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The $m$-$z$ relation for Type Ia supernovae is compatible with thecosmological concordance model if one assumes that the Universe is homogeneous,at least with respect to light propagation. This could be due to the densityalong 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 sightaveraging out if the sample is large enough. Statistical correlations (or lackthereof) between redshifts, residuals (differences between the observeddistance moduli and those calculated from the best-fitting cosmological model),and observational uncertainties suggest that the former scenario is the betterdescription, so that one can use the traditional formula for the luminositydistance safely without worry.

The $m$-$z$ relation for Type Ia supernovae: safety in numbers or safely without worry?