  Recently, the variability ratio (VR) effect size statistic has been used with
increasing frequency in the study of differences in variation of a measured
variable between two study populations. More specifically, the VR effect size
statistic allows for the detection of treatment effect heterogeneity (TEH) of
medical interventions. While a VR that is different from 1 is widely
acknowledged to implicate a treatment effect heterogeneity (TEH) the exact
relationship between those two quantities has not been discussed in detail thus
far.
  In this note we derive a precise connection between TEH and VR. In
particular, we derive precise upper and lower bounds on the TEH in terms of VR.
Moreover, we provide an exemplary simulation for which VR is equal to 1 and
there exist TEH.
  Our result has implications for the interpretation of VR effect size
estimates regarding its connection to treatment effect heterogeneity of
(medical) interventions.
