  Peculiar velocities of objects in the nearby universe are correlated due to
the gravitational pull of large-scale structure. By measuring these velocities,
we have a unique opportunity to test the cosmological model at the lowest
redshifts. We perform this test, using current data to constrain the amplitude
of the "signal" covariance matrix describing the velocities and their
correlations. We consider a new, well-calibrated "Supercal" set of low-redshift
SNe Ia as well as a set of distances derived from the fundamental plane
relation of 6dFGS galaxies. Analyzing the SN and galaxy data separately, both
results are consistent with the peculiar velocity signal of our fiducial
$\Lambda$CDM model, ruling out the noise-only model with zero peculiar
velocities at greater than $7\sigma$ (SNe) and $8\sigma$ (galaxies). When the
two data sets are combined appropriately, the precision of the test increases
slightly, resulting in a constraint on the signal amplitude of $A =
1.05_{-0.21}^{+0.25}$, where $A = 1$ corresponds to our fiducial model.
Equivalently, we report an 11% measurement of the product of the growth rate
and amplitude of mass fluctuations evaluated at $z_\text{eff} = 0.02$, $f
\sigma_8 = 0.428_{-0.045}^{+0.048}$, valid for our fiducial $\Lambda$CDM model.
We explore the robustness of the results to a number of conceivable variations
in the analysis and find that individual variations shift the preferred signal
amplitude by less than ${\sim}0.5\sigma$. We briefly discuss our Supercal SN Ia
results in comparison with our previous results using the JLA compilation.
