Observational error
Encyclopedia
Observational error is the difference between a measured
value of quantity and its true value. In statistics
, an error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process.
or uncertainty modeled by probability theory
is attributed to such errors, they are "errors" in the sense in which that term is used in statistics
; see errors and residuals in statistics
.
Every time we repeat a measurement with a sensitive instrument, we obtain slightly different results. The common statistical model
we use is that the error has two additive parts:
The systematic error
is sometimes called statistical bias. It is controlled by very carefully standardized procedures. Part of the education in every science
is how to use the standard instruments of the discipline.
The random error
(or random variation
) 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
). 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.
. In survey-type situations, these errors can be mistakes in the collection of data, including both the incorrect recording of a response and the correct recording of a respondent's inaccurate response.
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
value of quantity and its true value. In statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, an error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process.
Science and experiments
When either randomnessRandom variable
In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...
or uncertainty modeled by probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
is attributed to such errors, they are "errors" in the sense in which that term is used in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
; 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 the deviation of a sample from its "theoretical value"...
.
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 formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but...
we use is that the error has two additive parts:
- systematic errorSystematic errorSystematic errors are biases in measurement which lead to the situation where the mean of many separate measurements differs significantly from the actual value of the measured attribute. All measurements are prone to systematic errors, often of several different types...
which always occurs (with the same value) when we use the instrument in the same way, and - random errorRandom errorRandom errors are errors in measurement that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken...
which may vary from observation to observation.
The systematic error
Systematic error
Systematic errors are biases in measurement which lead to the situation where the mean of many separate measurements differs significantly from the actual value of the measured attribute. All measurements are prone to systematic errors, often of several different types...
is sometimes called statistical bias. It is controlled by very carefully standardized procedures. Part of the education in every science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
is how to use the standard instruments of the discipline.
The random error
Random error
Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity are taken...
(or random variation
Random variable
In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...
) 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. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....
). 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.
Surveys
The term observational error is also sometimes used to refer to response errors and some other types of non-sampling errorNon-sampling error
In statistics, non-sampling error is a catch-all term for the deviations from the true value that are not a function of the sample chosen, including various systematic errors and any random errors that are not due to sampling. Non-sampling errors are much harder to quantify than sampling errors ....
. In survey-type situations, these errors can be mistakes in the collection of data, including both the incorrect recording of a response and the correct recording of a respondent's inaccurate response.
See also
- errors and residuals in statisticsErrors and residuals in statisticsIn statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
- errorErrorThe word error entails different meanings and usages relative to how it is conceptually applied. The concrete meaning of the Latin word "error" is "wandering" or "straying". Unlike an illusion, an error or a mistake can sometimes be dispelled through knowledge...
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. ASTM, in standard E1847, defines replication as "the repetition of the set of all the treatment combinations to be compared in...
- statistical theoryStatistical theoryThe theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that...
- metrologyMetrologyMetrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...
- test methodTest methodA test method is a definitive procedure that produces a test result.A test can be considered as technical operation that consists of determination of one or more characteristics of a given product, process or service according to a specified procedure. Often a test is part of an experiment.The test...
- Propagation of uncertaintyPropagation of uncertaintyIn statistics, propagation of error is the effect of variables' uncertainties on the uncertainty of a function based on them...
- Instrument errorInstrument errorInstrument error refers to the combined accuracy and precision of a measuring instrument, or the difference between the actual value and the value indicated by the instrument . Measuring instruments are usually calibrated on some regular frequency against a standard...