Observational Error: Definition and Types
– Observational error is the difference between a measured value and its true value.
– Measurement errors can be random or systematic.
– Random errors lead to inconsistent values in repeated measurements.
– Systematic errors are introduced by repeatable processes inherent to the system.
– Systematic error may have a non-zero mean that is not reduced by averaging.
Characterization of Measurement Errors
– Measurement errors include random and systematic errors.
– Random errors result from unpredictable fluctuations in measurements.
– Systematic errors are predictable and affect results in a consistent manner.
– The ASME Performance Test Standard discusses systematic and random errors.
– Random error is related to the precision of a measurement instrument.
Sources of Systematic Error
– Imperfect calibration of instruments, such as zero error, can lead to systematic errors.
– Changes in the environment can interfere with measurements.
– Systematic errors can be present in estimates based on mathematical models.
– Systematic errors can be constant or proportional to the measured quantity.
– Drift, which are systematic errors changing during an experiment, are easier to detect.
Sources of Random Error
– Random or stochastic error is random from one measurement to the next.
– Stochastic errors tend to be normally distributed.
– Stochastic errors added to a regression equation account for unexplained variation.
– Stochastic errors can be the sum of many independent random errors.
– Stochastic errors affect the variation in measurements.
Effect of Observational Error
– Errors in measurements are modeled by probability theory in statistics.
– Standardized procedures can reduce systematic errors.
– Random errors may be uncontrollable due to factors like cost or changing measurements.
– Researchers can use tools like MTMM experiments to estimate question quality.
– Measurement error in regressors leads to attenuation bias.
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Observational error (or measurement error) is the difference between a measured value of a quantity and its unknown true value. Such errors are inherent in the measurement process; for example lengths measured with a ruler calibrated in whole centimeters will have a measurement error of several millimeters. The error or uncertainty of a measurement can be estimated, and is specified with the measurement as, for example, 32.3 ± 0.5 cm. (A mistake or blunder in the measurement process will give an incorrect value, rather than one subject to known measurement error.)
Measurement errors can be divided into two components: random and systematic. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged.[citation needed] For example, length measurements with a ruler accurately calibrated in whole centimeters will be subject to random error; a ruler incorrectly calibrated will also produce systematic error.
Measurement errors can be summarized in terms of accuracy and precision. Measurement error should not be confused with measurement uncertainty.
