Problems with Interval Estimation When Data are Adjusted via Calibration

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Abstract
The analysis of adjusted data arising from a linear calibration curve is considered. Although it is obvious that adjusted values contain errors due to estimation of the calibration curve, some investigators may be tempted to analyze such data as if they are true values of the property of interest. We illustrate some of the problems that arise if one applies “naive” analyses to calibrated data. In particular, it is shown that standard one-sample confidence intervals have actual confidence levels that are always less than the nominal value. We also propose and evaluate two other methods for constructing confidence intervals. Tolerance intervals derived from adjusted data also may yield deceiving results, having actual probability levels that are usually greater than the desired level but smaller in some cases.