A common practice in statistics is to take the log transformation of highly skewed data and construct confidence intervals for the population average on the basis of transformed data. However, when computed based on log-transformed data, the confidence interval is for the geometric instead of the arithmetic average and neglecting this can lead to misleading conclusions. In this paper, we consider an approach based on a regression of the two sample averages to convert the confidence interval for the geometric average in a confidence interval for the arithmetic average of the original untransformed data. The proposed approach is substantially simpler to implement when compared to the existing methods and the extensive Monte Carlo and bootstrapping simulation study suggests outperforming in terms of coverage probabilities even at very small sample sizes. Some real data examples have been analyzed, which support the simulation findings of the paper.

统计学中的一种常见做法是对高度偏斜的数据进行对数转换，并在转换后的数据的基础上构建总体平均值的置信区间。然而，当基于对数转换数据计算时，置信区间是几何平均值而不是算术平均值，忽略这一点可能会导致误导性结论。在本文中，我们考虑了一种基于两个样本平均值回归的方法，将几何平均值的置信区间转换为原始未转换数据的算术平均值的置信区间。与现有方法相比，所提出的方法实施起来要简单得多，而且广泛的蒙特卡洛和自举模拟研究表明，即使在非常小的样本量下，其在覆盖概率方面也表现出色。已经分析了一些真实的数据示例，这支持了本文的模拟结果。