  In wave chaotic scattering, statistical fluctuations of the scattering matrix
$S$ and the impedance matrix $Z$ depend both on universal properties and on
nonuniversal details of how the scatterer is coupled to external channels. This
paper considers the impedance and scattering variance ratios, $VR_z$ and
$VR_s$, where $VR_z=Var[Z_{ij}]/\{Var[Z_{ii}]Var[Z_{jj}] \}^{1/2}$,
$VR_s=Var[S_{ij}]/\{Var[S_{ii}]Var[S_{jj}] \}^{1/2}$, and $Var[.]$ denotes
variance. $VR_z$ is shown to be a universal function of distributed losses
within the scatterer. That is, $VR_z$ is independent of nonuniversal coupling
details. This contrasts with $VR_s$ for which universality applies only in the
large loss limit. Explicit results are given for $VR_z$ for time reversal
symmetric and broken time reversal symmetric systems. Experimental tests of the
theory are presented using data taken from scattering measurements on a chaotic
microwave cavity.
