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Observational error
 
 
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Observational error is the difference between a measured
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
 value of quantity and its true value. In statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
, an error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process.

When either randomness
Random variable

In mathematics, random variables are used in the study of Randomness and probability. They were developed to assist in the analysis of Game of chance, stochastic events, and the results of experiment by capturing only the mathematical properties necessary to answer probability questions....
 or uncertainty modeled by probability theory
Probability theory

Probability theory is the branch of mathematics concerned with analysis of Statistical randomness phenomena. The central objects of probability theory are random variables, stochastic processes, and event s: mathematical abstractions of determinism events or measured quantities that may either be single occurrences or evolve over time in an a...
 is attributed to such errors, they are "errors" in the sense in which that term is used in statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
; see errors and residuals in statistics
Errors and residuals in statistics

In statistics and Optimization , statistical errors and residuals are two closely related and easily confused measures of "deviation of a sample from the mean": the error of a sample is the deviation of the sample from the population mean or actual function, while the residual of a sample is the difference between the sa...
.

Every time we repeat a measurement with a sensitive instrument, we obtain slightly different results.






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Observational error is the difference between a measured
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
 value of quantity and its true value. In statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
, an error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process.

When either randomness
Random variable

In mathematics, random variables are used in the study of Randomness and probability. They were developed to assist in the analysis of Game of chance, stochastic events, and the results of experiment by capturing only the mathematical properties necessary to answer probability questions....
 or uncertainty modeled by probability theory
Probability theory

Probability theory is the branch of mathematics concerned with analysis of Statistical randomness phenomena. The central objects of probability theory are random variables, stochastic processes, and event s: mathematical abstractions of determinism events or measured quantities that may either be single occurrences or evolve over time in an a...
 is attributed to such errors, they are "errors" in the sense in which that term is used in statistics
Statistics

Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
; see errors and residuals in statistics
Errors and residuals in statistics

In statistics and Optimization , statistical errors and residuals are two closely related and easily confused measures of "deviation of a sample from the mean": the error of a sample is the deviation of the sample from the population mean or actual function, while the residual of a sample is the difference between the sa...
.

Every time we repeat a measurement with a sensitive instrument, we obtain slightly different results. The common statistical model
Statistical model

A statistical model is a set of mathematical equations which describe the behavior of an object of study in terms of random variables and their associated probability distributions....
 we use is that the error has two additive parts:
  1. systematic error
    Systematic error

    Systematic errors are biases in measurement which lead the situation where the mean of many separate measurements differs significantly from the actual value of the measured attribute....
     which always occurs (with the same value) when we use the instrument in the same way, and
  2. random error
    Random error

    Random errors are errors in measurement that lead to measured values being inconsistent when repeated measures of a time-invariant attribute or physical quantity are taken....
     which may vary from observation to observation.


The systematic error
Systematic error

Systematic errors are biases in measurement which lead the situation where the mean of many separate measurements differs significantly from the actual value of the measured attribute....
 is sometimes called statistical bias. It is controlled by very carefully standardized procedures. Part of the education in every science
Science

In its broadest sense, science refers to any systematic knowledge or practice. In its more usual restricted sense, science refers to a system of acquiring knowledge based on scientific method, as well as to the organized body of knowledge gained through such research....
 is how to use the standard instruments of the discipline.

The random error
Random error

Random errors are errors in measurement that lead to measured values being inconsistent when repeated measures of a time-invariant attribute or physical quantity are taken....
 (or random variation
Random variable

In mathematics, random variables are used in the study of Randomness and probability. They were developed to assist in the analysis of Game of chance, stochastic events, and the results of experiment by capturing only the mathematical properties necessary to answer probability questions....
) is due to factors which we cannot (or do not) control. It may be too expensive or we may be too ignorant of these factors to control them each time we measure. It may even be that whatever we are trying to measure is changing in time (see dynamic models), or is fundamentally probabilistic (as is the case in quantum mechanics -- see Measurement in quantum mechanics
Measurement in quantum mechanics

The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications....
). Random error often occurs when instruments are pushed to their limits. For example, it is common for digital balances to exhibit random error in their least significant digit. Three measurements of a single object might read something like 0.9111g, 0.9110g, and 0.9112g.

See also

  • errors and residuals in statistics
    Errors and residuals in statistics

    In statistics and Optimization , statistical errors and residuals are two closely related and easily confused measures of "deviation of a sample from the mean": the error of a sample is the deviation of the sample from the population mean or actual function, while the residual of a sample is the difference between the sa...
  • error
    Error

    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"....
     in general
  • Replication (statistics)
    Replication (statistics)

    In engineering, science, and statistics, replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated....
  • statistical theory
    Statistical theory

    The theory of statistics includes a number of topics:Statistical models of the sources of data and typical problem formulation:#survey sampling from a finite population...
  • metrology
    Metrology

    Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement....
  • test method
    Test method

    A test method is a definitive procedure that produces a test result. The test result can be qualititive , categorical, or quantititive . It can be a personal observation or the output of a precision measuring instrument....
  • Propagation of uncertainty
    Propagation of uncertainty

    In statistics, propagation of uncertainty is the effect of variables' uncertainty on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have Observational error which propagate to the combination of variables in the function....