Admin: 1 revision imported

2018-11-04T18:46:22Z

1 revision imported

148.75.114.21: /* Kinds of samples */

2018-11-03T22:02:02Z

‎Kinds of samples

New page

[[File:Simple random sampling.PNG|thumb|300px|A visual representation of selecting a [[simple random sample]]{{clarify|reason=It is not clear what is the sample. Explain the diagram!!|date=March 2018}}.]]

In [[statistics]] and [[quantitative research]] methodology, a '''data sample''' is a set of [[data]] collected and/or selected from a [[statistical population]] by a defined procedure.<ref>{{cite book |title=Introduction to Statistics and Data Analysis |first=Roxy |last=Peck|authorlink=Roxy Peck |author2=Chris Olsen |author3=Jay L. Devore |edition=3 |year=2008 |publisher=Cengage Learning |isbn=0-495-55783-8 |url=https://books.google.com/?id=2VkNiakfaUEC&printsec=frontcover&q= |accessdate=2009-08-04}}</ref> The elements of a sample are known as '''sample points''', '''[[Statistical unit|sampling units]]''' or observations{{citation needed|date=October 2017}}.

Typically, the population is very large, making a [[census]] or a complete [[enumeration]] of all the values in the population either impractical or impossible. The sample usually represents a subset of manageable size. Samples are collected and [[Statistic|statistic]]s are calculated from the samples, so that one can make [[inference]]s or [[extrapolation]]s from the sample to the population.

The data sample may be drawn from a population ''without replacement'' (i.e. no element can be selected more than once in the same sample), in which case it is a [[subset]] of a [[Statistical population|population]]; or ''with replacement'' (i.e. an element may appear multiple times in the one sample), in which case it is a multisubset.<ref name=BS1993>{{citation | title=Mathematical Foundations of Computer Science 1993. 18th International Symposium, MFCS'93 Gdańsk, Poland, August 30–September 3, 1993 Proceedings | editor1-first=Andrzej M. | editor1-last=Borzyszkowski | editor2-first=Stefan | editor2-last=Sokołowski | pages=281–290 | year=1993 | doi=10.1007/3-540-57182-5_20 | isbn=978-3-540-57182-7 | series=[[Lecture Notes in Computer Science]] | volume=711 | zbl=0925.11026 | url=http://www-igm.univ-mlv.fr/~berstel/Articles/1993SturmianPatriceMFCS.pdf }}</ref>

==Kinds of samples==

A '''complete sample''' is a set of objects from a parent population that includes ALL such objects that satisfy a set of well-defined selection criteria.<ref>Pratt,g J. W., Raiffa, H. and Schaifer, R. (1995). Introduction to Statistical Decision Theory. MIT Press, Cambridge,MA. {{MR|1326829}}</ref> For example, a complete sample of Australian men taller than 2m would consist of a list of '''every''' Australian male taller than 2m. But it wouldn't include German males, or tall Australian females, or people shorter than 2m. So to compile such a complete sample requires a complete list of the parent population, including data on height, gender, and nationality for each member of that parent population. In the case of human populations, such a complete list is unlikely to exist (the human population being in the billions). But, such complete samples are often available in other disciplines such as the set of players in a major sports league, the birth dates of the members of a parliament, or a complete magnitude-limited list of astronomical objects.

An '''unbiased (representative) sample''' is a set of objects chosen from a complete sample using a selection process that does not depend on the properties of the objects.<ref>Lomax, R. G. and Hahs-Vaughan, Debbie L. An introduction to statistical concepts (3rd ed).</ref> For example, an unbiased sample of Australian men taller than 2m might consist of a randomly sampled subset of 1% of Australian males taller than 2m. But one chosen from the electoral register might not be unbiased since, for example, males aged under 18 will not be on the electoral register. In an astronomical context, an unbiased sample might consist of that fraction of a complete sample for which data are available, provided the data availability is not biased by individual source properties.

The best way to avoid a biased or unrepresentative sample is to select a [[random sample]], also known as a probability sample. A random sample is defined as a sample where each individual member of the population has a known, non-zero chance of being selected as part of the sample.<ref>{{cite book
|author=[[William Gemmell Cochran|Cochran, William G.]]
|year=1977
|title=Sampling techniques
|edition=Third
|publisher=Wiley
|isbn=0-471-16240-X
}}</ref> Several types of random samples are [[simple random sample]]s, [[Systematic sampling|systematic samples]], [[stratified sampling|stratified random samples]], and [[Cluster sampling|cluster random samples]].

A sample that is not random is called a [[Non-random sampling|non-random sample]] or a [[Non-probability sample|non-probability sampling]].<ref>{{cite book
|author=[[Johan Strydom]]
|year=2005
|title=Introduction to Marketing
|edition=Third
|publisher=Wiley
|isbn=0-471-16240-X
}}</ref> Some examples of nonrandom samples are [[convenience sample]]s, [[judgment sample]]s, [[purposive sample]]s, [[quota sample]]s, [[snowball sampling|snowball samples]], and [[quadrature node]]s in [[quasi-Monte Carlo method]]s.

==Mathematical description of random sample==
In mathematical terms, given a [[probability distribution]] ''F'', a random sample of length ''n'' (where ''n'' may be any positive integer) is a set realizations of ''n'' [[Statistical independence|independent]], identically distributed ([[Independent and identically-distributed random variables|iid]]) random variables with distribution ''F''.<ref>[[Samuel S. Wilks]], ''Mathematical Statistics'', John Wiley, 1962, Section 8.1</ref>

A sample concretely represents the results of ''n'' experiments in which the same quantity is measured. For example, if we want to estimate the average height of members of a particular population, we measure the heights of ''n'' individuals. Each measurement is drawn from the probability distribution ''F'' characterizing the population, so each measured height <math>x_i</math> is the realization of a random variable <math>X_i</math> with distribution ''F''. Note that a set of random variables (i.e., a set of measurable functions) must not be confused with the realizations of these variables (which are the values that these random variables take). In other words, <math>X_i</math> is a function representing the measurement at the ''i''-th experiment and <math>x_i=X_i(\omega)</math> is the value obtained when making the measurement.

==See also==
*[[Estimation theory]]
*[[Replication (statistics)]]
*[[Sample size determination]]
*[[Sampling (statistics)]]
*[[Survey sampling]]

==Notes==
<references/>

==External links==
*[http://www.socialresearchmethods.net/kb/sampstat.php Statistical Terms Made Simple]

{{Authority control}}

[[Category:Sampling (statistics)]]

← Older revision	Revision as of 18:46, 4 November 2018
(No difference)

Sample (statistics) - Revision history

Admin: 1 revision imported

148.75.114.21: /* Kinds of samples */