The logarithmic transformation and the geometric mean in reporting experimental IgE results: what are they and when and why to use them?
The logarithmic transformation and the geometric mean in reporting experimental IgE results: what are they and when and why to use them?
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DOI：
10.1016/s1081-1206(10)60595-9
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发表时间：
2008-04-01
影响因子：
5.9
通讯作者：
Marshall, Gailen D.
中科院分区：
文献类型：
--
作者：
Olivier, Jake;Johnson, William D.;Marshall, Gailen D.
背景：免疫数据，如IgE和白细胞介素4，倾向于正偏态分布，具有较大数值的长尾。这使得基于正态分布理论的分析（例如，t检验和方差分析）存在问题，并且扭曲了作为集中趋势度量的样本平均值。这些问题可以通过分析经过日志转换的数据来解决。以这种方式分析的数据用几何平均值进行总结。目的：探讨对数变换和几何均数在免疫数据分析中的应用。方法：分析可以通过将数据转换为对数尺度来实现钟形（近似正态）分布。验证统计推断所需的钟形分布仅在转换后的尺度中实现。在总结研究成果时，统计分析人员通常会将均值和置信区间从对数尺度转换回原始的测量尺度。对数尺度的统计推断对数据仍然有效。将对数值的均值反变换到原尺度的结果就是几何均值。该统计数据较少受到数据正偏斜分布尾部异常大值的扭曲。结果：一个简单的例子用来说明这种类型的分析。结论：对数变换允许对阳性偏斜免疫数据进行有效的统计推断。这种分析的结果是几何均值，它比通常的样本均值更好地衡量了这种数据类型的集中趋势。
Background: Immunologic data, such as IgE and interleukin 4, tend to have positively skewed distributions with a long tail of larger values. This renders analyses based on normal distribution theory questionable (eg, t tests and analysis of variance) and distorts the sample mean as a measure of central tendency. These problems can be addressed through analysis of log-transformed data. Data analyzed in this fashion are summarized with the geometric mean.Objective: To elucidate the use of the logarithmic transform and the geometric mean in the analysis of immunologic data.Methods: The analysis may be conducted by transforming the data to a logarithmic scale to achieve a bell-shaped (approximately normal) distribution. The bell-shaped distribution needed to validate statistical inferences is only achieved in the transformed scale. In summarizing the research findings, the statistical analyst usually will transform means and confidence intervals from the logarithmic scale back to the original scale of measurement. Statistical inferences in the log scale remain valid for the data. The result of back transforming the mean of logarithmic values to the original scale is the geometric mean. This statistic is less subject to distortion by the unusually large values in the tail of the positively skewed distribution of the data.Results: A brief example is used to illustrate this type of analysis.Conclusions: Logarithmic transformation permits valid statistical inference for positively skewed immunologic data. A result of this analysis is the geometric mean, which is a better measure of central tendency of this data type than the usual sample mean.