] At that place have been several proposed methods of analyzing console data, including MANOVA, growth curves, and structural equation modeling with lagged effects.

Snowball sampling [edit]

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

Theoretical sampling [edit]

This section needs expansion. Yous can assist by adding to it. (July 2015)

Theoretical sampling^[13] occurs when samples are selected on the footing of the results of the data collected and then far with a goal of developing a deeper understanding of the area or develop theories. Farthermost or very specific cases might be selected in lodge to maximize the likelihood a phenomenon volition actually be observable.

Replacement of selected units [edit]

Sampling schemes may be without replacement ('WOR' – no element tin exist selected more than in one case in the same sample) or with replacement ('WR' – an element may appear multiple times in the 1 sample). For example, if nosotros catch fish, measure out them, and immediately return them to the h2o before continuing with the sample, this is a WR pattern, considering nosotros might end up catching and measuring the same fish more once. All the same, if we do not return the fish to the water or tag and release each fish after catching it, this becomes a WOR pattern.

Sample size determination [edit]

Formulas, tables, and ability function charts are well known approaches to determine sample size.

Steps for using sample size tables [edit]

Postulate the consequence size of involvement, α, and β.
Check sample size table^[14]
1. Select the table corresponding to the selected α
2. Locate the row corresponding to the desired ability
3. Locate the column respective to the estimated outcome size.
4. The intersection of the cavalcade and row is the minimum sample size required.

Sampling and data collection [edit]

Good data collection involves:

Post-obit the divers sampling process
Keeping the data in time gild
Noting comments and other contextual events
Recording non-responses

Applications of sampling [edit]

Sampling enables the selection of correct information points from within the larger data set to estimate the characteristics of the whole population. For example, there are about 600 one thousand thousand tweets produced every 24-hour interval. It is not necessary to look at all of them to determine the topics that are discussed during the 24-hour interval, nor is information technology necessary to look at all the tweets to determine the sentiment on each of the topics. A theoretical conception for sampling Twitter data has been developed.^[xv]

In manufacturing different types of sensory information such as acoustics, vibration, pressure, current, voltage and controller data are available at brusk fourth dimension intervals. To predict downwards-time it may not be necessary to look at all the information but a sample may exist sufficient.

Errors in sample surveys [edit]

Survey results are typically subject field to some error. Total errors can be classified into sampling errors and not-sampling errors. The term "error" here includes systematic biases as well every bit random errors.

Sampling errors and biases [edit]

Sampling errors and biases are induced past the sample blueprint. They include:

Selection bias: When the true selection probabilities differ from those assumed in calculating the results.
Random sampling error: Random variation in the results due to the elements in the sample being selected at random.

Not-sampling fault [edit]

Non-sampling errors are other errors which tin can impact final survey estimates, caused past problems in information collection, processing, or sample design. Such errors may include:

Over-coverage: inclusion of data from outside of the population
Nether-coverage: sampling frame does not include elements in the population.
Measurement error: eastward.g. when respondents misunderstand a question, or detect it hard to respond
Processing error: mistakes in data coding
Non-response or Participation bias: failure to obtain complete data from all selected individuals

After sampling, a review should be held^{[ past whom? ]} of the exact process followed in sampling, rather than that intended, in club to study any furnishings that whatever divergences might accept on subsequent analysis.

A particular problem involves non-response. Ii major types of non-response be:^[sixteen] ^[17]

unit of measurement nonresponse (lack of completion of whatsoever role of the survey)
particular non-response (submission or participation in survey just failing to complete one or more components/questions of the survey)

In survey sampling, many of the individuals identified as role of the sample may be unwilling to participate, not have the time to participate (opportunity cost),^[18] or survey administrators may not accept been able to contact them. 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 blueprint, offering incentives, and conducting follow-upward studies which make a repeated endeavour to contact the unresponsive and to narrate their similarities and differences with the rest of the frame.^[19] The effects tin also be mitigated past weighting the data (when population benchmarks are available) or by imputing data based on answers to other questions. Nonresponse is particularly a problem in internet sampling. Reasons for this problem may include improperly designed surveys,^[17] over-surveying (or survey fatigue),^[12] ^[twenty] ^{[ need quotation to verify ]} and the fact that potential participants may have multiple e-mail addresses, which they don't use anymore or don't check regularly.

