How many digits should be reported in forensic breath alcohol measurements?

Abstract

Uncertainty is an inherent property of all measurements. The magnitude of this uncertainty will determine the number of meaningful digits that should be reported in a measurement result. Several statistical arguments are considered providing evidence that three digit truncated results are more appropriate than two since the first significant digit of the combined uncertainty (standard deviation) in breath alcohol measurement is found in the third decimal place. Probably, the most compelling reason for reporting three digits is the significant reduction in combined uncertainty compared with the use of two digits. For a breath alcohol concentration of 0.089 g/210 L, the combined uncertainty for two digit results is ~0.0042 g/210 L, compared with 0.0031 g/210 L for three digit results. The historical practice of reporting two digit truncated results in forensic breath alcohol analysis has been largely based on the use of analog scale instruments with 0.01 g/210 L scale resolution. With today's modern digital instrumentation, this practice should be reconsidered. While the focus of this paper is on breath alcohol analysis, the general principles will apply to any quantitative analytical measurement.