Observational error

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.

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 repeated measurements. 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 alter the value observed and repeated identical measurements do not reduce such errors.^[2]

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 metallic ruler the temperature of which is not controlled will be affected by thermal expansion causing an additional systematic error resulting in limited accuracy.^[3]

^ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 978-0-19-920613-1
^ 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.
^ 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.

[Dodge-1] Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 978-0-19-920613-1

[Taylor-2] 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.

[3] 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.

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