Bias correcting confidence intervals for a nearly common property

An important problem in science is to determine when individual measurements taken under different conditions are measurements of a nearly common property. When they are, the proper and common practice is to combine these measurements into a single estimate. For example, when certifying standard reference materials (SRMs) several different types of measurement devices are commonly used. Each device has its own systematic error (bias) and it is not clear whether these devices are measuring nearly the same property. We say that devices are measuring nearly the same property if the population means from these devices are within the stated bounds on systematic error. It is assumed that each bias can be quantified so that a known bound on bias error can be calculated. This paper provides methods for testing whether these devices are measuring nearly the same property. The first method is based upon the usual bias correction to t-confidence intervals while the second, more powerful, method relies on a sophisticated bias correction to t-confidence intervals. If we do not reject the null hypothesis that the methods measure nearly the same property then techniques found in refs. l-3 can and should be applied to produce a single estimate as well as an uncertainty statement for the estimate of this nearly common property. We formulate the null hypothesis as stating that the means of the different measurements do not differ from a common value by more than the stated bounds on bias.