Abstract
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.
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Notes
We use “average” or “mean” interchangeably.
The use of bootstrapping was also suggested by one of the reviewers.
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Acknowledgements
The author thanks the Editor-in-Chief and referees for their valuable comments and constructive suggestions. This work was supported by Fundação para a Ciência e a Tecnologia, Grant UIDB/00315/2020.
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Curto, J.D. Inference about the arithmetic average of log transformed data. Stat Papers 64, 179–204 (2023). https://doi.org/10.1007/s00362-022-01315-x
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DOI: https://doi.org/10.1007/s00362-022-01315-x