A Quick and Easy Multiple-Use Calibration-Curve Procedure

Abstract

The standard multiple-use calibration procedure of Scheffe (1973) states that with probability 1 – δ, the proportion of calculated confidence intervals containing the true unknowns is at least 1 – α in the long run. The probability 1 – δ refers to the probability that the calibration experiment results in a “good” outcome. In Scheffe's formulation, a good outcome involves both coverage of the true underlying regression curve and an upper confidence limit for σ, the scale parameter. Scheffe's procedure is fairly difftcult for practitioners to apply, because it relies on tables that are not easy to use. A simpler notion of “goodness” that requires only the coverage of the underlying regression leads to easily calculated confidence intervals for the unknowns. In addition, these intervals are generally shorter than Scheffe's. An application example is given to illustrate the technique.