Data processing of microbial enumeration expressed as colony counts requires the use of specific statistical approaches due to the particular aspect of the analyte and the consideration of the variability related to the growth of microorganisms. A challenging matter in the organization of proficiency testing (PT) schemes for water microbiology is to provide representative, homogeneous and stable enough samples with the aim of assessing participants’ performance but also characterizing the accuracy of measurement. As a consequence, the proficiency testing design may help to make clear distinction between the different sources of variation and facilitate the subsequent error analysis associated with the analytical procedures of the participants. Besides, the statistical tools may be selected to provide explicit outcomes which enable the participants to interpret the data in line with other existing indicators such as those arising from validation studies or measurement uncertainty procedures in the laboratory quality assurance system. In this paper, the suitability of a Poisson–Gamma hierarchical generalized linear model is tested in order to evaluate the interlaboratory error, the batch homogeneity and the repeatability error from water microbiology PT. A probabilistic approach deriving from the negative binomial distribution is proposed for assessing the participating laboratories performance in terms of generalized z -score.

中文翻译：

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能力验证计划中水微生物计数变异性的不确定性模型

由于分析物的特定方面以及与微生物生长相关的变异性的考虑，以菌落计数表示的微生物计数的数据处理需要使用特定的统计方法。组织水微生物学能力验证 (PT) 计划的一个具有挑战性的问题是提供具有代表性、均质和足够稳定的样本，目的是评估参与者的表现，同时表征测量的准确性。因此，能力验证设计可能有助于明确区分不同的变异来源，并促进与参与者分析程序相关的后续错误分析。除了，可以选择统计工具来提供明确的结果，使参与者能够根据其他现有指标来解释数据，例如来自验证研究或实验室质量保证系统中的测量不确定性程序的指标。在本文中，测试 Poisson-Gamma 分层广义线性模型的适用性，以评估水微生物学 PT 的实验室间误差、批次同质性和重复性误差。提出了一种源自负二项式分布的概率方法，用于根据广义 z 分数评估参与实验室的表现。