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Normalized Relative Uncertainties and Applications to Confidence Intervals



Daniel E. Kelleher


The relative standard uncertainty (computed relative standard deviation of the mean) is shown to be intrinsically normalized when the averaged values all have the same sign. We exploit this fact to derive improved confidence intervals by pooling comparable relative standard uncertainties of different quantities (in a given sample, for example). Pooling allows one to characterize the underlying relative standard uncertainties associated with different independent determinations, and to increase the number of degrees of freedom. If there are a sufficiently large number of independently determined quantities, pooling their relative standard uncertainties can uncover systematic trends, and provide a sensitive detection of both high and low outliers. Pooling of this type is particularly advantageous when a small number of independent method results are available for a substantial number of different quqntities. A technique is developed to treat the typical case where the relative standard uncertainties exhibit a weak monotonic dependence on the magnitude of the different quantities. Generally the resulting relative confidence intervals will include the effects of type A uncertainties, and all type B uncertainties except those which the independent methods may have in common. Examples of the pooling technique are presented.
Computational Statistics


bias, confidence intervals, normalized, pooling, relative, uncertainty


Kelleher, D. (2008), Normalized Relative Uncertainties and Applications to Confidence Intervals, Computational Statistics (Accessed April 21, 2024)
Created October 16, 2008