The $m$-$z$ relation for Type Ia supernovae: safety in numbers or safely
  without worry?
  The $m$-$z$ relation for Type Ia supernovae is compatible with the
cosmological concordance model if one assumes that the Universe is homogeneous,
at least with respect to light propagation. This could be due to the density
along each line of sight being equal to the overall cosmological density, or to
`safety in numbers', with variation in the density along all lines of sight
averaging out if the sample is large enough. Statistical correlations (or lack
thereof) between redshifts, residuals (differences between the observed
distance moduli and those calculated from the best-fitting cosmological model),
and observational uncertainties suggest that the former scenario is the better
description, so that one can use the traditional formula for the luminosity
distance safely without worry.
