The uncertainty associated with the weighted mean of measurement data

摘要

Weighted mean has been used to combine means from several sets of measurements, which are either from different laboratories or based on different measurement methods. It is also often used in key comparisons and other inter-laboratory comparisons. However, the traditional estimator of the variance of the weighted mean underestimates the variance. Two new variance estimators are proposed with smaller biases, smaller mean square errors and much better coverage probabilities for the correspondingly formed intervals. In metrology, the uncertainties based on Type B evaluation which are not based on statistical analysis of data cannot be ignored. In the later part of this paper, the results are extended to the general case with both Type A and Type B uncertainty components being presented.