Survey weights [edit]

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 not include some in remote Scottish islands who would be inordinately expensive to sample. A cheaper method would exist to utilise a stratified sample with urban and rural strata. The rural sample could exist nether-represented in the sample, simply weighted up appropriately in the analysis to compensate.

More generally, data should normally be weighted if the sample pattern does not give each individual an equal chance of being selected. For instance, when households accept equal selection probabilities but one person is interviewed from within each household, this gives people from large households a smaller chance of existence interviewed. This tin exist accounted for using survey weights. Similarly, households with more than i telephone line have a greater gamble of being selected in a random digit dialing sample, and weights tin can adjust for this.

Weights can also serve other purposes, such as helping to correct for not-response.

Methods of producing random samples [edit]

Random number tabular array
Mathematical algorithms for pseudo-random number generators
Physical randomization devices such as coins, playing cards or sophisticated devices such every bit ERNIE

History [edit]

Random sampling by using lots is an old idea, mentioned several times in the Bible. In 1786 Pierre Simon Laplace estimated the population of France past using a sample, forth with ratio estimator. He also computed probabilistic estimates of the error. These were not expressed equally mod confidence intervals just equally the sample size that would exist needed to attain a particular upper bound on the sampling mistake with probability 1000/1001. His estimates used Bayes' theorem with a compatible prior probability and causeless that his sample was random. Alexander Ivanovich Chuprov introduced sample surveys to Imperial Russia in the 1870s.^{[ commendation needed ]}

In the US the 1936 Literary Digest prediction of a Republican win in the presidential election went badly amiss, due to astringent bias [1]. More than two million people responded to the written report with their names obtained through mag subscription lists and phone directories. It was not appreciated that these lists were heavily biased towards Republicans and the resulting sample, though very large, was deeply flawed.^[21] ^[22]

Notes [edit]

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

Robert Groves, et alia. Survey methodology (2010 2nd ed. [2004]) ISBN 0-471-48348-vi.

The other books focus on the statistical theory of survey sampling and crave some knowledge of basic statistics, as discussed in the following textbooks:

David Due south. Moore and George P. McCabe (February 2005). "Introduction to the exercise of statistics" (5th edition). W.H. Freeman & Company. ISBN 0-7167-6282-X.
Freedman, David; Pisani, Robert; Purves, Roger (2007). Statistics (fourth ed.). New York: Norton. ISBN978-0-393-92972-0. Archived from the original on 2008-07-06.

The unproblematic book by Scheaffer et alia uses quadratic equations from high-school algebra:

Scheaffer, Richard L., William Mendenhal and R. Lyman Ott. Elementary survey sampling, Fifth Edition. Belmont: Duxbury Printing, 1996.

More mathematical statistics is required for Lohr, for Särndal et alia, and for Cochran (classic^{[ citation needed ]}):

Cochran, William Yard. (1977). Sampling techniques (Tertiary ed.). Wiley. ISBN978-0-471-16240-vii.
Lohr, Sharon L. (1999). Sampling: Design and analysis. Duxbury. ISBN978-0-534-35361-2.
Särndal, Carl-Erik, and Swensson, Bengt, and Wretman, Jan (1992). Model assisted survey sampling. Springer-Verlag. ISBN978-0-387-40620-6. {{cite book}}: CS1 maint: multiple names: authors list (link)

The historically important books by Deming and Kish remain valuable for insights for social scientists (particularly about the U.S. census and the Institute for Social Research at the University of Michigan):

Deming, W. Edwards (1966). Some Theory of Sampling . Dover Publications. ISBN978-0-486-64684-8. OCLC 166526.
Kish, Leslie (1995) Survey Sampling, Wiley, ISBN 0-471-10949-five

References [edit]

