Anomalies in the analysis of calibrated data

This study examines the effects of calibration errors on model assumptions and data-analytic tools in direct calibration assays. These effects encompass induced dependencies, inflated variances, and heteroscedasticity among the calibrated measurements, whose distributions arise as mixtures. These anomalies adversely affect conventional inferences, including the inconsistency of sample means; the underestimation of measurement variance; and the distributions of sample means, sample variances, and student’s t as mixtures. Inferences in comparative experiments remain largely intact, although error mean squares continue to underestimate the measurement variances. These anomalies are masked in practice, as conventional diagnostics cannot discern the irregularities induced through calibration. Case studies illustrate the principal issues.