In statistics, sampling error is incurred when the statistical
characteristics of a population are estimated from a subset, or sample, of
that population. Since the sample does not include all members of the
population, statistics on the sample, such as means and quantiles, generally
differ from statistics on the entire population. For example, if one measures
the height of a thousand individuals from a country of one million, the
average height of the thousand is typically not the same as the average
height of all one million people in the country. Since sampling is typically
done to determine the characteristics of a whole population, the difference
between the sample and population values is considered a sampling error. Exact
measurement of sampling error is generally not feasible since the true
population values are unknown; however, sampling error can often be estimated by
probabilistic modeling of the sample. Description
= Random sampling = In statistics, sampling error is the
error caused by observing a sample instead of the whole population. The
sampling error is the difference between a sample statistic used to estimate a
population parameter and the actual but unknown value of the parameter. An
estimate of a quantity of interest, such as an average or percentage, will
generally be subject to sample-to-sample variation. These variations in the
possible sample values of a statistic can theoretically be expressed as
sampling errors, although in practice the exact sampling error is typically
unknown. Sampling error also refers more broadly to this phenomenon of random
sampling variation. Random sampling, and its derived terms
such as sampling error, imply specific procedures for gathering and analyzing
data that are rigorously applied as a method for arriving at results
considered representative of a given population as a whole. Despite a common
misunderstanding, "random" does not mean the same thing as "chance" as this idea
is often used in describing situations of uncertainty, nor is it the same as
projections based on an assessed probability or frequency. Sampling
always refers to a procedure of gathering data from a small aggregation
of individuals that is purportedly representative of a larger grouping
which must in principle be capable of being measured as a totality. Random
sampling is used precisely to ensure a truly representative sample from which
to draw conclusions, in which the same results would be arrived at if one had
included the entirety of the population instead. Random sampling can only be
used to gather information about a single defined point in time. If
additional data is gathered then comparison across time periods may be
possible. However, this comparison is distinct from any sampling itself. As a
method for gathering data within the field of statistics, random sampling is
recognized as clearly distinct from the causal process that one is trying to
measure. The conducting of research itself may lead to certain outcomes
affecting the researched group, but this effect is not what is called sampling
error. Sampling error always refers to the recognized limitations of any
supposedly representative sample population in reflecting the larger
totality, and the error refers only to the discrepancy that may result from
judging the whole on the basis of a much smaller number. This is only an "error"
in the sense that it would automatically be corrected if the totality were itself
assessed. The term has no real meaning outside of statistics.
According to a differing view, a potential example of a sampling error in
evolution is genetic drift; a change is a population’s allele frequencies due to
chance. For example, the bottleneck effect; when natural disasters
dramatically reduce the size of a population resulting in a small
population that may or may not fairly represent the original population. What
may make the bottleneck effect a sampling error is that certain alleles,
due to natural disaster, are more common while others may disappear completely,
making it a potential sampling error. Another example of genetic drift that is
a potential sampling error is the founder effect. The founder effect is
when a few individuals from a larger population settle a new isolated area.
In this instance, there are only a few individuals with little gene variety,
making it a potential sampling error. The likely size of the sampling error
can generally be controlled by taking a large enough random sample from the
population, although the cost of doing this may be prohibitive; see sample size
and statistical power for more detail. If the observations are collected from a
random sample, statistical theory provides probabilistic estimates of the
likely size of the sampling error for a particular statistic or estimator. These
are often expressed in terms of its standard error.
= Bias problems = Sampling bias is a possible source of
sampling errors. It leads to sampling errors which either have a prevalence to
be positive or negative. Such errors can be considered to be systematic errors.
= Non-sampling error = Sampling error can be contrasted with
non-sampling error. Non-sampling error is a catch-all term for the deviations
from the true value that are not a function of the sample chosen, including
various systematic errors and any random errors that are not due to sampling.
Non-sampling errors are much harder to quantify than sampling error.
See also Margin of error
Propagation of error Ratio estimator
Sampling Citations
Burns, N & Grove, S.K.. the Practice of Nursing research: Appraisal, Synthesis,
and Generation of evidence.. St. Louis, MO: Saunders Elsevier.
References Sarndal, Swenson, and Wretman, Model
Assisted Survey Sampling, Springer-Verlag, ISBN 0-387-40620-4
Fritz Scheuren. "What is a Margin of Error?", Chapter 10, in "What is a
Survey?", American Statistical Association, Washington, D.C. Accessed
2008-01-08 Campbell, Neil A.; Reece, Jane B.,
Biology, Benjamin Cummings, pp. 450–451 External links
NIST: Selecting Sample Sizes itfeature.com: Sampling Error