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Inference about the arithmetic average of log transformed data

Author

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  • José Dias Curto

    (Instituto Universitário de Lisboa (ISCTE-IUL), BRU-UNIDE
    Department of Quantitative Methods for Management and Economics)

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.

Suggested Citation

  • José Dias Curto, 2023. "Inference about the arithmetic average of log transformed data," Statistical Papers, Springer, vol. 64(1), pages 179-204, February.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01315-x
    DOI: 10.1007/s00362-022-01315-x
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    References listed on IDEAS

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    1. Zhenmin Chen & Jie Mi, 2001. "An approximate confidence interval for the scale parameter of the gamma distribution based on grouped data," Statistical Papers, Springer, vol. 42(3), pages 285-299, July.
    2. Michael Sherman & Arnab Maity & Suojin Wang, 2011. "Inferences for the ratio: Fieller’s interval, log ratio, and large sample based confidence intervals," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 313-323, September.
    3. Ayman Baklizi & B.M. Golam Kibria, 2009. "One and two sample confidence intervals for estimating the mean of skewed populations: an empirical comparative study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(6), pages 601-609.
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