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Observational error

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"Systematic bias" redirects here. For the sociological and organizational phenomenon, see Systemic bias.

Observational error (or measurement error) is the difference between a measured value of a quantity and its unknown true value.[1] 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.)

Scientific observations are marred by two distinct types of errors, systematic errors on the one hand, and random, on the other hand. The effects of random errors can be mitigated by the least squares method. Constant or systematic errors on the contrary must be carefully avoided, because they arise from one or more causes which constantly act in the same way, and have the effect of always altering the result of the experiment in the same direction. They therefore deprive of any value the observations that they impinge.[2][3] Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Random errors create measurement uncertainty. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system.[4] The distinction between systematic and random errors is far from being as sharp as one might think at first glance. In reality, there are no or very few random errors. As science progresses, the causes of certain errors are sought out, studied, their laws discovered. These errors pass from the class of random errors into that of systematic errors. The ability of the observer consists in discovering the greatest possible number of systematic errors to be able, once he has become acquainted with their laws, to free his results from them using a method or appropriate corrections.[5]

Measurement errors can be summarized in terms of accuracy and precision. For example, length measurements with a ruler accurately calibrated in whole centimeters will be subject to random error with each use on the same distance giving a slightly different value resulting limited precision; a ruler affected by temperature errors will produce an additional systematic error resulting in limited accuracy.Cite error: A <ref> tag is missing the closing </ref> (see the help page).[6]

These errors can be random or systematic. Random errors are caused by unintended mistakes by respondents, interviewers and/or coders. Systematic error can occur if there is a systematic reaction of the respondents to the method used to formulate the survey question. Thus, the exact formulation of a survey question is crucial, since it affects the level of measurement error.[7] Different tools are available for the researchers to help them decide about this exact formulation of their questions, for instance estimating the quality of a question using MTMM experiments. This information about the quality can also be used in order to correct for measurement error.[8][9]

Effect on regression analysis

If the dependent variable in a regression is measured with error, regression analysis and associated hypothesis testing are unaffected, except that the R2 will be lower than it would be with perfect measurement.

However, if one or more independent variables is measured with error, then the regression coefficients and standard hypothesis tests are invalid.[10] This is known as attenuation bias.[11]

See also

References

  1. ^ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 978-0-19-920613-1
  2. ^ Ritter, Elie. Manuel théorique et pratique de l'application de la méthode des moindres carrés au calcul des observations. Mallet-Bachelier. p. 7. Retrieved 16 February 2025.
  3. ^ John Robert Taylor (1999). An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. University Science Books. p. 94, §4.1. ISBN 978-0-935702-75-0.
  4. ^ "Systematic error". Merriam-webster.com. Retrieved 2016-09-10.
  5. ^ Perrier, Georges (1872–1946) Auteur du texte (1933). Cours de géodésie et d'astronomie / par G. Perrier. pp. 17–18.{{cite book}}: CS1 maint: numeric names: authors list (link)
  6. ^ Bland, J. Martin; Altman, Douglas G. (1996). "Statistics Notes: Measurement Error". BMJ. 313 (7059): 744. doi:10.1136/bmj.313.7059.744. PMC 2352101. PMID 8819450.
  7. ^ Saris, W. E.; Gallhofer, I. N. (2014). Design, Evaluation and Analysis of Questionnaires for Survey Research (Second ed.). Hoboken: Wiley. ISBN 978-1-118-63461-5.
  8. ^ DeCastellarnau, A. and Saris, W. E. (2014). A simple procedure to correct for measurement errors in survey research. European Social Survey Education Net (ESS EduNet). Available at: http://essedunet.nsd.uib.no/cms/topics/measurement Archived 2019-09-15 at the Wayback Machine
  9. ^ Saris, W. E.; Revilla, M. (2015). "Correction for measurement errors in survey research: necessary and possible" (PDF). Social Indicators Research. 127 (3): 1005–1020. doi:10.1007/s11205-015-1002-x. hdl:10230/28341. S2CID 146550566.
  10. ^ Hayashi, Fumio (2000). Econometrics. Princeton University Press. p. 187. ISBN 978-0-691-01018-2.
  11. ^ Angrist, Joshua David; Pischke, Jörn-Steffen (2015). Mastering 'metrics : the path from cause to effect. Princeton, New Jersey: Princeton University Press. p. 221. ISBN 978-0-691-15283-7. OCLC 877846199. The bias generated by this sort of measurement error in regressors is called attenuation bias.

Further reading

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