A MODIFIED GAUSS‐NEWTON ALGORITHM AND NINETY‐SIX WELL MICRO‐TECHNIQUE FOR CALCULATING MPN USING EXCEL SPREADSHEETS1

Abstract

Conventional most probable number (MPN) methods seek a calculated value for microbial concentration (Δ, mL‐1) which induces the total binomial probability function (Ptotal) to approach its maximum limit. In fact, such techniques are the only statistically compelling procedures available for determining MPN when utilizing a small set of observations per dilution (e.g., n = 3–8). However, as n approaches a large value, statistical routines which assume a normal distribution might be applied to ascertain the MPN. With this in mind, we produce herein a modified Gauss‐Newton “linearization” (curve fitting) algorithm for determining Δ (n = 96) from binomial micro‐plate assays which are readily automated using 96‐well micro‐plate readers. This technique, an iterative protocol, is less cumbersome than many traditional MPN procedures and has certain advantages. Data derived from this method were not only close to MPN estimations using a direct technique based on the conventional maximum probability resolution (MPR) concept but also displayed more favorable chi‐squared (X2) statistics.