Estimation of microbial densities from dilution count experiments.

Although dilution counts have been widely used in quantitative microbiology, their interpretation has always been widely discussed both in microbiology and in applied statistics. Maximum-likelihood (most-probable-number) methods hae generally been used to estimate densities from dilution experiments. It has not been widely recognized that these methods are intrinsically and statistically biased at the sample sizes used in microbiology. This paper presents an analysis of proposed method for correction of such biases, and the method was found to be robust for moderate deviations from Poisson behavior. For analyses at greater variance with the Poisson assumptions, the use of the Spearman-Karber method is analyzed and shown to yield an estimate of density of lesser bias than that produced by the most-probable-number method. Revised methods of constructing confidence limits proposed by Loyer and Hamilton (M.W. Loyer and M.A. Hamilton, Biometrics 40:907-916, 1984) are also discussed, and charts for the three- and four-decimal dilution series with five tubes per dilution are presented.