Gao Anli, Martos Perry
University of Guelph, Laboratory Services Division, 95 Stone Rd W, Guelph, ON N1H8J7, Canada.
J AOAC Int. 2018 Aug 10. doi: 10.5740/jaoacint.18-0161.
Estimation of measurement uncertainty (MU) has been extensively addressed in documents from standard authorities. In microbiology, bacterial counts are log transformed to get a more normal distribution. Unfortunately, the difference between using original and log-transformed data appears to not have been investigated even in publications focusing on MU estimation. Statistical formulae inferencing and estimation of MU using real bacterial enumeration datasets. Both mean and SD calculated from original data carry the same scale and unit as the original data. However, the mean of log-transformed data becomes a geometric mean in log, and the SD becomes the logarithm of a ratio. Furthermore, calculation of RSD obtained by dividing the SD by the mean is meaningless and misleading for log-transformed data. The ratio, the antilog of the SD of log-transformed data, copes with multiplicative and divisive relationships to geometric mean (without log), instead of the arithmetic mean. The ratio can be converted to an analog ratio, which is similar or almost identical to the RSD of the untransformed data, especially when the within-subject variation is small. When MU is estimated from multiple samples with different measurands, the calculated RSD of original data is independent of the mean and can be pooled; however, for log-transformed data, the SD can be combined to estimate the common uncertainty. Calculation and use of RSD of log-transformed data are meaningless and misleading. Procedures outlining the estimation and interpretation of MU from log-transformed data require re-evaluation.
测量不确定度（MU）的评估在标准权威机构的文件中已有广泛论述。在微生物学中，细菌计数需进行对数转换以获得更接近正态的分布。遗憾的是，即使在专注于MU评估的出版物中，使用原始数据和对数转换后的数据之间的差异似乎也未得到研究。使用实际细菌计数数据集进行MU的统计公式推导和评估。根据原始数据计算的均值和标准差与原始数据具有相同的量纲和单位。然而，对数转换后数据的均值在对数形式下成为几何均值，标准差则变为一个比值的对数。此外，对于对数转换后的数据，通过将标准差除以均值得到的相对标准偏差（RSD）的计算是无意义且具有误导性的。对数转换后数据标准差的反对数之比处理的是与几何均值（无对数形式）的乘除关系，而非算术均值。该比值可转换为类似或几乎等同于未转换数据RSD的模拟比值，尤其是当个体内变异较小时。当从具有不同被测量的多个样本估计MU时，计算得到的原始数据RSD与均值无关且可合并；然而，对于对数转换后的数据，标准差可合并以估计共同不确定度。对数转换后数据RSD的计算和使用是无意义且具有误导性的。概述从对数转换后数据估计和解释MU的程序需要重新评估。
