Sampling (statistics): Difference between revisions

Successful statistical practice is based on focused problem definition. In sampling, this includes defining the "[[Statistical population|population]]" from which our sample is drawn. A population can be defined as including all people or items with the characteristiccharacteristics one wishes to understand. Because there is very rarely enough time or money to gather 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 material from [[batch production|production]] is of high enough quality to be released to the customer, or should be sentenced for scrapscrapped or reworkreworked due to poor quality. In this case, the batch is the population.

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 case, the 'population' Jagger wanted to investigate was the overall behaviour of the wheel (i.e. the [[probability distribution]] of its results over infinitely many trials), while his 'sample' was formed from observed results from that wheel. Similar considerations arise when taking repeated measurements of someproperties physicalof characteristicmaterials such as the [[electrical conductivity]] of [[copper]].

This situation often 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 study the success rate of a new 'quit smoking' program on a test group of 100 patients, in order to predict the effects of the program if it were made available nationwide. Here the superpopulation is "everybody in the country, given access to this treatment" – a group whichthat does not yet exist, since the program isn'tis not yet available to all.

The population from which the sample is drawn may not be the same as the population aboutfrom which information is desired. Often there is a large but not complete overlap between these two groups due to frame issues etc. (see below). Sometimes they may be entirely separate – for instance, one might study rats in order to get a better understanding of human health, or one 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 concern precise is often well spent, because it raises many issues, ambiguities, and questions that would otherwise have been overlooked at this stage.

A '''probability sample''' is a sample in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can 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.

Probability sampling includes: [[Simple random sample|Simplesimple Randomrandom Samplingsampling]], [[Systematicsystematic sampling|Systematic Sampling]], [[Stratifiedstratified Samplingsampling]], Probability Proportional probability-proportional-to-size Size Samplingsampling, and [[Cluster sampling|Clustercluster]] or [[Multistagemultistage sampling|Multistage Sampling]]. These various ways of probability sampling have two things in common:

'''Nonprobability sampling''' is any sampling method where some elements of the population have ''no'' chance of selection (these are sometimes referred to as 'out of coverage'/'undercovered'), or where the probability of selection can'tcannot 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 selection of elements is nonrandom, nonprobability sampling does not allow the estimation of sampling errors. These conditions give rise to [[selection bias|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.

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:

Simple random sampling can be vulnerable to sampling error because the randomness of the selection may result in a sample that doesn'tdoes not 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 over represent 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.

For example, suppose we wish to sample people from a long street that starts in a poor area (house No. 1) and ends in an expensive district (house No. 1000). 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. Selecting (e.g.) 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. (Note that ifIf we always start at house #1 and end at #991, the sample is slightly biased towards the low end; by randomly selecting the start between #1 and #10, this bias is eliminated.)

Choice-based sampling is one of the stratified sampling strategies. In choice-based sampling,<ref>{{cite journal|last1=Scott|first1=A.J.|last2=Wild|first2=C.J.|year=1986|title=Fitting logistic models under case-control or choice-based sampling|journal=[[Journal of the Royal Statistical Society, Series B]]|volume=48|issue=2|pages=170–182|doi=10.1111/j.2517-6161.1986.tb01400.x |jstor=2345712}}</ref> 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 [[Sampling bias|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.

===Voluntary Samplingsampling===

Volunteers may be invited through advertisements in social media.<ref name=":1">{{Cite web|url = https://heal-info.blogspot.com/2017/07/voluntary-sampling-method.html|title = Voluntary Sampling Method combined with Social Media advertising|access-date = 18 December 2018 |website = heal-info.blogspot.com |series= Health Informatics |last = Ariyaratne | first = Buddhika | date= 30 July 2017}}{{unreliable source-inline?|date=December 2018}}</ref> The target population for advertisements can be selected by characteristics like location, age, sex, income, occupation, education, or interests using tools provided by the social medium. The advertisement may include a message about the research and link to a survey. After following the link and completing the survey , the volunteer submits the data to be included in the sample population. This method can reach a global population but is limited by the campaign budget. Volunteers outside the invited population may also be included in the sample.

'''[[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.

{{stubexpand section|date=July 2015}}

===Steps for using sample size tables===:

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

# '''[[Selection bias]]''': When the true selection probabilities differ from those assumed in calculating the results.

# '''[[Sampling error|Random sampling error]]''': Random variation in the results due to the elements in the sample being selected at random.

# '''Over-coverage''': inclusion of data from outside of the population

# '''Under-coverage''': sampling frame does not include elements in the population.

# '''Measurement error''': e.g. when respondents misunderstand a question, or find it difficult to answer

# '''Processing error''': mistakes in data coding

# '''[[Participation bias|Non-response or Participation bias]]''': failure to obtain complete data from all selected individuals

After sampling, a review should beis held{{by whom|date=July 2019}} of the exact process followed in sampling, rather than that intended, in order to study any effects that any divergences might have on subsequent analysis.

In [[survey sampling]], many of the individuals identified as part of the sample may be unwilling to participate, not have the time to participate ([[opportunity cost]]),<ref>Dillman, D.A., Smyth, J.D., & Christian, L. M. (2009). Internet, mail, and mixed-mode surveys: The tailored design method. San Francisco: Jossey-Bass.</ref> or survey administrators may not have 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 design, offering incentives, and conducting follow-up studies which make a repeated attempt to contact the unresponsive and to characterize their similarities and differences with the rest of the frame.<ref>Vehovar, V., Batagelj, Z., Manfreda, K.L., & Zaletel, M. (2002). "Nonresponse in web surveys". In: R. M. Groves, D. A. Dillman, J. L. Eltinge, & R. J. A. Little (Eds.), ''Survey nonresponse'' (pp. 229–242). New York: John Wiley & Sons.</ref> The effects can also be mitigated by 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,<ref name="Dillman et al 2002"/> over-surveying (or survey fatigue),<ref name="SM"/><ref>

</ref>{{qnrequest quotation|date=July 2019}}

and the fact that potential participants may have multiple e-mail addresses, which they don'tdo not use anymore or don'tdo not check regularly.

In many situations, the sample fraction may be varied by stratum and data will have to be weighted to correctly represent the population. Thus for example, a simple random sample of individuals in the United Kingdom might not include some in remote Scottish islands who would be inordinately expensive to sample. A cheaper method would be to use a stratified sample with urban and rural strata. The rural sample could be under-represented in the sample, but weighted up appropriately in the analysis to compensate.

* [[Sample size determination]]

More mathematical statistics is required for Lohr, for Särndal et alia, and for Cochran (classic:<ref>{{citationCite book |last=Cochran |first=William G. |title=Sampling Techniques, 3rd Edition needed|date=January1977-01-01 2017|publisher=John Wiley & Sons |isbn=978-0-471-16240-7 |edition=3rd |location=New York, NY |language=English}}):</ref>

* Chambers, R L, and Skinner, C J (editors) (2003), ''Analysis of Survey Data'', Wiley, {{isbn|0-471-89987-9}}

* [[W. Edwards Deming|Deming, W. Edwards]] (1975) On probability as a basis for action, ''The American Statistician'', 29(4), pp. &nbsp;146–152.