Editing Parameter (section)

===Statistics and econometrics===
{{main|Statistical parameter}}
In [[statistics]] and [[econometrics]], the probability framework above still holds, but attention shifts to [[statistical estimation|estimating]] the parameters of a distribution based on observed data, or [[Hypothesis testing|testing hypotheses]] about them. In [[Frequentist inference|frequentist estimation]] parameters are considered "fixed but unknown", whereas in [[Bayesian probability|Bayesian estimation]] they are treated as random variables, and their uncertainty is described as a distribution.{{Citation needed|date=July 2009}}<ref>{{Cite web |last=Efron |first=Bradley |date=2014-09-10 |title=Frequentist Accuracy of Bayesian Estimates |url=https://www.researchgate.net/publication/265339596 |access-date=2023-04-12 |website=researchgate.net}}</ref>

In [[estimation theory]] of statistics, "statistic" or [[estimator]] refers to samples, whereas "parameter" or [[estimand]] refers to populations, where the samples are taken from. A [[statistic]] is a numerical characteristic of a sample that can be used as an estimate of the corresponding parameter, the numerical characteristic of the [[statistical population|population]] from which the sample was drawn.

For example, the [[sample mean]] (estimator), denoted <math>\overline X</math>, can be used as an estimate of the ''mean'' parameter (estimand), denoted ''μ'', of the population from which the sample was drawn. Similarly, the [[sample variance]] (estimator), denoted ''S''<sup>2</sup>, can be used to estimate the ''variance'' parameter (estimand), denoted ''σ''<sup>2</sup>, of the population from which the sample was drawn. (Note that the sample standard deviation (''S'') is not an unbiased estimate of the population standard deviation (''σ''): see [[Unbiased estimation of standard deviation]].)

It is possible to make statistical inferences without assuming a particular parametric family of [[probability distribution]]s. In that case, one speaks of ''[[non-parametric statistics]]'' as opposed to the [[parametric statistics]] just described. For example, a test based on [[Spearman's rank correlation coefficient]] would be called non-parametric since the statistic is computed from the rank-order of the data disregarding their actual values (and thus regardless of the distribution they were sampled from), whereas those based on the [[Pearson product-moment correlation coefficient]] are parametric tests since it is computed directly from the data values and thus estimates the parameter known as the [[Correlation and dependence|population correlation]].