Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research

Jesus Gomez; Tibisay Rangel; Victor Gomez

doi:doi:10.11648/j.ijmri.20250101.12

Methodology Article |

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Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research

Jesus Gomez^*

, Tibisay Rangel

, Victor Gomez

Published in International Journal of Medical Research and Innovation (Volume 1, Issue 1)

Received: 7 September 2025 Accepted: 30 October 2025 Published: 8 December 2025

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Abstract

Research in fields such as biomedicine often generates data that do not conform to a normal distribution, exhibiting positive skewness (right skewness), as is characteristic of the log-normal distribution. In these scenarios, the use of the arithmetic mean (AM) and standard deviation (SD) can lead to misinterpretations of central tendency and dispersion, as the AM is sensitive to extreme values and overestimates wide numerical ranges. This paper presents a guide on the use of the Geometric Mean (GM), the Geometric Standard Deviation (GSD), and the Geometric Coefficient of Variation (GCV) as the most appropriate statistical tools for this type of data, as well as for sets with disparate numerical scales. The fundamental practical challenge of zero values, common in biomedical measurements such as viral loads or analyte concentrations, is addressed. A specific methodology for treating data with zeros is detailed and justified, consisting of the addition and subsequent subtraction of a unit to allow the calculation of geometric statistics. Finally, two approaches for calculating the Geometric Coefficient of Variation are analyzed and compared, highlighting its nature as a power basis rather than a simple mathematical ratio, and discussing its comparative utility despite its complex interpretation. The need for a better understanding and application of these metrics to improve the accuracy and reproducibility of data analyses is emphasized.

Published in	International Journal of Medical Research and Innovation (Volume 1, Issue 1)
DOI	10.11648/j.ijmri.20250101.12
Page(s)	14-19
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Geometric Mean, Geometric Standard Deviation, Geometric Coefficient of Variation, Log-normal Distribution

References

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[3]	Kirkwood, T. B. L. (1979). Geometric means and measures of dispersion. Biometrics, 35(4), 908-909.
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[5]	De La Cruz, R., & Kreft, J. U. (2018). Geometric mean extension for data sets with zeros. arXiv preprint arXiv: 1806.06403.
[6]	Kirkwood, T. B. L. (1993). Geometric standard deviation reply to Bohidar. Drug Development and Industrial Pharmacy, 19(3), 395-396.
[7]	Brandling-Bennett AD, Anderson J, Fuglsang H, Collins R. Onchocerciasis in Guatemala. Epidemiology in fincas with various intensities of infection. Am J Trop Med Hyg. 1981 Sep; 30(5): 970-81.
[8]	Humphries, L. (2010). The Geometric Coefficient of Variation. ThinkingApplied.com. Mind Tools: Applications and Solutions.
[9]	Wicklin, R. (April 27, 2011). Compute the geometric mean, geometric standard deviation, and geometric CV in SAS. The DO Loop. https://blogs.sas.com/content/iml/2019/10/02/geometric-mean-deviation-cv-sas.html
[10]	Habibzadeh F. Data Distribution: Normal or Abnormal? J Korean Med Sci. 2024; 39: e35. https://doi.org/10.3346/jkms.2024.39.e35
[11]	Hospitality. Institute. Log Transformation in Regression: Achieving Linearity. 2024 Mar 6. Disponible en: (Fuente sin URL proporcionada en los extractos).
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[13]	Feng C, Wang H, Lu N, Chen T, He H, Lu Y, et al. Log-transformation and its implications for data analysis. Shanghai Arch Psychiatry. 2014; 26(2): 105-8. https://doi.org/10.3969/j.issn.1002-0829.2014.02.009
[14]	Jones L, Barnett A, Vagenas D. Linear regression reporting practices for health researchers, a cross-sectional meta-research study. PLoS ONE. 2025; 20(3): e0305150. https://doi.org/10.1371/journal.pone.0305150
[15]	Benoit K. Linear Regression Models with Logarithmic Transformations. London: Methodology Institute, London School of Economics; 2011 Mar 17.
[16]	Motulsky HJ, Head T, Clarke PBS. Analyzing lognormal data: A nonmathematical practical guide. Pharmacol Rev. 2025; 77: 100049. https://doi.org/10.1016/j.pharmr.2025.100049

