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Should (T1 - T2) Have Larger Uncertainty Than T1?



Lee Y. G


In interlaboratory comparisons, laboratories sometimes use a transfer instrument to realize the value of a laboratory standard to compare the relative biases of their measurement processes and standards. One summary of interest from such comparisons is the pairwise difference between two laboratories' results, along with its expanded uncertainty, a confidence interval for the true difference. Since the labs have unequal variances, the confidence interval is usually computed by the Welch-Satterthwaite (denoted WS) procedure, which approximates the distribution of the pivot quantity used to compute the confidence interval by a Student's-t distribution with effective degrees of freedom defined as a function of the data.In the course of analyzing the data from a comparison of temperature realizations, an awkward and counterintuitive property of the WS procedure was observed. Namely, a confidence interval for a between-lab difference can be narrower than the corresponding interval for one of the component results. This occurs when at least one laboratory's uncertainty estimate has low degrees of freedom (say 1 or 2), and therefore has a large coverage factor from the Student's-t distribution, while the effective degrees of freedom for the combined uncertainty of the pairwise difference, obtained from the WS approximation, is larger.The typical reaction to this situation is to suspect the WS procedure of failing to achieve its nominal confidence level. However, this is not the correct explanation. In fact, situations exist where the confidence intervals for each laboratory's mean and for their pairwise difference all achieve the stated level of confidence even though the uncertainty of the difference is smaller than the uncertainty of at least one of its component results. This paper explains how this counterintuitive property of confidence intervals can be true.
Proceedings Title
International Sympoisum on Temperature and Thermal Measurements in Industry and Science | 8th | | VDE
Conference Dates
June 1, 2001
Conference Location
Berlin, GE
Conference Title


effective degrees of freedom, interlaboratory, key comparisons, temperature, uncertainty, Welch-Satterthwaite approx.


G, L. (2001), Should (T<sub>1</sub> - T<sub>2</sub>) Have Larger Uncertainty Than T<sub>1</sub>?, International Sympoisum on Temperature and Thermal Measurements in Industry and Science | 8th | | VDE, Berlin, GE (Accessed April 23, 2024)
Created June 1, 2001, Updated February 17, 2017