Home » Small Sample Confidence Intervals in Log Space Back-Transformed from Normal Space by Jason E Tisdel
Small Sample Confidence Intervals in Log Space Back-Transformed from Normal Space Jason E Tisdel

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

Jason E Tisdel

Published November 13th 2012
ISBN : 9781288294831
Paperback
76 pages
Enter the sum

 About the Book 

The logarithmic transformation is commonly applied to a lognormal data set to improve symmetry, homoscedasticity, and linearity. 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 applies the exponential function e to the parameter of interest in normal space to obtain the corresponding parameter of interest in the original space. The naive approach offers results that are often inadequate for practical purposes. 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.