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

Pietro Pollo, Szymon Marian Drobniak , Hamed Haselimashhadi, Malgorzata Lagisz, Ayumi Mizuno , Daniel W.A. Noble, Laura AB Wilson, Shinichi Nakagawa 

Biological differences between males and females are pervasive. Researchers often focus on sex differences in 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 while accounting for sampling error. 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 illustrate their potential using a large dataset of mice traits. For example, we found that females show, on average, greater skewness and kurtosis than males in both fat mass and heart weight. Although calculating Δsk, Δku, and ΔZr may require large sample sizes of individual data, technological advancements in data collection create increasing 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.