  We consider the form of Hubble diagrams that would be constructed by
observers in universes that are homogeneous but anisotropic, when averaged over
suitably large length-scales. This is achieved by ray-tracing in different
directions on the sky in families of exact inhomogeneous cosmological solutions
of Einstein's equations, in order to determine the redshifts and luminosity
distances that observers in these space-times would infer for distant
astrophysical objects. We compare the results of this procedure to the Hubble
diagrams that would be obtained by direct use of the large-scale-averaged
anisotropic cosmological models, and find that observables calculated in the
averaged model closely agree with those obtained from ray-tracing in all cases
where a statistical homogeneity scale exists. In contrast, we find that in
cosmologies with spaces that contain no statistical homogeneity scale that
Hubble diagrams inferred from the averaged cosmological model can differ
considerably from those that observers in the space-time would actually
construct. We hope that these results will be of use for understanding and
interpreting recent observations that suggest that large-scale anisotropy may
have developed in the late Universe.
