A Sampling Investigation of the Efficiency of Weighting Inversely as the Estimated Variance

Data of this kind may occur when k laboratories make separate determinations xi of the same physical or chemical quantity, each with an estimated standard error, or when a summary is being made of the results of k replicated experiments, in each of which the difference xi between a specified pair of treatments has been observed. In practices it cannot be taken for granted that the observations xi are all estimate, of the same mean a, because personal biases or local conditions of experimentation may render this assumption false. The discussion in this paper is confined to situations in which the assumption holds.