IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i1d10.1007_s00362-022-01315-x.html
   My bibliography  Save this article

Inference about the arithmetic average of log transformed data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01315-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-022-01315-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mi, Jie & Naranjo, Arlene, 2003. "Inferences about the scale parameter of the gamma distribution based on data mixed from censoring and grouping," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 229-243, April.
    2. Lu, Wanbo & Tsai, Tzong-Ru, 2009. "Interval censored sampling plans for the gamma lifetime model," European Journal of Operational Research, Elsevier, vol. 192(1), pages 116-124, January.
    3. Wanbo Lu & Tzong-Ru Tsai, 2009. "Interval censored sampling plans for the log-logistic lifetime distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(5), pages 521-536.
    4. Yanqing Wang & Suojin Wang & Raymond J. Carroll, 2015. "The direct integral method for confidence intervals for the ratio of two location parameters," Biometrics, The International Biometric Society, vol. 71(3), pages 704-713, September.
    5. N. O. A. S. Jourdain & D. J. Cole & M. S. Ridout & J. Marcus Rowcliffe, 2020. "Statistical Development of Animal Density Estimation Using Random Encounter Modelling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(2), pages 148-167, June.
    6. N. Balakrishnan & N. Martín & L. Pardo, 2017. "Empirical phi-divergence test statistics for the difference of means of two populations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 199-226, April.
    7. Peng Wang & Siqi Xu & Yi‐Xin Wang & Baolin Wu & Wing Kam Fung & Guimin Gao & Zhijiang Liang & Nianjun Liu, 2021. "Penalized Fieller's confidence interval for the ratio of bivariate normal means," Biometrics, The International Biometric Society, vol. 77(4), pages 1355-1368, December.
    8. B. M. Golam Kibria & Shipra Banik, 2013. "Parametric and nonparametric confidence intervals for estimating the difference of means of two skewed populations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2617-2636, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01315-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.