The traditional calibration problem is concerned with estimating the unknown value of an explanatory variable X corresponding to an observed value of a response variable Y that is assumed to be functionally related to X. The problem for which Y is related to X by a simple linear model has been discussed in the literature. This paper is concerned with obtaining a confidence interval for an unknown value of X corresponding to a specified or fixed value of Y, where Y and X are related through a known nonlinear function. Given a specified value y(c) of a response variable Y that is related to X through a known function, linear or nonlinear, a point estimate of x(c) can be found through the inverse function, if the inverse exists, or through an iterative search procedure. Two approaches are presented for determining a confidence interval for x(c), given a value y(c). When the inverse function exists, a confidence interval about x(c) can be obtained from the approximate distribution of x(c) triple-overdot, provides a symmetric confidence interval about x(c) triple-overdot. Confidence intervals based on the asymptotic of beta-triple-overdot are not symmetric about x(c) triple-overdot, which is particularly appropriate when considering nonlinear functions that have asymptotes. The technique based on the distribution of beta-triple-overdot is more general because it does not depend on having a closed form of the inverse function. A simulation study for sample sizes of 20, involving an exponential decay function, indicates that both approaches attained the desired confidence coefficient. A test procedure comparing two calibration points from different populations or treatment groups is presented. A simulation study of sample sizes of 20, involving an exponential decay function, indicates that the test procedure attains the desired level of significance with good power. Additional simulation studies may be necessary to determine the appropriateness of these techniques for different model types and/or sample sizes. An example from meat sciences research is presented demonstrating the techniques discussed.
