The degree to which a technology used for drinking water treatment physically removes or inactivates pathogenic microorganisms is commonly expressed as a log-reduction (or log-removal) and is of central importance to the provision of microbiologically safe drinking water. Many evaluations of water treatment process performance generate or compile multiple values of microorganism log-reduction, and it is common to report the average of these log-reduction values as a summary statistic. This work provides a cautionary note against misinterpretation and misuse of averaged log-reduction values by mathematically proving that the average of a set of log-reduction values characteristically overstates the average performance of which the set of log-reduction values is believed to be representative. This has two important consequences for drinking water and food safety as well as other applications of log-reduction: 1) a technology with higher average log-reduction does not necessarily have higher average performance, and 2) risk analyses using averaged log-reduction values as point estimates of treatment efficiency will underestimate average risk-sometimes by well over an order of magnitude. When analyzing a set of log-reduction values, a summary statistic called the effective log-reduction (which averages reduction or passage rates and expresses this as a log-reduction) provides a better representation of average performance of a treatment technology.

中文翻译：

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描述水处理过程的性能：为什么平均对数减少会产生误导性的统计数据。

用于饮用水处理的技术在物理上去除或灭活病原微生物的程度通常表示为对数减少（或对数去除），对于提供微生物安全的饮用水至关重要。对水处理过程性能的许多评估都可以生成或编译微生物对数减少的多个值，并且通常将这些对数减少值的平均值报告为摘要统计量。这项工作通过数学证明一组对数减少值的平均值过分夸大了被认为代表该组对数减少值的平均性能，从而提供了警告提示，以防止误解和滥用平均对数减少值。这对饮用水和食品安全以及对数减少的其他应用有两个重要影响：1）平均对数减少的技术不一定具有更高的平均性能，并且2）使用平均对数减少值的风险分析因为治疗效率的点估计值有时会低估平均风险一个数​​量级。当分析一组对数减少值时，称为有效对数减少的摘要统计信息（平均减少或通过率，并将其表示为对数减少）可以更好地表示处理技术的平均性能。2）使用平均对数减少值作为治疗效率的点估计值进行的风险分析有时会低估平均风险一个数​​量级。当分析一组对数减少值时，称为有效对数减少的摘要统计信息（平均减少或通过率，并将其表示为对数减少）可以更好地表示处理技术的平均性能。2）使用平均对数减少值作为治疗效率的点估计值进行的风险分析有时会低估平均风险一个数​​量级。当分析一组对数减少值时，称为有效对数减少的摘要统计信息（平均减少或通过率，并将其表示为对数减少）可以更好地表示处理技术的平均性能。