  We have compiled from the available literature a large set of radio
measurements of black hole binaries in the hard X-ray state for which
measurements of the gigahertz frequency radio spectral index are possible. We
separate the sample into `radio loud' and `radio quiet' subsets based upon
their distribution in the radio -- X-ray plane, and investigate the
distribution of radio spectral indices within each subset. The distribution of
spectral indices of the `radio loud' subset is well described by a Gaussian
distribution with mean spectral index $\alpha = +0.2$ and standard deviation
$0.2$ (here spectral index is defined such that a positive spectral index means
more flux at higher frequencies). The sparser sample for the `radio quiet'
subset can be approximated, less well, by a Gaussian with mean $\alpha = -0.2$
and standard deviation $0.3$; alternatively the simple mean of the distribution
of the radio quiet subset is $-0.3$. The two spectral index distributions are
different at high statistical significance. Confirming previous work in the
literature, we test to see if the differences in observed spectra could result
from different distributions of jet viewing angles, but find no evidence for
this. We conclude therefore that the jets in the two groups are physically
different in some way, and briefly discuss possible origins and further
possible diagnostics. Finally we note that extrapolating to lower frequencies
the two subsets move closer together in the radio -- X-ray plane, and
approximately merge into a single distribution at around 400 MHz.
