In applied mathematics, the difference between a value and an estimate of that value. In statistics, a common example is the difference between the mean age of a given group of people (see mean, median, and mode) and that of a sample drawn from the group. In numerical analysis, an example of round-off error is the difference between the true value of pi and commonly substituted expressions like
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The word error has different meanings and usages relative to how it is conceptually applied. The concrete meaning of the Latin word error means "wandering" or "straying". To the contrary of an illusion, an error or a mistake can sometimes be dispelled through knowledge (knowing that one is looking at a mirage and not at real water doesn't make the mirage disappear). However, some errors can occur even when individuals have the required knowledge to perform a task correctly. Examples include forgetting to collect your change after buying chocolate from a vending machine, forgetting the original document after making photocopies, and forgetting to turn the gas off after cooking a meal. These slip errors can occur when an individual is distracted by something else.
One reference differentiates between "error" and "mistake" as follows:
An ‘error' is a deviation from accuracy or correctness. A ‘mistake' is an error caused by a fault: the fault being misjudgment, carelessness, or forgetfulness. Now, say that I run a stop sign because I was in a hurry, and wasn't concentrating, and the police stop me, that is a mistake. If, however, I try to park in an area with conflicting signs, and I get a ticket because I was incorrect on my interpretation of what the signs meant, that would be an error. The first time it would be an error. The second time it would be a mistake since I should have known better.
In human behavior the norms or expectations for behavior or its consequences can be derived from the intention of the actor or from the expectations of other individuals or of a social grouping or from social norms. (See deviance.) Gaffes and faux pas can be labels for certain instances of this kind of error. More serious departures from social norms carry labels such as misbehavior and labels from the legal system, such as misdemeanor and crime. Departures from norms connected to religion can have other labels, such as sin.
Errors can occur even when individuals have the required knowledge to perform a task correctly. Examples include forgetting to collect your change after buying chocolate from a vending machine, forgetting the original document after making photocopies, and forgetting to turn the gas off after cooking a meal. These slip errors can occur when an individual is distracted by something else.
A grammatical or literary error is more embarrassing in the company of intellectuals, professors or serious students, just as errors of science can be embarrassing among scientists or doctors. The protagonist attorney in the film Liar Liar plays on the nature of truth revelation, however, and its ambiguous or unexpected consequences.
As used by some journalists, particularly sportswriters, "gaffe" becomes an imagined synonym for any kind of mistake, e.g., a dropped ball by a player in a baseball game. Philosophers and psychologists interested in the nature of the gaffe include Freud and Gilles Deleuze. Deleuze, in his Logic of Sense, places the gaffe in a developmental process that can culminate in stuttering.
See also Error bar.
One type of error is human error which includes cognitive bias. Human factors engineering is often applied to designs in an attempt to minimize this type of error by making systems more forgiving or error-tolerant.
In software engineering, the term error refers to an incorrect action or calculation performed by software. In general, an error results from a combination of a defect (code that does not correctly implement the requirements or intended behavior) and a fault (situation or event that exercises a program's susceptibility to error). If, as a result of the error, the system performs an undesired action or fails to perform a desired action, then this is referred to as a failure.
In software, defects are more commonly referred to as software bugs. It is important to note that a defect can exist in software but never give rise to an error (if no fault event ever occurs to exercise the defect). Similarly an error can occur without causing a failure if the program detects the error and recovers from it before it can give rise to a system failure.
An error may be detected by the software which can be handled by raising an exception. For instance, it is an error to attempt to write more files onto a disk that is full. Careful programmers write code that can handle errors that may occur, and prevent them from turning into failures; strategies for doing so include using error codes and using exception handling. Continuing past an unhandled error can cause error avalanche, a condition in which errors pile up and one or more failures occur. Also, in hierarchically structured systems, a complete failure of one component may constitute only a fault within a higher level system, which can be detected and corrected at a higher level.
In more general parlance, the term error is also used to describe incorrect actions on the part of a programmer. A syntax error is an ungrammatical or nonsensical statement in a program; one that cannot be parsed by the language implementation. A logic error is a mistake in the algorithm used, which causes erroneous results or undesired operation. Anti-patterns, or undesirable program design elements, may make it harder to detect or correct errors.
Sometimes referred to as PEBCAK, the output of computer errors by the computer as a result of actions by the user, rather than by the software programmer, can lead to a lot of head-scratching.
The cybernetician Gordon Pask held that the error that drives a servomechanism can be seen as a difference between a pair of analogous concepts (in a servomechanism, the current state and the goal state). Later he suggested error can also be seen as an innovation or a contradiction depending on the context and perspective of interacting (observer) participants. The founder of Management cybernetics, Stafford Beer, applied these ideas most notably in his Viable System Model.
In philately, an error refers to a postage stamp or piece of postal stationery that exhibits a printing or production mistake that differentiates it from a normal specimen or from the intended result. Examples are stamps printed in the wrong color or missing one or more colors, printed with a vignette inverted in relation to its frame, produced without any perforations on one or more sides when the normal stamps are perforated, or printed on the wrong type of paper. Legitimate errors must always be produced and sold unintentionally. Such errors may or may not be scarce or rare. A design error may refer to a mistake in the design of the stamp, such as a mislabeled subject, even if there are no printing or production mistakes.
"Intelligence errors are factual inaccuracies in analysis resulting from poor or missing data; intelligence failure is systemic organizational surprise resulting from incorrect, missing, discarded, or inadequate hypotheses."
Unit leader behaviours are crucial in creating a culture in which openness of discussing errors, through their open and stimulating behaviour, are used as an example for the others. The unit performance outcomes consist of factors such as quality of interpersonal relations, unit performance and detected error rates. The leader behaviour and the performance outcomes result in shared beliefs. The shared beliefs of error report that first of all, everybody should accept that making mistakes is normal and that it will not be used against one (Helmreich, 1988). Further, the more errors are reported and discussed, the bigger the incentive should be to report and solve other errors.
Jones (1999) adds that technocratic movements have a positive influence on error correction due improved communication. Technological improvements stimulate collaborate thinking and striving for optimalization of systems. Through this, error correction is maximalized. Tsuvijek (1988) implies how technology on one hand can improve error correction, but on the other hand cause more errors due to decreased human intervention.
In mathematics, computer science, telecommunication, and information theory, error correction has a very precise meaning discussed in the article about error detection and correction.
Psychology of error
Error in reasoning
Errors in language
Error diagnosis and prevention