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APA Style

Gomez, J., Rangel, T., Gomez, V. (2025). Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research. International Journal of Medical Research and Innovation, 1(1), 14-19. https://doi.org/10.11648/j.ijmri.20250101.12

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ACS Style

Gomez, J.; Rangel, T.; Gomez, V. Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research. Int. J. Med. Res. Innovation 2025, 1(1), 14-19. doi: 10.11648/j.ijmri.20250101.12

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AMA Style

Gomez J, Rangel T, Gomez V. Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research. Int J Med Res Innovation. 2025;1(1):14-19. doi: 10.11648/j.ijmri.20250101.12

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@article{10.11648/j.ijmri.20250101.12,
  author = {Jesus Gomez and Tibisay Rangel and Victor Gomez},
  title = {Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research},
  journal = {International Journal of Medical Research and Innovation},
  volume = {1},
  number = {1},
  pages = {14-19},
  doi = {10.11648/j.ijmri.20250101.12},
  url = {https://doi.org/10.11648/j.ijmri.20250101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmri.20250101.12},
  abstract = {Research in fields such as biomedicine often generates data that do not conform to a normal distribution, exhibiting positive skewness (right skewness), as is characteristic of the log-normal distribution. In these scenarios, the use of the arithmetic mean (AM) and standard deviation (SD) can lead to misinterpretations of central tendency and dispersion, as the AM is sensitive to extreme values and overestimates wide numerical ranges. This paper presents a guide on the use of the Geometric Mean (GM), the Geometric Standard Deviation (GSD), and the Geometric Coefficient of Variation (GCV) as the most appropriate statistical tools for this type of data, as well as for sets with disparate numerical scales. The fundamental practical challenge of zero values, common in biomedical measurements such as viral loads or analyte concentrations, is addressed. A specific methodology for treating data with zeros is detailed and justified, consisting of the addition and subsequent subtraction of a unit to allow the calculation of geometric statistics. Finally, two approaches for calculating the Geometric Coefficient of Variation are analyzed and compared, highlighting its nature as a power basis rather than a simple mathematical ratio, and discussing its comparative utility despite its complex interpretation. The need for a better understanding and application of these metrics to improve the accuracy and reproducibility of data analyses is emphasized.},
 year = {2025}
}

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TY  - JOUR
T1  - Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research
AU  - Jesus Gomez
AU  - Tibisay Rangel
AU  - Victor Gomez
Y1  - 2025/12/08
PY  - 2025
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DO  - 10.11648/j.ijmri.20250101.12
T2  - International Journal of Medical Research and Innovation
JF  - International Journal of Medical Research and Innovation
JO  - International Journal of Medical Research and Innovation
SP  - 14
EP  - 19
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.ijmri.20250101.12
AB  - Research in fields such as biomedicine often generates data that do not conform to a normal distribution, exhibiting positive skewness (right skewness), as is characteristic of the log-normal distribution. In these scenarios, the use of the arithmetic mean (AM) and standard deviation (SD) can lead to misinterpretations of central tendency and dispersion, as the AM is sensitive to extreme values and overestimates wide numerical ranges. This paper presents a guide on the use of the Geometric Mean (GM), the Geometric Standard Deviation (GSD), and the Geometric Coefficient of Variation (GCV) as the most appropriate statistical tools for this type of data, as well as for sets with disparate numerical scales. The fundamental practical challenge of zero values, common in biomedical measurements such as viral loads or analyte concentrations, is addressed. A specific methodology for treating data with zeros is detailed and justified, consisting of the addition and subsequent subtraction of a unit to allow the calculation of geometric statistics. Finally, two approaches for calculating the Geometric Coefficient of Variation are analyzed and compared, highlighting its nature as a power basis rather than a simple mathematical ratio, and discussing its comparative utility despite its complex interpretation. The need for a better understanding and application of these metrics to improve the accuracy and reproducibility of data analyses is emphasized.
VL  - 1
IS  - 1
ER  -

