Sampling error
Encyclopedia
Random sampling
In statisticsStatistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, sampling error or estimation error is the error
Errors and residuals in statistics
In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
caused by observing a sample instead of the whole population. The sampling error can be found by subtracting the value of a parameter from the value of a statistic.
In nursing research, a sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter (Bunns & Grove, 2009).
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
Statistic
A statistic is a single measure of some attribute of a sample . It is calculated by applying a function to the values of the items comprising the sample which are known together as a set of data.More formally, statistical theory defines a statistic as a function of a sample where the function...
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.
An 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 makes 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 sampling error. Another example of genetic drift that is a 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 sampling error.
The likely size of the sampling error can generally be controlled by taking a large enough random sample
Random sample
In statistics, a sample is a subject chosen from a population for investigation; a random sample is one chosen by a method involving an unpredictable component...
from the population, although the cost of doing this may be prohibitive; see sample size
Sample size
Sample size determination is the act of choosing the number of observations to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample...
and statistical power
Statistical power
The power of a statistical test is the probability that the test will reject the null hypothesis when the null hypothesis is actually false . The power is in general a function of the possible distributions, often determined by a parameter, under the alternative hypothesis...
for more detail. If the observation
Observation
Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...
s are collected from a random sample, statistical theory
Statistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
provides probabilistic
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
estimates of the likely size of the sampling error for a particular statistic
Statistic
A statistic is a single measure of some attribute of a sample . It is calculated by applying a function to the values of the items comprising the sample which are known together as a set of data.More formally, statistical theory defines a statistic as a function of a sample where the function...
or estimator
Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result are distinguished....
. These are often expressed in terms of its standard error
Standard error (statistics)
The standard error is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate....
.
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 errorNon-sampling error
In statistics, 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 errors ....
. 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 error
Systematic error
Systematic errors are biases in measurement which lead to the situation where the mean of many separate measurements differs significantly from the actual value of the measured attribute. All measurements are prone to systematic errors, often of several different types...
s and any random errors that are not due to sampling. Non-sampling errors are much harder to quantify than sampling error.