Effect size for difference between variances / Levene's test

Question

I have tested a hypothesis of equal variances (using Levene's test), and would like to report an effect size alongside the significance test. Unfortunately, I cannot seem to find any references to a way to calculate an effect size for differences in variances (ideally eta², but that is very much secondary). Does a method exist? If so, I would be very happy about a formula (or, ideally, R package).

Answer 1

From Wolfgang Viechtbauer, "the (log transformed) ratio of the coefficient of variation of the two groups (also called the coefficient of variation ratio) can be a useful measure (Nakagawa et al., 2015). If focus is solely on the variability of the measurements within the two groups, then the (log transformed) ratio of the standard deviations (also called the variability ratio) can be used (Nakagawa et al., 2015)."

Nakagawa, S., Poulin, R., Mengersen, K., Reinhold, K., Engqvist, L., Lagisz, M., & Senior, A. M. (2015). Meta‐analysis of variation: ecological and evolutionary applications and beyond. Methods in Ecology and Evolution, 6(2), 143-152.