The Statistical Construction of a Single Standard from Several Available Standards

In the case of physical quantities for which no international standards exist, such as microwave power and microwave noise, it may be desirable to establish an international standard by combination of the data from several laboratory standards. Even if there is an international standard, it conceivably might be replaced by a new composite standard, for example the mean of several laboratory atomic-time standards. A weighted mean may be preferable. It is noted that the "best" combination of observations for estimating a theoretical mean or median value depends on the theoretical frequency distribution from which the observations are drawn. Since the theoretical distribution for observations from different laboratories would in general be unknown, two weighted means are suggested which are reasonably good for many distributions, allowing for wild observations particularly, and in which the weight of each observation depends only on its order when the observations are ordered in size. The efficiencies of these and other estimates are evaluated for each of four distributions.