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'''Measurement error''' is the difference between the true value of a measurement and the measured value. This discrepancy can be caused by a variety of factors including measurement instrument accuracy, [[environmental]] conditions, operator error, misreading of scales, and more. Measurement error can be systematic or random. Systematic errors are errors that occur in every measurement and can be corrected by calibrating the measuring instrument. Random errors are errors that occur randomly and cannot be corrected.

==Example of Measurement error==
Examples of measurement errors include:
* '''Instrument error''': This occurs when the measuring instrument is not accurate or precise, resulting in readings that are different from the actual value.
* '''Environmental error''': This occurs when environmental factors, such as temperature or humidity, affect the accuracy of the measurement.
* '''Operator error''': This occurs when the operator does not follow the proper procedure for taking a measurement, resulting in incorrect readings.
* '''Misreading of scales''': This occurs when the operator does not accurately read the scale on the measuring instrument, resulting in incorrect readings.

The formula for calculating measurement error is:
<math>\text{Measurement Error} = \text{Measured Value} - \text{True Value}</math>

This formula shows that the measurement error is the difference between the measured value and the true value. This formula is used to calculate the amount of error that is present in a measurement and can help identify where the error might be coming from. For example, if the measured value is lower than the true value, then the error might be due to operator error or misreading of scales. On the other hand, if the measured value is higher than the true value, then the error might be due to instrument accuracy or environmental factors.

==Formula of Measurement error==
The formula for calculating the measurement error is given by: 

Measurement Error = Measured Value - True Value

In other words, the measurement error is the difference between the measured value and the true value of the quantity being measured. This formula is used to determine the amount of error in a given measurement.

==When to use Measurement error==
Measurement error should be used in any situation where precision is necessary, such as in scientific experiments, engineering projects, and other areas where accuracy is important. Measurement error can be used to identify sources of error, determine the accuracy of a measurement, and help improve the accuracy of future measurements. Measurement error can also be used to evaluate the [[quality]] of a measurement, compare different measuring instruments, and improve the design of measuring instruments.

==Types of Measurement error==
Measurement error can be classified into two main categories: systematic and random. Systematic errors are errors that occur in every measurement and can be corrected by calibrating the measuring instrument. Random errors are errors that occur randomly and cannot be corrected.

==Steps of Measurement error==
The steps of measurement error include:
* '''Identifying the source of the error''': This involves pinpointing exactly where the error is coming from, such as an instrument or operator error.
* '''Quantifying the error''': This involves determining the magnitude of the error, such as how much the reading is off from the actual value.
* '''Correcting the error''': This involves making the necessary adjustments to correct the error, such as calibrating the instrument or retraining the operator.
* '''Verifying the correction''': This involves confirming that the correction was successful and that the error has been eliminated.

In summary, the steps of measurement error involve identifying the source of the error, quantifying the error, correcting the error, and verifying the correction. By following these steps, it is possible to eliminate measurement errors and ensure accurate readings.

==Problems related to Measurement error==
Measurement error can lead to inaccurate results and incorrect conclusions when analyzing data. The limitations of measurement error include:
* Measurement error can lead to overestimation or underestimation of the true value.
* Measurement error can lead to incorrect assumptions about the distribution of data, leading to incorrect conclusions about the data.
* Measurement error can lead to incorrect correlations or relationships between variables that are not actually present.
* Measurement error can lead to incorrect decisions or conclusions based on the data.

==Other approaches related to Measurement error==
There are a variety of approaches that can be used to minimize measurement error. These include:
* '''Ensuring the accuracy and precision of the measuring instrument''': This can be done by regularly calibrating the instrument and replacing any worn or damaged parts.
* '''[[Training]] operators''': Operators should be trained on proper procedures for taking measurements and should be regularly monitored to ensure accuracy.
* '''Setting up a controlled [[environment]]''': Environmental factors should be monitored and controlled to ensure accuracy of measurements.

In summary, there are a variety of approaches that can be used to minimize measurement error. These include ensuring the accuracy and precision of the measuring instrument, training operators, and setting up a controlled environment. By taking these steps, measurement error can be minimized and more accurate measurements can be taken.

{{infobox5|list1={{i5link|a=[[Systematic error]]}} &mdash; {{i5link|a=[[Measurement uncertainty]]}} &mdash; {{i5link|a=[[Statistical hypothesis]]}} &mdash; {{i5link|a=[[Residual standard deviation]]}} &mdash; {{i5link|a=[[Precision and recall]]}} &mdash; {{i5link|a=[[Standardized regression coefficients]]}} &mdash; {{i5link|a=[[Asymmetrical distribution]]}} &mdash; {{i5link|a=[[Statistical methods]]}} &mdash; {{i5link|a=[[Experimental error]]}} }}

==References==
* Bland, J. M., & Altman, D. G. (1996). ''[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2351401/pdf/bmj00548-0038.pdf Measurement error]''. BMJ: British medical journal, 312(7047), 1654.
* Bound, J., Brown, C., & Mathiowetz, N. (2001). ''[https://scholar.google.comftp://nozdr.ru/biblio/kolxoz/G/GL/Handbook%20of%20econometrics,%20Vol.5%20(Elsevier,%202001)(ISBN%200444823409)(O)(741s)_GL_.pdf#page=572 Measurement error in survey data]''. In Handbook of econometrics (Vol. 5, pp. 3705-3843). Elsevier.
* Chesher, A. (1991). ''[https://scholar.archive.org/work/wh7f4mfzrrd7pf5lgiivlz2pye/access/wayback/http://staff.ustc.edu.cn/~ynyang/group-meeting/2012-/error-in-variable/effectmeasurementerror.pdf The effect of measurement error]''. Biometrika, 78(3), 451-462.
[[Category:Statistics]]