Fermentation tube test statistics for direct water sampling and comments on the Thomas formula

This article describes a new interpretation of the Fermentation Tube Test (FTT) performed on water samples drawn from natural waters polluted by faecal bacteria. A novel general procedure to calculate the Most Probable Number of bacteria (MPN) in natural waters has been derived for the FTT for both direct and independent repetitive multiple water sampling. The generalization based on solving the newly proposed equation allows consideration of any a priori frequency distribution g(n) of bacterial concentration in analysed water as opposed to the unbounded uniform a priori distribution g(n) assumed in the standard procedures of the Standard Methods of Examining Water and Wastewater and ISO 8199:1988. Also a statistical analysis of the Thomas formula is presented. It is demonstrated that the Thomas formula is highly inaccurate. The authors propose, therefore, to remove the Thomas formula from the Standard Methods of Examining Water and Wastewater and ISO 8199:1988 altogether and replace it with a solution of the proposed generalized equation.