statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, the term "error" arises in two ways. Firstly, it arises in the context of

decision making In psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the cognitive process resulting in the selection of a belief or a course of action among several possible alternative options. It could be either rati ...

, where the probability of error may be considered as being the probability of making a wrong decision and which would have a different value for each type of error. Secondly, it arises in the context of

statistical modelling A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, ...

(for example regression) where the model's predicted value may be in error regarding the observed outcome and where the term probability of error may refer to the probabilities of various amounts of error occurring.

Hypothesis testing

hypothesis testing A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...

, two types of ''

error An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'. In statistics ...

'' are distinguished. *

Type I error In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the fa ...

s which consist of rejecting a

null hypothesis In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...

that is true; this amounts to a false positive result. *

Type II error In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the fa ...

s which consist of failing to reject a null hypothesis that is false; this amounts to a false negative result. The probability of error is similarly distinguished. * For a Type I error, it is shown as α (alpha) and is known as the ''size'' of the test and is 1 minus the specificity of the test. This quantity is sometimes referred to as the confidence of the test, or the level of significance (LOS) of the test. * For a Type II error, it is shown as β (beta) and is 1 minus the

power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...

or 1 minus the sensitivity of the test.

Statistical and econometric modelling

The fitting of many

models A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

in statistics and

econometrics Econometrics is the application of Statistics, statistical methods to economic data in order to give Empirical evidence, empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," ''The New Palgrave: A Dictionary of ...

usually seeks to minimise the difference between observed and predicted or theoretical values. This difference is known as an ''error'', though when observed it would be better described as a '' residual''. The error is taken to be a

random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...

and as such has a

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...

. Thus distribution can be used to calculate the probabilities of errors with values within any given range. Errors and residuals Statistical hypothesis testing {{statistics-stub