Parametric statistics is a branch of statistics which assumes that sample data comes from a population that can be adequately modeled by a
probability distribution that has a fixed set of
parameters
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
.
Conversely a non-parametric model does not assume an explicit (finite-parametric) mathematical form for the distribution when modeling the data. However, it may make some assumptions about that distribution, such as continuity or symmetry.
Most well-known statistical methods are parametric.
Regarding nonparametric (and semiparametric) models,
Sir David Cox has said, "These typically involve fewer assumptions of structure and distributional form but usually contain strong assumptions about independencies".
Example
The
normal family of distributions all have the same general shape and are ''parameterized'' by
mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the '' ari ...
and
standard deviation. That means that if the mean and standard deviation are known and if the distribution is normal, the probability of any future observation lying in a given range is known.
Suppose that we have a sample of 99 test scores with a mean of 100 and a standard deviation of 1. If we assume all 99 test scores are random observations from a normal distribution, then we predict there is a 1% chance that the 100th test score will be higher than 102.33 (that is, the mean plus 2.33 standard deviations), assuming that the 100th test score comes from the same distribution as the others. Parametric statistical methods are used to compute the 2.33 value above, given 99
independent
Independent or Independents may refer to:
Arts, entertainment, and media Artist groups
* Independents (artist group), a group of modernist painters based in the New Hope, Pennsylvania, area of the United States during the early 1930s
* Independ ...
observations from the same normal distribution.
A
non-parametric
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distri ...
estimate of the same thing is the maximum of the first 99 scores. We don't need to assume anything about the distribution of test scores to reason that before we gave the test it was equally likely that the highest score would be any of the first 100. Thus there is a 1% chance that the 100th score is higher than any of the 99 that preceded it.
History
Parametric statistics was mentioned by
R. A. Fisher in his work ''
Statistical Methods for Research Workers'' in 1925, which created the foundation for modern statistics.
See also
*
Aggregated distribution
*
All models are wrong
*
Inverse problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...
*
Parametric model
*
Sufficient statistic
References
{{DEFAULTSORT:Parametric Statistics
Statistical inference