Definitions

# error

[er-er]
error, in law: see appeal.

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 227 and shorter versions like 3.14159. Truncation error results from using only the first few terms of an infinite series. Relative error is the ratio of the size of an error to the size of the quantity measured, and percentage error is relative error expressed as a percent.

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.

## Human behavior

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.

### Oral and written language

An individual language user's deviations from standard language norms in grammar, syntax, pronunciation and punctuation are sometimes referred to as errors. However in light of the role of language usage in everyday social class distinctions, many feel that linguistics should be descriptive rather than prescriptive to avoid reinforcing dominant class value judgments about what linguistic forms should and should not be used. See also Error analysis.

### Gaffe

A gaffe is a verbal mistake, usually made in a social environment. The mistake may come from saying something that is true, but inappropriate. It may also be an erroneous attempt to reveal a truth. Finally, gaffes can be malapropisms, grammatical errors or other verbal and gestural weaknesses or revelations through body language. Actually revealing factual or social truth through words or body language, however, can commonly result in embarrassment or, when the gaffe has negative connotations, friction between people involved.

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.

### Medicine

See medical error for a description of error in medicine.

## Statistics

In statistics, an error is not a "mistake" but is a difference between a computed, estimated, or measured value and the true, specified, or theoretically correct value.

## Experimental science

Error is the difference between a measured value and the true value of a quantity or attribute. Thus, it is the factor that limits the precision and accuracy of the result of a measurement. Errors can be divided into two components: random error and systematic error. Random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading. Systematic error is predictable, and typically constant or proportional to the true value. If the cause of the systematic error can be identified, then it can usually be eliminated. The total error, which results from the sum of the two components, is also referred to as uncertainty.

## Engineering

In engineering, an error is a difference between the desired and actual performance or behavior of a system or object. (In computational mechanics, when solving a system such as Ax=b there is a distinction between the "error" — the inaccuracy in x — and residual—the inaccuracy in Ax.)

Engineers often seek to design systems in such a way as to mitigate or preferably avoid the effects of error, whether unintentional or not.

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.

Errors in a system can also be latent design errors that may go unnoticed for years, until the right set of circumstances arises that cause them to become active. See also Observational error.

### Aviation

See aviation safety for a description of how flying has been made safer by making the aviation system more error-tolerant.

### Telecommunication

In telecommunications, an error is a deviation from a correct value caused by a malfunction in a system or a functional unit. An example would be the occurrence of a wrong a bit caused by an equipment malfunction. (Sources: Federal Standard 1037C and MIL-STD-188). See also error-correcting code and error-detecting code. A soft error is a deviation from a correct value which does not necessarily imply a malfunction.

### Computer programming

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.

## Cybernetics

The word cybernetics stems from the Greek el:Κυβερνήτης (kybernētēs, steersman, governor, pilot, or rudder — the same root as government). In applying corrections to the trajectory or course being steered Cybernetics can be seen as the most general approach to error and its correction for the achievement of any goal. The term was suggested by Norbert Wiener to describe a new science of control and information in the animal and the machine. Wiener's early work was on noise.

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.

## Biology

In biology, an error is said to occur when perfect fidelity is lost in the copying of information. For example, in an asexually reproducing species, an error (or mutation) has occurred for each DNA nucleotide that differs between the child and the parent. Errors in this sense are not judged as "good" or "bad", although an error may make an organism either more or less adapted to its environment.

## Baseball

In baseball, an error is judged by the official scorer when a runner advances a base because of a fielding mistake, and perfect play would have prevented the advancement, and the mistake was physical. Mental misjudgments are not errors. Failing to get more than one out on a given play is not an error. Application of this rule is necessarily subjective. See error (baseball).

## Philately

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.

## Governmental policy

Within United States government intelligence agencies, such as Central Intelligence Agency agencies, error refers to intelligence error, as previous assumptions that used to exist at a senior intelligence level within senior intelligence agencies, but has since been disproven, and is sometimes eventually listed as unclassified, and therefore more available to the American public and citizenry of the United States. The Freedom of information act provides American citizenry with a means to read intelligence reports that were mired in error. Per United States Central Intelligence Agency's website (as of August, 2008), intelligence error is described as:

"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."

## Numismatics

In numismatics, an error refers to a coin or medal that has a minting mistake, similar to errors found in philately. Because the U.S. Bureau of the Mint keeps a careful eye on all potential errors, errors on U.S. coins are very few and usually very scarce. Examples of numismatic errors: extra metal attached to a coin, a clipped coin caused by the coin stamp machine stamping a second coin too early, double stamping of a coin.

## Error correction

Norman (1986, 1988) argued that because error is inevitable, ‘designers’ should minimize the causes of error, make it possible to undo erroneous actions and make it easier to discover and correct errors. Edmondson’s research focuses on pinpointing specific conditions on group levels which can influence the degree of errors caught and corrected. Although her study was in a specific sector (medicine) some of her conditions can be generalized: a) Unit Leader behaviours. b) Unit performance outcomes c) Unit shared beliefs.

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.

## References

Psychology of error

Error in reasoning

Errors in language

Error diagnosis and prevention