^ Lance, P. & Hattori, A. (2016). Sampling and Evaluation. Web: Measure out Evaluation. pp. vi–8, 62–64. {{cite book}}: CS1 maint: multiple names: authors listing (link)
^ Salant, Priscilla, I. Dillman, and A. Don. How to conduct your own survey. No. 300.723 S3. 1994.
^ ^a ^b ^c ^d Robert Thousand. Groves; et al. (2009). Survey methodology . ISBN978-0470465462.
^ Lohr, Sharon 50. Sampling: Pattern and analysis.
^ Särndal, Carl-Erik, and Swensson, Bengt, and Wretman, Jan. Model Assisted Survey Sampling. {{cite book}}: CS1 maint: multiple names: authors listing (link)
^ Scheaffer, Richard L., William Mendenhal and R. Lyman Ott. (2006). Elementary survey sampling . {{cite book}}: CS1 maint: multiple names: authors list (link)
^ Scott, A.J.; Wild, C.J. (1986). "Plumbing equipment logistic models under case-command or option-based sampling". Periodical of the Regal Statistical Lodge, Serial B. 48 (two): 170–182. JSTOR 2345712.
^ ^a ^b
- Lohr, Sharon Fifty. Sampling: Design and Analysis.
- Särndal, Carl-Erik, and Swensson, Bengt, and Wretman, January. Model Assisted Survey Sampling. {{cite book}}: CS1 maint: multiple names: authors list (link)
^ Shahrokh Esfahani, Mohammad; Dougherty, Edward (2014). "Event of split sampling on classification accurateness". Bioinformatics. thirty (2): 242–250. doi:10.1093/bioinformatics/btt662. PMID 24257187.
^ Ariyaratne, Buddhika (30 July 2017). "Voluntary Sampling Method combined with Social Media advertising". heal-info.blogspot.com. Health Information science. Retrieved 18 Dec 2018. ^{[ unreliable source? ]}
^ Lazarsfeld, P., & Fiske, K. (1938). The" console" as a new tool for measuring stance. The Public Opinion Quarterly, 2(4), 596–612.
^ ^a ^b Groves, et alia. Survey Methodology
^ "Examples of sampling methods" (PDF).
^ Cohen, 1988
^ Deepan Palguna, Vikas Joshi, Venkatesan Chakaravarthy, Ravi Kothari and L. 5. Subramaniam (2015). Analysis of Sampling Algorithms for Twitter. International Joint Conference on Artificial Intelligence. {{cite conference}}: CS1 maint: multiple names: authors listing (link)
^ Berinsky, A. J. (2008). "Survey non-response". In: West. Donsbach & K. W. Traugott (Eds.), The Sage handbook of public opinion inquiry (pp. 309–321). Thousand Oaks, CA: Sage Publications.
^ ^a ^b Dillman, D. A., Eltinge, J. L., Groves, R. Thou., & Little, R. J. A. (2002). "Survey nonresponse in design, data collection, and analysis". In: R. M. Groves, D. A. Dillman, J. 50. Eltinge, & R. J. A. Little (Eds.), Survey nonresponse (pp. three–26). New York: John Wiley & Sons.
^ Dillman, D.A., Smyth, J.D., & Christian, L. Thou. (2009). Internet, mail, and mixed-mode surveys: The tailored design method. San Francisco: Jossey-Bass.
^ Vehovar, Five., Batagelj, Z., Manfreda, Grand.L., & Zaletel, 1000. (2002). "Nonresponse in web surveys". In: R. M. Groves, D. A. Dillman, J. 50. Eltinge, & R. J. A. Little (Eds.), Survey nonresponse (pp. 229–242). New York: John Wiley & Sons.
^ Porter; Whitcomb; Weitzer (2004). "Multiple surveys of students and survey fatigue". In Porter, Stephen R (ed.). Overcoming survey research problems. New directions for institutional research. San Francisco: Jossey-Bass. pp. 63–74. ISBN9780787974770 . Retrieved xv July 2019.
^ David S. Moore and George P. McCabe. "Introduction to the Practice of Statistics".
^ Freedman, David; Pisani, Robert; Purves, Roger. Statistics.

Standards [edit]

ISO [edit]

ISO 2859 serial
ISO 3951 serial

ASTM [edit]

ASTM E105 Standard Practise for Probability Sampling Of Materials
ASTM E122 Standard Practice for Computing Sample Size to Approximate, With a Specified Tolerable Error, the Average for Characteristic of a Lot or Process
ASTM E141 Standard Practice for Acceptance of Evidence Based on the Results of Probability Sampling
ASTM E1402 Standard Terminology Relating to Sampling
ASTM E1994 Standard Practice for Use of Process Oriented AOQL and LTPD Sampling Plans
ASTM E2234 Standard Practice for Sampling a Stream of Product by Attributes Indexed by AQL

ANSI, ASQ [edit]

ANSI/ASQ Z1.4

U.South. federal and military standards [edit]

MIL-STD-105
MIL-STD-1916

External links [edit]

Media related to Sampling (statistics) at Wikimedia Commons

ingersollglind1989.blogspot.com

Source: https://en.wikipedia.org/wiki/Sampling_(statistics)