Small Sample Confidence Intervals in Log Space Back-Transformed from Normal Space

摘要

The logarithmic transformation is commonly applied to a lognormal data set to improve symmetry, homoscedasticity, and liearity. Simple to implement and easy to understand, the logarithm function transforms the original data to closely resemble a normal distribution. Analysis in the normal space provides point estimates and confidence intervals, but transformation back to the original space using the naive approach yields confidence intervals of impractical width. The naive approach offers results that are often inadequate for practical purpose. We present an alternative approach that provides improved results in the form of decreased interval width, increased confidence level, or both. Our alternative approach yields dramatically improved results at small sample sizes drawn from the right tail of the lognormal distribution.