Abstract
Uncertainty assignments in the sequel of least squares adjustments comply with the formalism as used in the context of functional relationships.
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Notes
- 1.
Here, \(\bar{\beta}_{k}\) acts as a random variable. For the sake of readability, however, capital letter will not be used in case of Greek symbols.
- 2.
Nevertheless, we might wish to average “ad hoc”, i.e. without resorting to the method of least squares. Let us average the measurements of two masses. Ignoring the option that the associated true values differ grossly, the quotations m 1=1/4 kg and m 2=3/4 kg, each being accurate to about ±1 mg, produce the mean \(\bar{m}=1/2\) kg. However, the associated uncertainty exceeds the assumed uncertainties of the input data by a factor of 250 000. The uncertainty has been blown up since the true values of the masses differed. We are sure, uncertainties should be due to measurement errors and not to deviant true values. This drastically exaggerating example elucidates that the averaging of means implies far-reaching consequences if done inappropriately.
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M. Grabe, On the assignment of uncertainties within the method of least squares. Poster Paper, Second International Conference on Precision Measurement and Fundamental Constants, Washington, DC, 8–12 June 1981
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Grabe, M. (2014). Uncertainties of Least Squares Estimators. In: Measurement Uncertainties in Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-04888-8_11
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DOI: https://doi.org/10.1007/978-3-319-04888-8_11
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