Beyond sex differences in mean: meta-analysis of differences in skewness, kurtosis, and correlation

Biological differences between males and females are pervasive. Researchers often focus on sex differences in the mean or, occasionally, in variation, albeit other measures can be useful for biomedical and biological research. For instance, differences in skewness (asymmetry of a distribution), kurtosis (heaviness of a distribution’s tails), and correlation (relationship between two variables) might be crucial to improve medical diagnosis and to understand natural processes. Yet, there are currently no meta-analytic ways to measure differences in these metrics between two groups. We propose three effect size statistics to fill this gap: Δsk, Δku, and ΔZr, which measure differences in skewness, kurtosis, and correlation, respectively. Besides presenting the rationale for the calculation of these effect size statistics, we conducted a simulation to explore their properties and used a large dataset of mice traits to illustrate their potential. For example, in our case study, we found that females show, on average, a greater correlation between fat mass and heart weight than males. Although calculating Δsk, Δku, and ΔZr will require large sample sizes of individual data, technological advancements in data collection create increase opportunities to use these effect size statistics. Importantly, Δsk, Δku, and ΔZr can be used to compare any two groups, allowing a new generation of meta-analyses that explore such differences and potentially leading to new insights in multiple fields of study. DOI https://doi.org/10.32942/X20K9W Subjects Ecology and Evolutionary Biology

covariance, individual participant meta-analysis, meta-regression, nonnormality, normal distribution, sex characteristics Dates Published: 2025-03-29 06:08 Last Updated: 2026-02-24 05:14 Older Versions License CC-By Attribution-NonCommercial-NoDerivatives 4.0 International Additional Metadata Conflict of interest statement: None Data and Code Availability Statement: All data and code used in this study are available at: https://github.com/pietropollo/new_effect_size_statistics. Language: English