Determinations based on duplication of readings

Abstract

This paper is concerned with a stati sti cal estimation procedure in which measureme nts of a quan· tity are ta~en until two ide ntical readings are obtained; thi s duplicated value is then take n as the estimate of the magnitude of the quantity concerned. The properties of this estimation procedure have been investigated numerically , under the assumptions that the individual observations are rounded values of measure ments whic h have a normal distribution, and this estimator is compared with the arithmetic mean of two observations. It is shown that an arithmetic mean of two observations from the rounded distribution is almost always superior to the es timator described above. The exception is where the rounding interval is so wide a nd the round ing lattice is so advantageously placed that the only real reason for taking repeat measure me nts would be as a protection against gross errors.