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

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.