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Author Information

Jesus Gomez

School of Pharmacy, Central University of Venezuela,Caracas, Venezuela

Contact Email

http://orcid.org/0000-0002-7682-1011
Tibisay Rangel

School of Pharmacy, Central University of Venezuela,Caracas, Venezuela

Contact Email

http://orcid.org/0000-0003-1170-3046
Victor Gomez

School of Mathematics, Central University of Venezuela, Caracas, Venezuela

Contact Email

http://orcid.org/0009-0005-8847-8598

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APA Style

Gomez, J., Rangel, T., Gomez, V. (2025). Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research. International Journal of Medical Research and Innovation, 1(1), 14-19. https://doi.org/10.11648/j.ijmri.20250101.12

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ACS Style

Gomez, J.; Rangel, T.; Gomez, V. Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research. Int. J. Med. Res. Innovation 2025, 1(1), 14-19. doi: 10.11648/j.ijmri.20250101.12

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AMA Style

Gomez J, Rangel T, Gomez V. Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research. Int J Med Res Innovation. 2025;1(1):14-19. doi: 10.11648/j.ijmri.20250101.12

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@article{10.11648/j.ijmri.20250101.12,
  author = {Jesus Gomez and Tibisay Rangel and Victor Gomez},
  title = {Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research},
  journal = {International Journal of Medical Research and Innovation},
  volume = {1},
  number = {1},
  pages = {14-19},
  doi = {10.11648/j.ijmri.20250101.12},
  url = {https://doi.org/10.11648/j.ijmri.20250101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmri.20250101.12},
  abstract = {Research in fields such as biomedicine often generates data that do not conform to a normal distribution, exhibiting positive skewness (right skewness), as is characteristic of the log-normal distribution. In these scenarios, the use of the arithmetic mean (AM) and standard deviation (SD) can lead to misinterpretations of central tendency and dispersion, as the AM is sensitive to extreme values and overestimates wide numerical ranges. This paper presents a guide on the use of the Geometric Mean (GM), the Geometric Standard Deviation (GSD), and the Geometric Coefficient of Variation (GCV) as the most appropriate statistical tools for this type of data, as well as for sets with disparate numerical scales. The fundamental practical challenge of zero values, common in biomedical measurements such as viral loads or analyte concentrations, is addressed. A specific methodology for treating data with zeros is detailed and justified, consisting of the addition and subsequent subtraction of a unit to allow the calculation of geometric statistics. Finally, two approaches for calculating the Geometric Coefficient of Variation are analyzed and compared, highlighting its nature as a power basis rather than a simple mathematical ratio, and discussing its comparative utility despite its complex interpretation. The need for a better understanding and application of these metrics to improve the accuracy and reproducibility of data analyses is emphasized.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Geometric Statistical Measures in the Analysis of Skewed and Zero-Valued Data: Implications for Biomedical Research
AU  - Jesus Gomez
AU  - Tibisay Rangel
AU  - Victor Gomez
Y1  - 2025/12/08
PY  - 2025
N1  - https://doi.org/10.11648/j.ijmri.20250101.12
DO  - 10.11648/j.ijmri.20250101.12
T2  - International Journal of Medical Research and Innovation
JF  - International Journal of Medical Research and Innovation
JO  - International Journal of Medical Research and Innovation
SP  - 14
EP  - 19
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.ijmri.20250101.12
AB  - Research in fields such as biomedicine often generates data that do not conform to a normal distribution, exhibiting positive skewness (right skewness), as is characteristic of the log-normal distribution. In these scenarios, the use of the arithmetic mean (AM) and standard deviation (SD) can lead to misinterpretations of central tendency and dispersion, as the AM is sensitive to extreme values and overestimates wide numerical ranges. This paper presents a guide on the use of the Geometric Mean (GM), the Geometric Standard Deviation (GSD), and the Geometric Coefficient of Variation (GCV) as the most appropriate statistical tools for this type of data, as well as for sets with disparate numerical scales. The fundamental practical challenge of zero values, common in biomedical measurements such as viral loads or analyte concentrations, is addressed. A specific methodology for treating data with zeros is detailed and justified, consisting of the addition and subsequent subtraction of a unit to allow the calculation of geometric statistics. Finally, two approaches for calculating the Geometric Coefficient of Variation are analyzed and compared, highlighting its nature as a power basis rather than a simple mathematical ratio, and discussing its comparative utility despite its complex interpretation. The need for a better understanding and application of these metrics to improve the accuracy and reproducibility of data analyses is emphasized.
VL  - 1
IS  - 1
ER  -

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