Haas C N
Pritzker Department of Environmental Engineering, Illinois Institute of Technology, Chicago 60616.
Appl Environ Microbiol. 1989 Aug;55(8):1934-42. doi: 10.1128/aem.55.8.1934-1942.1989.
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.
尽管稀释计数法在定量微生物学中已被广泛应用，但其解读在微生物学和应用统计学领域一直备受广泛讨论。最大似然法（最可能数法）通常被用于从稀释实验中估计密度。然而，尚未得到广泛认可的是，这些方法在微生物学中使用的样本量下存在内在的统计学偏差。本文对一种用于校正此类偏差的提议方法进行了分析，发现该方法对于泊松行为的适度偏差具有稳健性。对于与泊松假设差异较大的分析，对Spearman-Karber方法的使用进行了分析，并表明其产生的密度估计偏差小于最可能数法。还讨论了Loyer和Hamilton（M.W. Loyer和M.A. Hamilton，《生物统计学》40:907 - 916，1984）提出的构建置信限的修订方法，并给出了每个稀释度有五支试管的三位和四位小数稀释系列的图表。
