The CV is dead, long live the CV!

Abstract

Abstract Biology has an increasing need to reconsider the tools used to assess the variability of measurements, in addition to their central tendency. More than 100 years after Pearson's publication, most biologists still use the “good old” Pearson's coefficient of variation, PCV, despite its documented flaws such as sensitivity to excess zero values and/or irrelevant low mean values, which may compromise its use in some biological applications. A new statistic was developed in 2017 by Kvålseth, KCV, which is easy to implement. Unlike PCV, KCV is bounded (between 0 and 1), and it can be computed from PCV, ensuring backward compatibility with past studies. In addition to simulated data, we used the recent MASTREE+ database comprising the time series of the fruiting dynamics of perennial plants worldwide to compare the properties of PCV and KCV. Using as a benchmark the loose hump‐shaped relationship between the interannual variability of fruiting and latitude, KCV led to significant increase in statistical power as it required almost half as many time series as PCV to detect the relationship. Perhaps most importantly, simulated data showed that KCV allows huge reductions in the length of time series required to estimate the population true variability, saving more than half the duration of long‐term monitoring if fruiting fluctuations are very large, which is common in perennial plant species. Compared to the widely used PCV, KCV has great accuracy for estimating and analysing variability in biology, while strongly increasing statistical power. Selecting appropriate tools to assess the variability of measurements is crucial, particularly where the variability is of primary biological interest. Using Kvålseth's KCV is a promising avenue to circumvent the well‐known issues of the former Pearson’ PCV, its properties remain to be explored in other fields of biology, for purposes other than purely statistical ones (e.g. estimating heritability or evolvability of traits).

Keywords

• Kvålseth's coefficient of variation
• masting
• MASTREE+
• Pearson's coefficient of variation
• scale invariant statistics of variability