Alcohol calculations and their uncertainty

Abstract

A dilution model is widely used to link blood alcohol concentration and the quantity of alcohol consumed. Whilst some authors use the total body water formulation of that model, others use the Widmark Factor formulation. A paper by Forrest gave a table of example values of the Widmark Factor and Barbour, based on Forrest's work and using Forrest's computer program, subsequently presented Forrest's results by way of a chart. Whilst the results of Forrest and Barbour are often used interchangeably, there is a significant difference between them on the factors for women. This paper examines the source of the unexpected discrepancy. It is essential to quote an error range, in blood alcohol concentration calculations, for the results. The extent of that error range was investigated by Gullberg who also employed the Widmark Factor formulation. Gullberg concluded that when reporting a calculated blood alcohol concentration, a coefficient of variation of ± 21% should be applied. Similarly, Gullberg concluded that when calculating the volume of drink, a coefficient of variation of 12½ % should be applied. The present paper derives and publishes the formulae for calculating this coefficient of variation. It is then shown that Gullberg's conclusions are mistaken: the coefficient of variation is not some fixed percentage but must be calculated in each case.

Keywords: Widmark; alcohol; calculations; error; uncertainty.