We analyse the effect that peculiar velocities have on the cosmological inferences we make using luminosity distance indicators , such as type Ia supernovae .
In particular we study the corrections required to account for ( a ) our own motion , ( b ) correlations in galaxy motions , and ( c ) a possible local under- or over-density .
For all of these effects we present a case study showing the impact on the cosmology derived by the Sloan Digital Sky Survey-II Supernova Survey ( SDSS-II SN Survey ) .

Correcting supernova redshifts for the cosmic microwave background ( CMB ) dipole slightly over-corrects nearby supernovae that share some of our local motion .
We show that while neglecting the CMB dipole would cause a shift in the derived equation of state of \Delta w \sim 0.04 ( at fixed \Omega _ { m } ) the additional local-motion correction is currently negligible ( \Delta w \mbox { $\ > \stackrel { < } { { } _ { \sim } } \ > $ } 0.01 ) .

We then demonstrate a covariance-matrix approach to statistically account for correlated peculiar velocities .
This down-weights nearby supernovae and effectively acts as a graduated version of the usual sharp low-redshift cut .
Neglecting coherent velocities in the current sample causes a systematic shift of \Delta w \sim 0.02 .
This will therefore have to be considered carefully when future surveys aim for percent-level accuracy and we recommend our statistical approach to down-weighting peculiar velocities as a more robust option than a sharp low-redshift cut .